## 1 Introduction
Factors that influence the interface friction angle (\(\delta\)) have been stated in the literature as internal friction angle of soil (\(\phi\)), moisture content, soil density, soil type, the surface roughness of the material, soil particle shapes (angular or round), relative roughness (surface roughness of the material divided by soil particle mean diameter (D50)), percentage of coarse grains, the levels of normal stress, soil, and shearing rate [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. Researchers attempted to conduct small- and large-scale model pile load experiments to better understand the behavior of shaft friction capacity of non-displacement (bored or drilled shaft) piles due to the high expense of full-scale pile load studies. The mobilized unit shaft resistance of the bored pile in sand is usually influenced by some factors such as the initial relative density of sand and stress state [37; 38; 39], the roughness between soil and pile material [40; 41; 42; 43; 44]. The surface roughness of a pile is usually introduced as a normalized roughness ratio (\(\rm R_{n}=R_{t}/D_{50}\)), where \(\rm R_{t}\) is the maximum surface profile height, and \(\rm D_{50}\) is the mean particle size diameter of the soil mass, as shown in Figure 1[9; 40]. [PERSON] et al. [45] employed a calibration chamber test and two-dimensional finite element analysis using a two-surface-plasticity constitutive model to examine the behavior of bored pile under axial load in sand. It was discovered that the ultimate unit shaft resistance is considerably influenced by the K value and the relative density of soil. Additionally, they demonstrated that in comparable circumstances, a small-size model pile produces far more unit shaft resistance than a full-scale pile. Due to the high degree of soil parameter uncertainty and the intricate pile-soil load transmission process, estimating the shaft frictional resistance of piles has been a controversial subject among researchers until now. Very little research has been carried out in the literature on shaft resistance of full-scale model piles under axial load in sand [43]. Most of the studies have used small-scale steel model piles under tensile load experimentally to back-calculate the K value from the friction capacity of the pile shaft [46; 47; 48]. Research dealing with shaft friction resistance of timber and composite model piles (concrete-filled FRP and PVC) under axial load in the sand was not encountered. The purpose of this study is to examine the shaft friction resistance of four different non-displacements (pre-installed) model piles embedded in sand, including closed-end steel pipe piles, timber piles and two composite piles (FRP and PVC filled with concrete). At different relative densities, the test sand's internal friction angle was found by conducting a series of shear box experiments. The interface friction angle between sand and pile material was determined using an interface shear test (IST). In addition, a surface roughness test was carried out to obtain the maximum surface roughness of all model piles. Model pile tests were executed under axial load in such a method that the end (point) bearing of the pile does not exist, and the whole pile capacity was produced from lateral friction resistance between the pile shaft and the neighbouring soil. Additionally, it aims to determine how the relative density of sand affects the shaft resistance of non-displacement piles and back-calculate the K value using the results of model pile load tests.