## 1 Introduction
In contrast, the microstructure of compacted loess can differ significantly from intact loess, despite having the same grain-size distribution (GSD) and mineral composition [18; 19; 22; 37]. This difference arises because the inter-particle carbonate cementations are disrupted during the remolding process [14; 19; 35]. However, the scanning electron microscopy (SEM) technique only provides two-dimensional (2D) images, leading to the results obtained from SEM being highly dependent on the chosen observation direction and section, resulting in significant errors in the statistical analysis of pores [38]. Meanwhile, MIP is a destructive method that forces non-wetting mercury into the soil under high pressure, making it impossible to detect isolated pores and accurately assess pore morphologies [34]. Additionally, MIP may underestimate pore sizes due to the \"ink-bottle\" effect, where smaller necks between larger pores skew the results [39]. Due to the inherent limitations of the MIP and SEM methods, a full understanding of the three-dimensional microstructural similarities and differences between intact and compacted loess remains incomplete. In recent years, high-resolution, non-destructive micro-computed tomography (micro-CT) has emerged as a promising alternative for studying soil microstructure [40; 41; 42; 43; 44; 45]. This technique uses a series of high-resolution CT images to build a 3D microstructure model of the soil. With the aid of image processing programs, micro-CT can provide detailed information about the soil's pore size, connectivity, grain size, grain shape, grain sphericity, and orientation. Previous research has highlighted the shortcomings of 2D SEM images, particularly in capturing the 3D characteristics of pores and their connectivity, underscoring the superior capability of micro-CT in these areas [38]. Nevertheless, researchers can only obtain 3D reconstructed pore structures on the scale of hundreds of micrometers when the CT scan resolution reaches 1 \(\upmu\)m [18; 41; 42]. Given the inherent heterogeneity of loess, it is necessary to assess whether these small-scale 3D pore structures are representative. The Representative Volume Element (RVE) is a crucial concept in the mechanics and physics of random heterogeneous materials [30; 46; 47]. It is defined as the smallest volume of a heterogeneous material that is large enough to statistically represent the microstructural heterogeneities [47]. If the volume is too small, even a slight increase in size can lead to significant changes in its characteristics. Once the volume exceeds a certain critical value, these characteristics stabilize and no longer change with further size increments. This critical value is known as the RVE size [30; 46]. The determination of RVE size is widely applied in the precise analysis of three-dimensional fracture networks within jointed rock masses [48; 49; 50]. However, its application in accurately analyzing soil microstructure based on CT scans remains limited. In this study, 3D pore microstructures of intact and remolded loess from the two typical engineering projects (i.e., GMLR and MECC) in the Loess Plateau of China were reconstructed using serial CT images with a voxel size of 1 \(\upmu\)m\({}^{3}\). A workflow for determining the geometrical RVE is introduced. The three-dimensional microstructures are segmented into a series of cubes of varying dimensions to identify the structure's representative volume element (RVE) and assess the uniformity of both loess types. The pore network of the RVE is quantitatively analyzed to characterize the microstructure. In addition, a detailed quantitative assessment and comparison of 3D structural parameters across different volume sizes is conducted, which aids in the evaluation of the uniformity between intact and remolded specimens. The research is expected to offer an in-depth understanding of the 3D geometrical characteristics of the intact and remolded loess and further provide insights into the study of the micro-mechanism of loess behavior.