Sustainable development goals for site-specific and customized design have brought needs to assess and quantify the stratigraphic uncertainty in three-dimensional (3D) modelling. The interpretation of uncertainty distribution with limited boreholes has always been challenging in 3D space, which is curial in engineering applications such as borehole sampling. In this study, we propose a rigorous random field-based framework to model the 3D stratigraphic uncertainty distribution with improved physical interpretation. Rather than offering constants or physically ambiguous models for Scales of Fluctuation (SoFs) as previous research, the framework adopts a series of SoFs calibrated by fitting stratum characteristics, to cope with local site-specificity in large geological sites. To evaluate the performance of the proposed framework, hypothetical cases are firstly used to demonstrate its applications in both 2D and 3D scenarios. The effectiveness of the proposed model is verified by borehole layout scheme optimization. Then, the proposed framework is applied to the 4 km-long geological site of the immersed tunnel of Hong Kong-Zhuhai-Macao Bridge using 246 boreholes, which is to date the first study on large 3D stratigraphic uncertainty modelling. Finally, a comprehensive discussion is presented for correct physical interpretation of SoFs, comparative studies and determination of important parameters, aiming at evaluating the compatibility in all scenarios. The novel method is proved to be effective in 3D uncertainty modelling for geological stratigraphy with improved physical interpretability, which provides guidelines for underground design.