Proceedings of the
9th International Symposium for Geotechnical Safety and Risk (ISGSR)
25 – 28 August 2025, Oslo, Norway
Editors: Zhongqiang Liu, Jian Dai and Kate Robinson

Shape Function-Based KL Expansion Method for Discretizing Irregular Random Fields

Zhihao Jianga, Xiaohui Tanb, Shanwei Liuc and Xiaoliang Houd

School of Resources and Environmental Engineering, Hefei University of Technology, Hefei, China.

ajiangzh@mail.hfut.edu.cn

btanxh@hfut.edu.cn

cshanweiliu@whu.edu.cn

dxlhou@hfut.edu.cn

ABSTRACT

The Karhunen-Loève (KL) expansion is widely used to simulate soil spatial variability but faces challenges in efficiently discretizing irregular random fields.A shape function-based KL (SFKL) discretization method is proposed in this study, where shape functions are combined with Lagrange interpolation to transform multidimensional integrals into matrix assembly operations. This approach significantly improves the computational efficiency and accuracy while addressing the limitations of OSEmethods forirregulardomains. Case studies demonstrate the effectiveness of the proposed method, showing that the SFKL method achieves lower discretization errors and requires fewer expansion terms than the OSE method in irregular domains.

Keywords: Random field, Karhunen-Loève expansion, Shape functions, Slope, Spatial variability, Irregular domain.


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