ArticleOpen Access http://dx.doi.org/10.26855/jamc.2025.12.006
Usage Frequency on Historic Stone Stairs: A Quantitative Model Based on Archard’s Wear Law
Ruiying Cao, Hongyan Zheng, Jiahang Wu, Wenchao Zhang*
School of Mathematics and Statistics, Huizhou University, Huizhou 516007, Guangdong, China.
*Corresponding author:Wenchao Zhang
This research was partially supported by the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2022A1515110634) and the Teaching Quality and Educational Reform Engineering Project of Huizhou University (Project Nos. HuiYuanFa [2023] 158 and HuiYuanFa [2024] 173).
Published: December 31,2025
Abstract
This study develops a novel quantitative model to estimate the historical usage frequency of stone stairs by integrating Archard’s wear law with dynamic systems theory. The model establishes a mathematical relationship between measured wear depth and cumulative usage frequency, incorporating key parameters such as material wear coefficient, error correction factors, and standardized biomechanical load. This approach provides a rapid, low-cost computational alternative to traditional archaeological wear analysis techniques. Numerical simulations in MATLAB validate the model’s ability to accurately reproduce characteristic wear patterns, including central tread wear and differential wear between ascent and descent paths. A sensitivity analysis identifies and ranks the influence of critical input parameters on the outputs. The paper concludes with a discussion of the model’s limitations, primarily regarding parameter estimation in archaeological contexts, and suggests future research directions such as integration with 3D scanning data. This work contributes to digital heritage conservation by offering a tool for inferring historical pedestrian traffic.
Keywords
Archard’s wear law; Dynamic systems; Usage frequency; Visual simulation; Interdisciplinary research
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How to cite this paper
Usage Frequency on Historic Stone Stairs: A Quantitative Model Based on Archard’s Wear Law
How to cite this paper: Ruiying Cao, Hongyan Zheng, Jiahang Wu, Wenchao Zhang. (2025) Usage Frequency on Historic Stone Stairs: A Quantitative Model Based on Archard’s Wear Law. Journal of Applied Mathematics and Computation, 9(4), 266-271.
DOI: http://dx.doi.org/10.26855/jamc.2025.12.006