A Study on Stair Wear Prediction Based on Archard’s Equation and Gaussian Simulation
DOI:
https://doi.org/10.54097/yawxst60Keywords:
Wear Depth, Usage Frequency, Archard Equation, Pedestrian Flow Patterns.Abstract
Ancient stone stairs provide tangible evidence of historical human activity, where their wear patterns reflect how people used and moved through these spaces over time. To quantitatively analyze the relationship between wear depth and usage frequency, this study proposes a stair wear prediction model based on Archard’s wear equation. The model integrates key factors such as usage frequency, material hardness, and wear coefficients. Using laser scanning and photogrammetry data, this study optimized the model parameters via least squares and genetic algorithms, obtaining the spatial distribution of wear across a 12×4 stair grid. Further analysis of pedestrian flow patterns revealed that ascending movement causes lighter, edge-focused wear, while descending movement results in deeper, centralized wear due to gravitational effects. By modeling short-term intensive and long-term distributed pedestrian usage with Gaussian distribution functions, this study simulated the corresponding wear characteristics and evaluated them using uniformity, concentration, and smoothness indices. The results demonstrate that high-frequency usage leads to deeper, smoother, and more centralized wear, whereas low-frequency usage produces shallower and more dispersed wear. These findings provide a reliable method for reverse inferring usage patterns of ancient stairs and offer valuable guidance for digital archaeology and heritage conservation.
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