Slipping is a major cause of injury and hospitalization in the USA and globally. Slipping occurs when the instantaneous friction between the shoe and floor is less than the required friction. While floor roughness is a key factor contributing to friction, prior investigations have primarily used stylus profilometry, which is incapable of measuring roughness at small scales, below approximately 1 micron in lateral size. In the present research, the small-scale roughness was quantified using cross-section scanning electron microscopy (SEM). Three different flooring materials were investigated, including tiles of ceramic and two different types of quarry stones, whose friction coefficients had been previously characterized. The surfaces were cross-sectioned, imaged at magnifications from 250 to 100,000 times, and then the surface profiles were extracted using image analysis. The SEM topography was combined with stylus profilometry measurements, using the power spectral density (PSD), to achieve multi-scale characterization of features ranging from a scan size of 4 mm down to a resolution of 10 nm. The results demonstrate meaningful differences in topography at different length scales, where surfaces with widely varying roughness at one scale were indistinguishable at another. The measurements further showed that floor-tile roughness has self-affine fractal-like character, with hierarchical roughness extending from the micron-scale down to the nanoscale, much of which is undetectable using conventional techniques. Overall, this research supports the investigation of small-scale roughness as a potential missing factor in the understanding of floor topography and its causal effect on slip-and-fall accidents.

在美国和全球，滑倒是受伤和住院的主要原因。当鞋子和地板之间的瞬时摩擦力小于所需摩擦力时，就会发生滑倒。虽然地板粗糙度是导致摩擦的一个关键因素，但之前的研究主要使用触笔轮廓测量法，它无法测量横向尺寸约 1 微米以下的小尺度粗糙度。在本研究中，使用横截面扫描电子显微镜 (SEM) 对小尺度粗糙度进行量化。研究了三种不同的地板材料，包括陶瓷砖和两种不同类型的采石，它们的摩擦系数之前已经过表征。对表面进行横截面，放大倍数为 250 到 100,000 倍，然后使用图像分析提取表面轮廓。SEM 形貌与使用功率谱密度 (PSD) 的触针轮廓测量相结合，以实现特征的多尺度表征，范围从 4 mm 的扫描尺寸到 10 nm 的分辨率。结果表明，不同长度尺度的地形存在有意义的差异，其中一个尺度上粗糙度变化很大的表面在另一个尺度上无法区分。测量进一步表明，地砖粗糙度具有自仿射分形特征，分级粗糙度从微米级延伸到纳米级，其中大部分使用常规技术无法检测到。全面的，