# A Simulation of Tire Hydroplaning Based on Laser Scanning of Road Surfaces
## 5 Analysis of Uniformity Index of Pavement Texture  
In order to comprehensively evaluate the influence of pavement texture on anti-slip, The Anti-Slip Comprehensive Texture Index (ACTI) is proposed. To comprehensively evaluate the uniformity of pavement texture and its influence on skid resistance under wet conditions, the Anti-Slip Comprehensive Texture Index (ACTI) is introduced. This model integrates three core components--benchmark compliance,  
Figure 20: Comparison of OGFC and SMA pavement textures: (**a**) SMA rutting plate; (**b**) OGFC rutting plate; (**c**) SMA road surface; (**d**) OGFC road surface. asymmetrically weighted variation, and gain-controlled spatial compensation--into a unified framework. Specifically, the ACTI is formulated as:  
\[\text{ACTI}=\underbrace{\sqrt{\frac{\mu}{T}}}_{\text{Benchmark \ Compliance}}\cdot\underbrace{\exp{(-\frac{\sum{w_{i}}\cdot|\text{MDP}_{i}-\mu|}{\mu})}}_{ \text{Asymmetric\ Weighting}}\cdot(\underbrace{1+\frac{\text{N}_{\text{high}}}{\text{n }}\cdot\frac{1}{1+\sigma_{\text{high}}})}_{\text{Gain\ Control}}) \tag{15}\]  
Here, \(\mu\) denotes the mean texture depth, and T = 0.5 mm serves as the benchmark threshold. The weight wi is designed to penalize insufficient texture more heavily than it rewards excessive texture, and is defined as:  
\[\text{w}_{\text{i}}= \begin{cases}2.0\cdot\frac{\text{T}-\text{MDP}_{\text{i}} }{\text{n}},\text{MDP}_{\text{i}}<T\\ 0.5\cdot\frac{\text{MDP}_{\text{i}}-\text{T}}{\mu},\text{MDP}_{\text{i}}\geq T \end{cases}  \tag{16}\]  
The gain control term enhances the ACTI value when numerous high-texture subregions exist with low internal variability. In this context, \(\text{N}_{\text{high}}\) represents the count of subregions where \(\text{MDP}_{\text{i}}\geq\text{T}+0.05\) mm, and \(\sigma_{\text{high}}\) denotes the standard deviation of these subregions. The total number of measurement sub-regions, n, is typically set to nine. This formulation ensures sensitivity to both global texture levels and local deviations. Benchmark compliance prevents overvaluation based solely on high averages; asymmetric weighting highlights texture deficiencies; and gain control enhances robustness against sporadic high readings. Consequently, the ACTI is particularly suitable for evaluating different asphalt mixtures, such as AC, SMA, and OGFC, on a unified scale. The key parameters and their engineering significance are summarized as follows:  
T (reference texture depth) can be adjusted based on requirements and minimum texture height requirements for different regions. \(\mu\) (Mean texture depth): \(\mu=\mu=\frac{1}{\text{n}}\sum_{\text{i=1}}^{\text{n}}\text{MDP}_{\text{i}}\). It indicates the average texture condition. \(\text{w}_{\text{i}}\) (Asymmetric weighting function): Defined above. It penalizes low texture and rewards high texture. \(\text{N}_{\text{high}}\) (Count of high-texture subregions): \(\text{MDP}_{\text{i}}\geq\text{T}+0.05\) mm. It identifies effective anti-skid texture points. \(\sigma_{\text{high}}\) (Standard deviation of high-texture zones): \(\sqrt{\frac{1}{\text{N}_{\text{high}}}\sum_{\text{i\in high}}{(\text{MDP}_{ \text{i}}-\mu_{\text{high}})^{2}}}\). It evaluates the uniformity of high-texture contributions. n (Total number of measurement subregions): Defined by the sampling grid (e.g., n = 9). It reflects the resolution of surface measurements. The article provides a classification standard and engineering interpretation based on a construction depth of 0.5 mmACTI, as shown in Table 8.