# Investigation on Hydroplaning Behaviors of a Patterned Tire on a Steel Bridge Deck Pavement
## 1 Introduction  
Hydroplaning on pavement in rainy conditions is a common phenomenon threatening driving safety [1]. When a vehicle runs on a wet pavement, the water between the tire and pavement flows under the contact force at the tire-pavement interface. Some water is drained through the channels formed by the tire pattern and pavement surface macrotexture, while the undrained water can generate the hydrodynamic pressure to the tire, which can reduce the contact between the tire and pavement. Once the vehicle reaches a critical speed, the tire floats entirely on the water and vehicle instability occurs [1,2]. This phenomenon is called hydroplaning and the critical speed is called the hydroplaning speed. Hydroplaning is the main cause of accidents in rainy days, and reducing the risk of hydroplaning is of great importance to driving safety. Hydroplaning behaviors on an asphalt pavement are related to the tire characteristics, pavement surface topography, and water film on the pavement surface. The early research on hydroplaning behaviors was carried out by experimental methods. [PERSON] et al. [1] studied the effect of the tire inflation pressure on the hydroplaning speed. The studies contributed to the development of the well-known NASA (National Aeronautics Space Administration, Washington, DC, USA) hydroplaning equation, as shown in the Equation (1) which is still widely used as of today. \[\left\{ \begin{array}{l}V_{h,rolling}=6.36\sqrt{P}\\ V_{h,locked}=5.43\sqrt{P}\end{array} \right. \tag{1}\]where \(V_{h,rolling}\) and \(V_{h,local}\) are the hydroplaning speeds for rolling tire and locked tire, respectively, [km/h], and \(P\) is the inflation pressure, [kPa]. The NASA hydroplaning equation can be used to obtain the hydroplaning speeds for smooth tires with closed pattern trends, and for rib-tread tires on fluid-covered runways where the fluid depth exceeds the tire tread depth [2]. However, the effects of the pavement surface topography, water film depth, and some other tire characteristics are not involved in the NASA hydroplaning equation. [PERSON] et al. [3] developed a hydroplaning equation based on the hydroplaning test, and the quantitative relationship between tire inflation pressure, tire pattern depth, water film thickness, pavement surface macrotexture characteristic, and hydroplaning speed was determined in the equation. The equation, named the Gallaway hydroplaning equation, is shown in Equation (2). \[\left\{ \begin{array}{l}V_{P}=(SD)^{0.04}(P_{t})^{0.03}(TRD+1)^{0.06}A\\ A=\max\{[\frac{10.409}{P_{t}^{0.00}}+3.507],[\frac{28.952}{P_{t}^{0.00}}-7.819]( MTD)^{0.04}\}\end{array} \right. \tag{2}\]  
where \(V_{p}\) is the hydroplaning speed, [mph]; \(SD\) is the slip ratio of tire, [%], which is defined as the ratio of the slip speed to the vehicle speed; \(P_{t}\) is the tire inflation pressure, [psi]; \(TRD\) is the tire pattern depth, [1/32 inch]; \(t_{w}\) is the water film thickness, [inch]; \(MTD\) is the mean texture depth of pavement surface. However, the hydroplaning test needs a demanding site and equipment, and it has a high test cost and potential safety hazards. Therefore, the experimental studies are not widely applied to the hydroplaning analysis. In view of the complex dynamics involved in the hydroplaning behaviors, the numerical simulation has been applied to hydroplaning analysis since the 1970s. At present, the finite element (FE) simulation technology based on the Couple Eulerian-Lagrangian (CEL) algorithm has become an important method for hydroplaning analysis. Many researchers conducted numerical studies to reveal the influence of tire pattern characteristics on hydroplaning behaviors [4; 5; 6]. The purpose of these studies is for the safety design of tires, but the influence of pavement surface topography is not well modeled. [PERSON] et al. [7; 8] developed a tire-fluid-pavement interaction model to evaluate the driving safety on a wet asphalt pavement, and revealed the influences of water film depth and pavement surface texture on the hydroplaning speed.