The interaction between the evolution of an ice jam and the local scour at bridge piers becomes much more complicated due to the evolution of both the channel bed and ice jam. Thus, research work regarding this topic has been hardly conducted. In the present study, experiments under different flow conditions with three different pier shapes were carried out. Through laboratory experiments, the development of scour holes around bridge piers under open flow, ice-covered, and ice-jammed flow conditions was compared. The results show that under the same hydraulic condition and with the same ice discharge rate (Qi/Q), the development of an initial ice jam with a local scour around bridge piers along the entire flume takes a relatively short time. However, it takes a longer time for an ice jam to achieve an equilibrium state. With the presence of a local scour at bridge piers, after an ice jam reaches an equilibrium state, the ice jam thickness, water level, and water depth for flow are relatively larger compared to that without a local scour at the pier. The equilibrium ice jam thickness around the pier is negatively correlated with the initial flow Froude number. When the development of an initial ice jam is dominated by a mechanical thickening process, the rate of the development of a scour hole around a pier is faster. On the other hand, when the development of an initial ice jam is dominated by a hydraulic thickening process, the development of a scour hole around a pier can be treated as a scour process under an ice-covered flow condition. An equation was developed to determine the scour depth around a pier under an ice-jammed flow condition by considering related factors such as the flow Froude number, ice jam thickness, and ice discharge rate. The results of this research can provide a reference for bridge design and safety protection, as well as the interaction mechanism of local scour and ice jam evolution.

Compared to the scour around a single pier, the local scour process around tandem double piers is much more complicated. Based on laboratory experiments in a flume, we conducted the scour process around tandem double piers under an ice-covered flow condition. The results showed that when the pier spacing ratio L/D = 2 (where L = the pier spacing distance, and D = the pier diameter), the rear pier (the downstream one) will intensify the horseshoe vortex process behind the front pier, and the scour depth around the front pier will increase by about 10%. As the pier spacing ratio L/D increases, the scour depth around the front pier will gradually decrease. When the pier spacing ratio L/D = 5, sediment scoured around the front pier begins to deposit between these two piers. To initiate a deposition dune between piers, the pier spacing distance under an ice-covered condition is about 20% more than that under an open flow condition. The results also showed that the existence of the rear pier will lead to an increase in the length of the scour hole but a decrease in the depth of the scour hole around the front pier. The local scour around the front pier interacts with the local scour of the rear pier. The maximum scour depth of the scour hole around the rear pier increases first, then decreases and increases again afterward. When the pier spacing ratio L/D = 9, the scour depth around the rear pier is the least. With an increase in the pier spacing ratio, the influence of the local scour around the front pier on the local scour around the rear pier gradually decreases. When the pier spacing ratio L/D is more than 17, the scour around the front pier has hardly any influence on that around the rear pier. The scour depth around the rear pier is about 90% of that around the front pier.

No abstract

To calculate the critical depth and the least specific energy of steady non-uniform flows in open channels, one has to solve the polynomial equations. Sometimes, the polynomial equations are too difficult to get them solved. In this study, the theory of algebraic inequality has been used to derive formulas for determining the critical depth and the least specific energy of a steady non-uniform flow in open channel. The proposed method has been assessed using examples. Results using this new method have been compared to those using other conventional methods by engineers and scientists. It is found that the proposed method based on algebraic inequality theory not only makes the calculation process to be easy, but also gives the best calculation results of the critical depth and the least specific energy of a steady nonuniform flow.

Ice problems in channels for water transfer in cold regions seriously affect the capacity and efficiency of water conveyance. Sometimes, ice problems such as ice jams in water transfer channels create risk during winter periods. Recently, water temperature and environmental factors at various cross-sections along the main channel of the middle route of the South-to-North Water Transfer Project in China have been measured. Based on these temperature data, the heat balance state of this water transfer channel has been investigated. A principal component analysis (PCA) method has been used to analyze the complex factors influencing the observed variations of the water temperature, by reducing eigenvector dimension and then extracting the principal component as the input feature. Based on the support vector machine (SVM) theory, a new approach for judging the heat loss or heat gain of flowing water in a channel during winter periods has been developed. The Gaussian radial basis is used as the kernel function in this new approach. Then, parameters have been optimized by means of various methods. Through the supervised machine learning process toward the observed water temperature data, it is found that the air–water temperature difference and thermal conditions are the key factors affecting the heat loss or heat absorption of water body. Results using the proposed method agree well with those of measurements. The changes of water temperature are well predicted using the proposed method together with the state of water heat balance.