Impacts of bridge piers on water level during ice jammed period in bend channel–An experimental study *

Jun Wang(王軍), Shu-yi Li(李淑祎),Pang-pang Chen(陳胖胖) ,Tao Wang(汪濤) ,Jueyi Sui

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Impacts of bridge piers on water level during ice jammed period in bend channel–An experimental study*

Jun Wang1(王軍), Shu-yi Li1(李淑祎),Pang-pang Chen1(陳胖胖) ,Tao Wang1(汪濤) ,Jueyi Sui2

1.2.

Ice jam, bend channel, bridge pier, increment of water level

Introduction

River ice is an important hydrologic factor in the temperate and polar environment. An ice cover alters the hydraulics of an open channel by imposing an extra boundary to the flow, altering the water level and the flow velocity as compared to the ice free case. Under specific conditions such as with continuous vast amount of incoming frazil ice from the upstream due to low temperature, the ice jam may be formed. The ice jam can result in a significant increase of the water level and thus the ice flooding, and the damage of hydraulic structures[1,2]. Without doubt, the changes of the water level caused by the river ice jams attract the interest of many researchers and engineers in the world. Based on long term field observations of ice jams at the Hequ reach of the Yellow River, Sui et al.[3]studied the mechanisms of the ice accumulation and the changes of the water level. They pointed out that there is an inter-dependence between the evolu- tion of the frazil jams and the associated variation of the water levels during the ice jamming period. More specifically, the variation of the water levels and the evolution of the ice jams depend not only on the flow rate, but also on the ice discharge, the configuration of the channel section, and climatic factors.

The river bend is one of important locations and plays an important role during the formation of the ice jams such as the Hequ ice jams in the Yellow river[3]. The thickness distribution of the ice jam along a river bend is an important topic of the river ice hydraulics, which is the least understandable subject. Due to the two transverse circulation cells under the ice-covered condition along a river bend, the ice jam thickness varies both in the longitudinal direction and the transverse direction (normal to the flow direction)[4].

Fig. 1 Setup of the S-shaped flume in the laboratory

The interaction between the river ice jam and the bridge piers was investigated by some researchers. Based on the experiments conducted in the laboratory, Tyminski[10]used 7 different bridge piers to assess their different impacts on the passing flow discharge and ice. It was pointed out that the streamline-shaped bridge pier can minimize the increase of the water level in front of the bridge piers. Also, the streamline- shaped bridge piers cannot easily cause the ice jam around the bridge piers.

To assess the impacts of the bridge piers on the variations of the water level and the ice movement during the river breakup period, Hou et al.[11]and Yu et al.[12]conducted experiments under different flow conditions as well as with different structure layouts. An ice movement model covering a channel section of 15 km long upstream to the project was built by Deng et al.[13]to study the ice run around the site of Wuda railroad bridge under different flow ice densities and different flow rates

Wang et al.[14]investigated the critical condition for the initiation of the ice cover around the bridge piers. Based on the experiments carried out in the laboratory, they developed an equation for determi- ning the critical floe concentration for forming an ice cover. Wang et al.[15]studied the stress in the ice jam in the vicinity of a bridge pier. By developing a governing equation for describing the equilibrium state of an ice jam, the stability of the ice jam around the bridge piers is analyzed. Wang et al.[16]investi- gated the evolution of an ice jam around bridge piers of different diameters. Compared to the results with- out the bridge pier, it wasfoundthattheformationof an ice jam in the downstream of the bridge pier was faster than that in the upstream. The thickness distri- bution of the ice jam was clearly different in front of the bridge piers from that behind the bridge piers in different stages of the ice jam.

1. Experiment setup

The experiments are conducted in the “S-shaped” flume at Hefei University of Technology, China. As shown in Fig. 1, the flume has a length of 25.17 m and a width of 0.60 m.

In the present study, experiments for the varia- tions of the water level caused by the ice jam are carried out in the S-shaped bend channel with and without the bridge piers. To assess the impacts of the bridge piers on the variations of the water level under the ice jammed condition, 3 different arrangements of the bridge piers are considered, (1) only one single pier locates in the straight section between 2 bend sections (defined as “pier setup-1”), (2) only one single pier locates at the apex of the concave bank of the bend section (defined as “pier setup-2”), (3) one pier locates in the straight section between 2 bend sections and another one locates at the bend apex (defined as “pier setup-3”).

2. Results and analyses

2.1 Impacts of bridge piers on ice accumulation in the S-shaped channel

2.1.1 Ice accumulation in bend channel with “pier setup-1”

We investigate the impact of the bridge pier on the ice accumulation along the S-shaped channel, when only one single pier is installed in the straight section between 2 bend sections (defined as “pier setup-1”).

Before the ice particles reach the bridge pier in the bend channel, the bridge pier does not affect the movement of the ice particles. Because of the trans- versal current, the floating ice particles are transported downstream along the concave bank. This experiment confirms the findings of Sui et al.[4]who used one 180° bend flume to study the ice accumulation in a bend channel. However, once the ice particles reach the bridge pier, because of the influence of the bridge pier on the flow structure, the ice particles are rolled and dived or submerged under the water, and then delivered around the bridge pier to the downstream.

Once the model ice particles reach the front of the model ice cover in the downstream channel section from CS-25 to CS-26, the ice particles stop moving further downstream. Rather, they gradually form a layer of ice particles, namely, a ice cover. Due to the flowing current, some ice particles will be forced to dive and accumulate under the formed ice cover. The initial ice jam starts to form, and is pro- gressed upstream. At the beginning of the experiment, the ice particles are hardly dived in front of the ice jam edge (jam head). Once the jam head approaches the bridge piers, due to the contraction caused by the bridge pier, the flow velocity increases. Thus, in the vicinity of the bridge piers, many ice particles are forced to dive or submerge under the initial ice jam. As a consequence, the ice jam gradually thickens.

Fig. 2 (Color online) The thickest ice jam in the middle of flume downstream of bridge pier

2.1.2 Ice accumulation in bend channel with “pier setup-2”

We study the impact of different locations of the bridgepierontheiceaccumulationalongthe S-shaped channel, when only one single pier is located at the bend apex (defined as “pier setup-2”).

Results indicate that, there is no obvious diffe- rence between the formation processes of the initial ice jams with “pier setup-2” and with “pier setup-1”. During the thickening process of the initial ice jam in the vicinity of the bridge pier, the ice jam along the convex bank is clearly thicker than that along the concave bank. Affected by the changes of the flow structure around the bridge piers, the initial ice jam in the vicinity of the bridge piers is gradually eroded and scoured. The ice particles are delivered to the down- stream of the bridge pier. As a consequence, the ice accumulation in the middle of the flume downstream of the bridge pier becomes very thick, as shown in Fig. 2(b). During the thickening process of the ice jam, due to the scouring process resulted from the current in the vicinity of the bridge pier, the thickest accumulation of the ice jam in the middle of the flume downstream of the bridge pier is gradually scoured. With the increase of the accumulation thickness, the ice jam accumulation in the middle of the flume downstream of the bridge pier becomes thinner, and becomes thicker along the channel walls. Gradually, the area of the scouring hole in the ice jam decreases. Eventually, in the vicinity of the bridge pier, the ice jam along the convex bank becomes thicker; and becomes thinner along the concave bank. Upstream of the bridge pier, the ice jam accumulation along the convex bank becomes thicker and thicker. However, the ice jam accumulation along the concave bank becomes thinner and thinner, until an open spot appears.

2.1.3 Ice accumulation in bend channel with “pier setup-3”

We study the impact of the bridge pier on the ice accumulation in the S-shaped channel, when one pier is located at the bend apex and another one in the straight section between 2 bend sections (defined as “pier setup-3”).

After the incoming ice particles enter the bend channel, the moving process of the ice particles in the bend channel with “pier setup-3” is nearly the same as that under the conditions of “pier setup-1” and “pier setup-2”. During the formation of the initial ice jam, we normally have more ice accumulation along the convex bank of the bend channel than along the concave bank. During the thickening process of the ice jam, in the vicinity of the bend apex (where one pier is located), along the convex bank, the ice jam is thicker than that along the concave bank. With a gradual increase in the accumulation of the ice jam, the ice accumulation along the convex bank further thickens, and that along the concave bank becomes further thinner until an open spot appears. Experi- ments show that the open spots firstly appear along the concave bank downstream of the straight section connecting the two bends. The ice jam thickness along the connecting section between 2 bends is nearly uniform across the channel at the beginning, and then becomes thicker along the channel walls and thinner in the middle of the channel. Affected by the current caused by the bridge pier due to the channel contrac- tion, many ice particles are forced to dive and sub- merge under the initial ice jam and delivered to the downstream. As a consequence, the ice accumulation in the middle of the flume downstream of the bridge pier becomes significantly thick, especially at CS-18 (the apex of the bend where the bridge pier is located).

2.2 Impacts of bridge piers on changes in water level

Based on the experimental study of the ice accu- mulation in a straight flume with bridge piers, Wang et al.[14]indicated that the water level could not be increased upstream of the bridge piers, provided that the ice jam could not be developed to the upstream of the bridge piers. Further more, the increase of the water level caused by the ice jam at the cross section upstream of the bridge piers is less than that at the same cross section without bridge piers in the channel. On the other side, if the ice jam can be developed upstream of the bridge pier, the increase of the water level at the cross section upstream of the bridge pier is more than that at the same cross section without the bridge pier in the channel.

Fig. 3 Comparison of increments of water level caused by ice jam with bridge pier with those without ice pier

Figures 3(a)-3(d) show comparisons of the varia- tions of the water levels caused by the ice jam with the bridge pier (located at CS-15 in the straight channel between 2 bends) with those without the bridge pier. As shown in these figures, during the development process of the initial ice jam, the increment of the water level with the bridge pier in the channel is normally greater than that without bridge piers. With the presence of the bridge pier in the channel, it becomes easier for the initial ice jam to be developed as an equilibrium ice jam. Additionally, when the ice jam is under the equilibrium condition, the increment of the water level with the bridge pier in the channel is less than that without the bridge pier. Results show that the increments of the water level caused by the ice jam with the bridge pier in the bend channel are different from those in a straight channel, as indicated by Wang et al.[16]. The difference may be due to the flow structures, since the flow in the straight channel could be considered as a steady uniform flow, but the flow is a steady non-uniform flow in the bend channel. The transversal circulation flow in the bend channel results in a different ice jam accumulation, namely, more ice accumulation along the convex bank and less along the concave bank. Thus, the increment of the water level in a bend channel is different from that in a straight channel.

Table 1 shows the difference of the time for the ice jam to reach an equilibrium condition in a bend channel with a bridge pier located at CS-15 compared to that without the bridge pier. One can see from this table, with the presence of the bridge pier in the bend channel, it takes less time for an initial ice jam to be developed as an equilibrium ice jam. Since the presence of the ice jam in the bend channel results in a contraction of the channel and changes the flow struc- ture in the vicinity of the bridge pier, the transport capacity of the ice particles increases. Thus, the development of the ice jam with the bridge pier in the bend channel becomes faster than that without the bridge pier.

2.3 Impacts of different location of bridge piers on the increments of water level

Results regarding the effects of the bridge piers inthebendchannelonthe icejam accumulation indi- catethatboththehydraulicconditionandthe incoming ice discharge in the bend channel with the bridge pier have similar impacts on the variation of the water level during the ice-jammed period as those without the bridge pier. Also the effects of both the hydraulic condition and the incoming ice discharge on the variation of the water level during the ice jammed period in the bend channel are the same as those in the straight channel. In the following section, the impacts of different locations of the bridge piers in the bend channel on the increments of the water level caused by the equilibrium ice jam are discussed.

Table1Time for ice jam to reach equilibrium condition in bend channel with bridge pier compared to that without bridge pier

Figures 4(a)-4(d) show the variations of the water level caused by the equilibrium ice jam with the bridge pier at different locations as compared to those without the bridge pier. One can see from Figs. 4(a)- 4(d), that the increment of the water level caused by the equilibrium ice jam with the bridge pier in the channel is less than that without the bridge pier. Results indicate that the increment of the water level caused by the equilibrium ice jam with “pier setup-2” is less than that with “pier setup-1”. The increment of the water level caused by the equilibrium ice jam with “pier setup-3” is less than that with “pier setup-1”, but more than that with “pier setup-2”. Once the bridge pier is installed, due to the decrease of the flow cross sectional area, the flow velocity increases. The tran- sport capacity of the ice particles increases, therefore, the thickness of the equilibrium ice jam decreases, resulting in a decrease of the water level during the equilibrium ice jammed period. Thus, the water level during the equilibrium ice jammed period with the bridge pier in the bend channel is less than that without the bridge pier. The difference of the arrange- ment of the bridge pier also affects the water level. It is found that the ice particles become much easier to get dived or submerged in a water with “pier setup-2” than that with “pier setup-1”, namely, much more ice particles are delivered to the downstream. Therefore, both the equilibrium ice jam and the associated water level with “pier setup-2” are less than those with “pier setup-1”.Onecanseefromexperimentsthatthe incrementofthewaterlevelwith“piersetup-3”is between that with “pier setup-2” and that with “pier setup-1”. One can say that the effects of the interac- tion of two bridge piers on the equilibrium ice jam and the associated water level should be considered in the real practice.

2.4 Empirical equation for determining the increment of water level

Wang and Nie[20]derived the following formula for describing the water level during the ice period

Based on experimental data, they proposed the following empirical equation for determining the water level

With consideration of the impacts of the pier diameter and its locations on the water level during the ice jammed period as well as other variables, the water level during the ice jammed period can be described by the following generalformula

Neglecting dependent and unimportant variables, Eq. (4) can be further expressed as follows

Fig. 4 Comparison of increments of water level during equili- brium ice jammed period with bridge pier at different locations with those without ice pier

Based on the data from the experiments carried out in the hydraulic laboratory of Hefei University of Technology, Eq. (5) can be further written as follows

Fig. 5 Relationship between water levels and related variables

2.5 Relationship between increment of water level and ice jam volume

Based on the field observations of the ice jams in the Hequ Reach of the Yellow River in China, Sui et al.[4]pointed out that there was a linear relationship between the increment of the water level and that of the river ice jam (the difference between the thickness of the equilibrium ice jam and that of the initial ice jam). The ice jam accumulation in the bend channel is more complicated than that in the straight channel. Two transversal currents result in more accumulation along the convex bank than along the concave bank. The presence of the bridge pier in the bend channel changes the flow structure and makes the accumula- tion process of the ice jam in the bend channel much more complicated. Thus, it is not easy to describe the relationship between the increment of the water level and the ice jam thickness for the bend channel with bridge piers. Experiments show that the more the ice accumulation, the more the increment of the water level. It means that the volume of the ice jam plays a key role in the changes of the water level. So, there should be a relationship between the increment of the water level and the ice jam volume.

As shown in Fig. 6, considering all pier-setups, including that without a bridge pier in the bend channel, the dependence of the increment of the water level on the ice jam volume can be described by the following relationship

where is the increment of the water level, is the water depth under the open flow condition with the same discharge, is the total volume of the ice accumulation in the bend channel, is the total volume of the water in the bend channel.

One can see from Fig. 6, regardless of the presence of the bridge piers or not in the bend channel, the increment of the water level during the equili- brium ice jammed period increases with the increase of the volume of the ice jam accumulation. Given the same volume of the ice accumulation, the increment of the water level with the “pier setup-2” is a little bit more than that with the “pier setup-1”. It means that with the same ice accumulation in the bend channel, a single pier located at the bend apex will cause more increase of the water level than that with a single pier located in the straight section connecting two bend sections.

3. Conclusions

In the present study, the variation of the water level in an S-shaped channel is studied for various arrangements of bridge piers. Comparing to the varia- tion of the water level without bridge piers in the bend channel, the following conclusions are drawn:

(1) The increment of the water level during the equilibrium ice jammed period with a bridge pier is less than that without a bridge pier in the bend channel. Also, it takes less time for the ice jam to reach an equilibrium condition in the bend channel with a bridge pier than without the bridge pier.

(2) The difference of the arrangement of bridge piers also affects the increment of the water level. The increment of the water level caused by the ice jam with “pier setup-2” (with only one single pier being located at the bend apex) is less than that with “pier setup-1” (with only one single pier being located in the straight section between 2 bend sections). The increment of the water level with “pier setup-3” (with two piers, one being located in the straight section between 2 bend sections and another at the bend apex) is less than that with “pier setup-1”, but more than that with “pier setup-2”.

(3) Considering the impacts of the pier diameter and the pier location on the increment of the water level, an empirical equation between the increment of the water level and all related variables is developed based on experimental data collected in the S-shaped flume. The calculation for the increment of the water level using this equation gives very good result.

(4) Considering all pier-setups including that without a bridge pier in the S-shaped bend channel, the dependence of the increment of the water level on the ice jam volume can be described by a quadratic function. Results show that the more the ice accumu- lation, the more the increment of the water level. With the same ice accumulation in the bend channel, a single pier located at the bend apex will cause more increase of the water level than that with a single pier located in the straight section connecting two bend sections.

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(August 11, 2016,Accepted October 30, 2016)

?China Ship Scientific Research Center 2018

* Project supported by the National Natural Science Foundation of China (Grant No. 51379054).

Jun Wang (1962-), Male, Ph. D., Professor,

E-mail: junwanghfut@126.com

Jueyi Sui,

E-mail: jueyi.sui@unbc.ca