(1)
1Jueyi
Sui, 1Bryan W.
Karney, 2Zhaochu
Sun
1Dept. of Civil Engr., University of Toronto, ON, Canada, M5S 1A4
phone/fax: (416) 978-7776, Email: karney@civ.utoronto.ca
2Dept.
of Civil Engr., Hefei University of Technology, Anhui, China
Abstract: Using field measurements of frazil jams in the Hequ Reach of the Yellow River, this paper discusses the mechanism of evolution of frazil jams. An empirical relationship between ice thickness and hydraulic parameters is established. The critical Froude number from the equilibrium ice jam to the overloaded ice jam is about 0.075, with the dimensionless jam thickness about 0.40. Experimental studies were conducted to obtain further insights into characteristic features of the evolution of frazil jams and the dependence of jam evolution on ice concentration. The experimental analysis shows a similar jam evolution to the lower reach of the Hequ Reach. Using 22 groups data of St. Lawrence River, it is found the relationship between the dimensionless thickness of ice jam (hanging dam) and the Froude number of the St. Lawrence River has a similar tendency to those at the Hequ reach.
Keywords: frazil ice, ice jam, froude number, dimensionless jam thickness, ice concentration
A major consequence of ice cover formation on northern rivers is the jamming that occurs during spring breakup of the cover and, to a lesser degree, during the freeze-up period. Due to their large aggregate thickness and hydraulic resistance relative to those of sheet ice, jams tend to cause unusually high water stages. This has repercussions in many operational and design problems such as the overturning moment on river structures due to moving ice, flooding and associated stage-frequency relationships during freeze-up and, in spring, river bed scour due to surges from released jams (Beltaos, 1983). Based on field measurements of frazil jams from 1982 to 1989 in the Hequ Reach, and on lab work, this paper focuses on the mechanism of frazil jam evolution and the influence of ice discharge on the evolution of frazil jam. Supplemental data from the St. Lawrence River (Michel, 1984) allows some interesting comparison with the work conducted in this paper.
As shown in Fig. 1, the Hequ Reach is situated on the middle reaches of the Yellow River, between 39° and 40°N and 110° and 112°E, and extends from Longkou Gorge (near Sect. 1) to Tianqiao Power Dam (Sect. 22) over a length of 70 km. After passing Sect. 1, the river broadens and meanders. The river width between Sect. 2 and Sect. 8 in the upper Hequ Reach usually exceeds 500 m, but is more than 600 m at Sect. 5, 6 and 7. Between Sect. 4 and Sect. 6, it attains a 1500 m width, with numerous shoals. The river width in the lower Hequ Reach between Sect. 11 and Sect. 17 is usually less than 400 m. The slope of the riverbed is more than 0.15% between Sect. 1 and Sect. 2, more than 0.06% between Sect. 2 and Sect. 7, and less than 0.06% between Sect. 7 and Sect. 17. Upstream from Longkou Gorge, there exists a 100 ~ 200 km open water reach with numerous rapids due to high velocities. Due to cold winter temperatures, an enormous amount of frazil ice is generated in this open water stretch, which contributes to the formation and accumulation of large frazil jams in the Hequ Reach.
The Hequ Reach experienced over 100 days of jamming each year from 1982 to1989. Frazil ice jams of tremendous size have often formed upstream of Shiyaobu (near Sect. 10), leading to high water levels and causing a serious ice flood disaster in 1982 (Sun, et al, 1986). Since then, measurements of a variety of factors such as water levels, thickness of the ice sheet and frazil jams, current velocities under ice jams, water and air temperatures along this river reach have been made each winter. The long-term daily mean air temperature (1955–1986) at the Hequ meteorological station turns to sub-zero on Nov. 16, about the same date as the average frazil ice running date (Nov. 20). On average, air temperature rise above zero on March 7 with 108 days of sub-zero temperature. The mean air temperature during this period – 7°C.
Field investigations showed that after the formation of the initial frazil jams along Hequ Reach, most of frazil ice generated in the open water reach is stored in the upper reach jams between Sect. 1 and Sect. 10, with only a small proportion transported downstream. Thus, the formation of the initial jam causes the upper reach jams to grow rapidly while the lower reach jams evolve slowly due to the reduced rate of frazil ice supply. Obviously, the upper reach jams are different from the lower reach jams between Sect. 10 and Sect. 17. Frazil jams between Sect. 17 and Sect. 22 form in the reservoir and are termed reservoir jams. This paper primarily considers the upper reach and lower reach jams.
It is found that there is an interdependence between the evolution of frazil jams and the correspondent variation in water levels during the ice jamming period. More specifically, the variation in water levels and evolution of frazil jams depend not only on discharge, but also on frazil ice concentration, the configuration of channel section and climatic factors. Sui, 1988; Sun 1986; Sun and Sui 1990 summarized 5 regularities that prevail with respect to variation in water levels and frazil movement.
Factors affecting the evolution of a frazil jam include the oncoming stream flow, the hydraulic slopes in the reach, the morphology and geology of the river reach, oncoming ice discharge, ice composition, and many others. Oncoming ice concentration and ice composition directly affect the size and shape of the ice jam. For a given water discharge, larger ice concentration can lead to serious accumulation of the jam, dramatical increases in water level, increased flow velocity and intensified sediment erosion of the riverbed. Conceptually at least, the variation of water level during the ice period may be related to the following variables, although some of them are interdependent:
(1)
in which: H = mean overall depth (m); v = mean velocity of flow under ice jam (m/s); h = mean effective depth of water under jam (m); S = hydraulic slope; nb, ni = roughness coefficient of river bed and ice jam respectively; r, r’ = density of water and frazil (kg/m3) respectively; d50 = median diameter of frazil particles (m); sd = mean square deviation of grain size of frazil particles; qi = oncoming ice discharge per unit width of river (m3/s.m); t = mean thickness of jam (m); B = width of river (m); L = total length of frazil jam, DL = length of frazil jam between the computation section and frontal edge of ice jam.
Field investigation shows the frazil particles are generally uniform, with mean particle diameters between 7 and 11 mm and the major portion of ice particles being of this size. The frazil particles that traveled over a long distance through fast-flowing open-water reach with rapids upstream from Hequ Reach tend to be more round in shape than those that have traveled through reaches with slower velocities (Shen and Wang, 1995). Thus, for simplicity, r’, sd , d50 and r may be considered as constants. Therefore, dimension analysis comes (1) to be rewritten as
(2)
The v/(gH)0.5 term describes hydraulic condition under frazil jam condition. The second term of right-hand side of (2) is frazil ice concentration. As is mentioned above, most of oncoming frazil ice is stored in the upper jam reach and only a small amount is transported to the lower jam reach. Due to difference in ice input, the features of the upper reach jam and lower reach jam are quite different, and they should be analyzed separately. However, for both technological and economical reasons, it is virtually impossible to conduct the measurement of ice discharge during the ice period. The DL/L term of the right-hand side of (4) is the dimensionless jam length. The location of frontal edge at Longkou gorge, is not completely stable, as it sometimes propagates about 10 km upstream from section 1, and at other times moves downstream of this section. However, as this behavior is not considered here, nor is the influence of the dimensionless length of the ice jam. In view of this, only the relationship between t/H and v/(gH)0.5 is investigated in more detail in order to describe the dependence of t/H on v/(gH)0.5 under an ice jam condition for both the upper reach jams and lower reach jams in Hequ Reach of the Yellow River.
Analyses are carried out on 139 groups of data observed at upper reach jams and 271 groups of data at lower reach jams. The relationships between t/H and v/(gH)0.5 are shown in Fig. 2. Obviously, because of different frazil ice replenishment, the results between t/H and v/(gH)0.5 are different. For the upper reach jams, the relationship is approximated by:
(3)
For the lower reach jams the relationship is:
(4)
Not surprisingly, the correlation is far from perfect. The scattering shown in Fig. 2 is expected due to the uncertainty of the accuracy of measurements, non-uniform particle size and channel irregularities. The tendency of the curves reflects the dependence the t/H on the frazil jam parameter v/(gH)0.5 as well as frazil ice replenishment.
For the upper reach jam, the larger the v/(gH)0.5 , the larger the t/H. Conversely, for the lower reach jams, the larger the v/(gH)0.5 is, the smaller the t/H. Eqs. (3) and (4) provide an approximate empirical description of frazil jams evolution at the Hequ Reach.
To further study the frazil jam evolution, experimental studies were conducted in a non-refrigerated condition using a horizontal 36 m-long, 0.5 m-wide, 0.6 m-deep flume which comprises one 180° bend and connected by 16.8 m-long and 4.8 m-long straight reaches. Frazil ice was simulated using wax particles that were 5mm thick and right parallelepiped. The ice cover was simulated using foamed plastics. An ice hopper located at the upstream reach was used to discharge “ice” at controlled rates into the flume. The tests were run under steady flow and ice concentration conditions. Once the input Qi /Q equals the output value, the ice jam was considered to be equilibrium, and the experiment was terminated.
The process of frazil jam formation and evolution in the lab is similar to that at the Hequ Reach. Figs. 3 ~ 6 describe the relation between t/H and related parameters. The t/H depends to a large extent on the parameter that describes hydraulic parameter under frazil jam condition v/(gH)0.5. The smaller the v/(gH)0.5, the larger the t/H. The Qi /Q and DL/L influence also the ice thickness during the evolution of frazil jam. The larger the Qi /Q, the larger is the t/H. The larger the DL/L, the smaller is the t/H. The regression relationship between t/H and v/(gH)0.5, Qi /Q and DL/L is described as follows:
(5)
Equation (5) shows the dependence of t/H on the Froude number under ice condition v/(gH)0.5, Qi /Q and jam dimension DL/L. Clearly, the v/(gH)0.5 and Qi /Q play a strategic role in the evolution of ice jam. The DL/L, however, has only minor influence on t/H.
Using Michel’s 22 groups of data of St. Lawrence River from 1947 to 1950 (Michel, 1984, Table 1 and 2), Fig. 7 showed the relationship between t/H and v/(gH)0.5. It is found that the results of the St. Lawrence River has a similar tendency to those at the Hequ reach of the Yellow River, even though the field measurements at the St. Lawrence River are less intensive than those on the Hequ Reach. The data of ice-dam lies on the upper limb of the figure, just as it did for the Hequ Reach. The data of ice-jamming process (including shoving and packing) lie on the lower limb of the figure. The turning point of t/H is about 0.3, with the Froude number under ice condition about 0.045.
This paper focuses on the preliminary
insights into characteristic features of the evolution of frazil jams during
ice-jam periods. The dimensionless thickness of ice jam (t/H) depends mainly on
the Froude number under ice condition (v/(gH)0.5),
ice concentration in water (Qi /Q),
and the jam dimension (DL/L).
v/(gH)0.5 and Qi
/Q play a crucial role on the evolution of ice jam. The DL/L,
however, has only a relatively minor influence on t/H.
The results of the Hequ Reach show the Froude number at the turning point from
equilibrium ice jam to hanging dam is about 0.075, with the t/H
about 0.40. Comparison between the results of the Hequ Reach and those of St.
Lawrence River has been conducted. The relationship between the thickness of ice
jam (hanging dam) and the Froude number of the St. Lawrence River has a similar
tendency to those at the Hequ reach of the Yellow River.
Acknowledgments
Supports provided by Shanxi Bureau of Water Conservancy, Chinese Natural Sciences Foundation and NSERC - Natural Sciences and Engineering Research Council of Canada are appreciated. The experiments ware conducted at Hefei University of Technology.
References
[1] Beltaos, S. (1983). “River ice jam: theory, case studies and application,” Journal of Hydraulic Engineering, ASCE 109(10), 1338-1359.
[2] Michel, B. (1984) “Comparison of field data with theories on ice cover progression in large rivers” Canadian Journal of Civil Engineering, Vol. 11, 798-814.
[3] River Ice Jams (1995), Beltaos, S. (ed.), Water Resources Publ., Colorado, USA.
[4] Shen, H. T., and Wang, D., (1995). “Under cover transport and accumulation of frazil granules,” Journal of Hydraulic Engineering, ASCE 121(2), 184-195.
[5] Sui, J. (1988). “Computation of water level at Hequ Reach of the Yellow River in ice periods,” Research report, Hefei University of Technology, China.
[6] Sun, Z., and Sui, J. (1990). “Calculation of water level in a river reach with frazil ice jam,” Proc., IAHR Symp., Espoo, Finland, Vol. II, 756-765.
[7] Sun, Z., Yang, S., and Yao., K. (1986).
“Prototype observation and study of ice jam at Hequ section of the Yellow
River,” Proc., IAHR Symp., Iowa, Vol. II, 39-48.
Fig. 1 The Hequ Reach of the Yellow River
Fig. 2 Relationship between t/H and v/(gH)0.5
Fig. 3 Relationship between t/H and
under ice jam condition (Hequ Reach) v/(gH)0.5 under jamming condition(Lab)
Fig. 4 Relationship between t/H
Fig. 5 Relationship between
t/H and DL/L
and
Qi/Q (Lab) with
different Qi/Q (Lab)
