EXPERIMENTAL STUDY OF DAM-BREAK FLOW IN CASCADE RESERVOIRS WITH STEEP BOTTOM SLOPE*

XUE Yang, XU Wei-lin, LUO Shu-jing, CHEN Hua-yong, LI Nai-wen

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China, E-mail: gist1116@163.com

XU Ling-jun

College of Water Conservancy and Hydropower Engineering, Xi’an University of Technology, Xi’an 710048, China

EXPERIMENTAL STUDY OF DAM-BREAK FLOW IN CASCADE RESERVOIRS WITH STEEP BOTTOM SLOPE*

XUE Yang, XU Wei-lin, LUO Shu-jing, CHEN Hua-yong, LI Nai-wen

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China, E-mail: gist1116@163.com

XU Ling-jun

College of Water Conservancy and Hydropower Engineering, Xi’an University of Technology, Xi’an 710048, China

Dam break can cause a significant disaster in the downstream, especially, in a valley with cascade reservoirs, which would aggravate the disaster extent. The experimental studies of the dam-break flow of cascade reservoirs are few and far between at the present. Most of related studies concern the failure of a single dam.. This article presents an experimental study of the characteristics of an instantly filled dam-break flow of cascade reservoirs in a rectangular glass flume with a steep bottom slope. A new method was used to simulate the sudden collapse of the dam. A series of sensors for automatic water-levels were deployed to record the rapid water depth fluctuation. The experimental results show that, the ratio of the initial water depth of the downstream reservoir to that of the upstream reservoir would greatly affect the flood peak water depth in the downstream reservoir area and in the stream channel behind the downstream dam, while the influence of the dam spacing is insignificant. In addition, the comparison between the single reservoir and the cascade reservoirs shows some difference in the dam-break flow pattern and the stage hydrograph at the corresponding gauging points.

dam-break flow, cascade reservoirs, instantly full dam break, steep bottom slope

Introduction

The dam-break flood can cause disasters in the downstream, it would propagate in rivers in the form of standing wave, and the wave crest would generate a sudden rise of water levels along its path[1]. In recent years, more and more studies were devoted to the dam-break problems due to the destructive power. Cochard and Ancey[2]developed a new imaging system, consisting of a digital camera coupled with a synchronized micro-mirror projector, to accurately measure the dam-break surge’s free-surface variations with time. Eaket et al.[3]experimentally obtained thethree-dimensional water surface profile and the flow velocities associated with the dam break events of the scale model by using video stereoscopy for the measurement of the unsteady open channel flow. Frazao and Zech[4]reported an experimental study of a dambreak flow in an initially dry channel with a 90° bend. Zhou et al.[5]performed dam-break flow experiments and compared the results with three CADAM tests: a channel with a 45obend, a channel with a 90obend, and a straight channel with a triangular bump in the bed. Yan and Cao[6]conducted a series of flume experiments over erodible bed to study the landslide dambreak flooding. Niu et al.[7]experimentally studied landslide dam-break flooding over the fixed-bed in open channels. Sun et al.[8]experimentally obtained the variation of hydraulic characteristics in the closure process of a dam-breach. Zhang et al.[9]studied the effects of the cohesive strength of the filling of the cohesive homogeneous earth dam on the breach formation in the world’s highest prototype tests, and presented three breach mechanisms: the source-tracingerosion of the dam body in the form of “multilevel head-cut”, the “two-helix flow” erosion of the dam crest and the collapse of breach sidewalls due to instability. Li et al.[10]deduced the similarity scales of the head-cut migration rate and the time of the flow process of the homogeneous embankment failure due to overtopping flow, and conducted several experiments to verify the two similarity criteria. The IMPACT project[11]of European Union investigated the breaching mechanism of embankment dams in five large-scale field tests and twenty-two laboratory tests, and related studies[12-14]were also conducted in the United States and New Zealand. Furthermore, a number of results of simulations of dam-break flows[15-23]were reported. However, they only concern the dam-break of a single reservoir, not cascade reservoirs.

Fig.1 Sketch of the flume and the layout of gauging points (unit: m)

In China, due to the growing demands of electricity supply and flood control, a great number of cascade reservoirs and hydropower stations were built in several rivers, especially in southwest China. However, once an upstream dam collapses, the dam-break flood would lead very likely to the failure of the downstream dam, thus a chain reaction will be resulted, and a great flood catastrophe would happen in the downstream region. In this respect, very few experimental studies were devoted to the dam-break flow of cascade reservoirs. Model tests would be effective to deal with the dam-break problem, therefore, a series of flume experiments were carried out to study the characteristics of the dam-break flood of cascade reservoirs.

1. Experimental setup

The experiments were carried out at State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University. There are relatively large number of cascade reservoirs on southwest rivers in southwest China, mostly at river valleys with a steep bottom slope. However, for the model test, if

Fig.2 Structure of plates

the bed slope of the experimental flume is consistent with that of the natural river, a very long flume must be built to lay out cascade reservoirs, which is difficult to accomplish in the test room. In view of test conditions, a rectangular glass flume of 20 m×0.5 m×0.8 m, and of a bottom slope of 12o, is used, as shown in Fig.1. Two flat plates are designated as the upstream and downstream dams in the flume, and they are 0.6 m long, 0.5 m wide and 0.1 m thick. And ten water probes are placed along the centerline of the flume to record the highly transient water depths. It is necessary to note that, the probes cannot be placed at the dam site due to the confine of the plates, so twogauging Points P0and P6were put adjacent to the dam site. Therefore, the stage hydrographs of P0and P6can be treated approximately as the stage hydrographs of the dam sites. Additionally, a high-resolution digital camera is placed on the side of the downstream dam to capture the propagation process of the dam-break flows in the channels around the downstream dam.

Fig.3 Water depth histories at Points P0-P9(L=7.8m , H1=0..494m , H2=0.496m)

In traditional experiments, the rapid rise of the plate[3-4,24]is used to simulate the instantaneous and complete collapse of a dam. In this study, however, a new method of sudden and full collapse of a dam, is adopted, with the plate falling down rapidly to the downstream channel,to trigger a condition of the down-stream dam breaking. The structure of the flat plate is shown in Fig.2. The plates are hinged to the bottom of the flume by two stainless steel hinges. Several magnets are placed on the fixation frame installed above the flume, in order to attract the plate with sheet iron inside it. So a trigger condition of the dam break can be set through adjusting the size and the number of magnets. In this experiment, three magnets, with size of 0.05 m×0.05 m×0.03 m, are used to generate the bearing capacity for the plate, and the ultimate bearing capacity of the plate is the force equal to the hydrostatic pressure in the water depth of 0.53 m. Once the force acting on the plate goes beyond the ultimate bearing capacity, the plate fell down very quickly to the downstream channel. The plate falling time is less than 0.35 s, to simulate an instantly filled dam break.

2. Experimental data and analyses

The tests consist of three cases, with the dam spacingLof 7.8 m, 9.8 m and 11.8 m, respectively. Initial water depths of reservoirs before dam breaking range from 0.184 m to 0.531 m. The channel bed behind dams is initially dry. The time interval between consecutive sampling points of the water probes is 0.02 s.

Fig.4 Flow patterns near the downstream dam

2.1Propagation process of dam-break flow

Figure 3 shows the stage hydrographs of all gauging points under a typical test condition.H1andH2stand for the initial water depth of the upstream reservoir and the downstream reservoir, respectively. When an instantaneous and complete collapse of the upstream dam occurs, the water of the upstream reservoir pours down in a very short time. A typical stage hydrograph in front of the dam, in which the gauging Point P0is located, is shown in Fig.3(a). As shown in Figs.3(b)-3(e), along the channel behind the upstream dam, the peak stages of the dam-break flow decrease, and the curves of the water depth become flat gradually. When the dam-break flow resulting from the collapse of the upstream dam occurs in the downstream reservoir, and interacts with the water of the downstream reservoir, it gives rise to a surge in the downstream reservoir (see Fig.4(a)). The propagation of the surge raises the water level of the downstream reservoir. As the forces acting on the downstream dam exceed its ultimate bearing capacity, the dam breaks in consequence (see Fig.4(b)). Because the outflow discharge at the dam site section is less than the inflow discharge, a backwater will occur (see Fig.4(c)). Then, the water level heads up constantly and the water surface fluctuates greatly on the channel behind the downstream dam. That process continues until the end of the flood peak caused by the upstream. Due to the influence of the backwater, in the curves of the stage hydrograph of the descending process, multi-peaks may occur in front of the downstream dam. The closer the gauging point is to the dam, the more peaks will occur (see Fig.3(f)-3(g)). Additionally, because of the backwater, the water depths behind the dam are at a high flood water depth in a flood process. As shown in Figs.3(h)-3(j), in the stage hydrographs of the Points P7-P9, the main peak is not clearly shown, except a number of “sawteeth” of similar sizes.

In addition, it can be seen from Fig.3 that, when the upstream dam suddenly collapses, the emptying time of the upstream reservoir is about 3.4 s. Then the wavefront of the dam-break flow arrives at gauging Point P1at aboutt=0.4s. Att=2.0s, the wavefront reaches Point P5in the downstream reservoir. At aboutt=2.1s, the wavefront reaches Point P6, in front of the downstream dam, and the water depth of P6rises rapidly to the crest at aboutt=2.4s. At this moment, the downstream dam breaks suddenly due to the overload. After that, the wavefront reaches Points P7, P8and P9at aboutt=2.6 s, 2.8 s and 3.2 s, respectively. However, unlike the upstream reservoir, the emptying time of the downstream reservoir is about 3.6 s.

2.2Effects of the ratio of the initial water depth

In this article, the relative flood peak water depthHp/H0is defined as the ratio of the flood peak water depthHpto the initial water depthH0, andαstands for the ratio of the initial water depth of the downstream reservoirH2to that of the upstream reservoirH1. When the dam-break flow resulting from the collapse of the upstream dam propagates to the downstream reservoir, it has an additive effect and raises the water level. The relative flood peak water depth reflects the extent of the additive effect, and the extent is influenced by the ratio of the initial water depth of the downstream reservoir to that of the upstream reservoir.

Fig.5 Relationship betweenHp/H0andαat P5and P6for three schemes

The relationships betweenHp/H0andαat P5and P6, located in front of the downstream dam, are shown in Fig.5. It can be seen that, as a whole, the values ofHp/H0decrease as the values ofαincrease. In other words, the extents of the additive effect caused by the upstream dam-break flow become smaller in the downstream reservoir, as the ratio of the initial water depth of the downstream reservoir to that of the upstream reservoir gets larger. However, the influence ofαuponHp/H0will reach a critical state whenαis 1.0. Whenα＜1.0, the values ofHp/H0grow fast with the decrease ofα, that is to say, the additive effect gets more and more prominent rapidly. The extents of the additive effect are comparatively large in this range. On the other hand, whenα＞1.0, the relation curve betweenHp/H0andαrises but a little with the decrease ofα. The extents of the additive effect are small, and the values ofHp/H0are not more than 2.0. Asαapproaches infinity,H2is far greater thanH1, and the effect of the upstream dam failing on the waters of the downstream reservoir tends to be negligible, so the value ofHp/H0is close to 1.0. From Figs.5(a) and 5(b), it can be seen that, asαis 1.0, the correspondingHp/H0is about 2.0 and 1.5, respectively. That is to say, as the dam-break flow propagates from Point P5to Point P6, the flood storage effect of the downstream reservoir weakens the extent of the additive effect. On the whole, the two curves betweenHp/H0andαrise a little, and the degree of the additive effect becomes small.

Fig.6 Relationship betweenHpandαat P7and P8for three schemes

The gauging Points P7and P8are on the channel behind the downstream dam, and the initial water depthsH0are zero at the two points. The relationships betweenHpandαare shown in Fig.6. It is seen that there is a critical point at 1.0, just as in Fig.5. Whenα＜1.0, the values ofHpvary little withα.The variations ofHpare not more than 0.1 m at Point P7, and they are within 0.05 m at Point P8. On the other side, whenα＞1.0, with the increase ofα, the values ofHpdecrease gradually, and approach to a characteristic value, which is the flood peak water depth resulting from the collapse of the downstream dam only. Comparing Fig.5(a) and Fig.5(b), it can be seen that the peak stages of the dam-break flow decrease along the channel behind the downstream dam. In addition, though there is a similar curve trend, the fluctuation of flood peak water depth at Point P7is larger than that at Point P8, whenαisless than 1.0. By observing and analyzing the evolution process of the dam-break flow, when the surge spreads quickly to the downstream dam, a part of the waters would jump over the dam due to inertia, and join the main stream in the channel behind the dam. Nevertheless, the location of P7happens to be within a converging area.

2.3Effects of the distance of dams

From Fig.5 and Fig.6, it can be seen that for the variations of dam spacing, the relationships betweenHp/H0andαat Points P5-P6, and the relationships betweenHpandαat Points P7-P8, respectively, have a good agreement.. Before the downstream reservoir water reaches the upstream dam, the long channel behind the dam is initially dry. During the time when this channel keeps dry, the water surface profile of the upstream dam-break flow is close to a flat shape, almost parallel to the channel bed. And with the increase of the dam spacing, the amplitude of the wavefront of the upstream dam-break flow changes little at the end of the backwater of the downstream reservoir. Therefore, the dam spacing has no significant effect on the flood peak water depth of the downstream reservoir area and the stream channel behind the downstream dam.

2.4Comparisons of the dam-break flows between asingle dam and cascade dams

The characteristics of the dam-break flow resulting from the instantaneous and complete collapse of a single storage dam are investigated by utilizing only the downstream dam in this experiment. The arrangements of gauging points are the same as above, so are the test water depths. The stage hydrographs of gauging Points P6-P9under the sudden complete failure of a single dam and cascade dams are shown in Fig.7(a) and Fig.7(b), respectively. The instant of the downstream dam failure, under the condition of the cascade dams breaking in turns, is indicated by a vertical dashed line in Fig.7(b).

By a comparative analysis of the stage hydrographs at Points P6-P9between a single dam breaking and cascade dams breaking, it can be seen that, at P6, the former is a smooth descending curve, while the latter is a dropdown curve with secondary peaks after the downstream dam collapses. The number of secondary peaks reflects the turbulence intensity of the dam-break flow at this point. At Points P7-P9, the flood peak due to the breaking of cascade dams becomes more prominent than that due to a single dam breaking. After rising up to the peak rapidly, the descending process of the former also produces a smooth curve, and as the gauging points are far from the dam site, the values of peak stage gradually diminish and the hydrographs become flat. However, the latter produces several saw-toothed peaks, and the increase of the peaks means more severe fluctuation of the water surface. Also, the time duration of flood peak gets longer as a result of the increase of the water, and in the vicinity of the downstream dam the channel keeps a high water depth during the flood peak process. Otherwise, as far as the emptying time goes, the former is about 3.4 s, and the latter is approximately 3.6 s. Based on the analysis of the propagated process of the dam-break flows, it is observed that the differences of the dam-break flows between a single dam and cascade dams are mainly caused by the backwater in the downstream reservoir area.

Fig.7 Stage hydrographs of single dam and cascade dams

3. Conclusions

In this study, a series of flume experiments over steep bed slopes were carried out to compare the characteristics of the dam-break flow under the condition of the instantaneous and complete collapse of cascade dams in turns, and the influences of the variation of the reservoir water depth and the dam spacing on the dam-break flow parameters. Furthermore, an instantly complete failure of a single dam testing was performed on this model, and the differences of the dam-break flows between a single dam and cascade dams were studied.

The ratioαof the initial water depth of the downstream reservoir to that of the upstream reservoir has a significant impact on the flood peak water depth in the downstream reservoir area and the stream channel behind the downstream dam. In the downstream reservoir area, the upstream dam-break flowwould generate a surge with an additive effect on the water depth. The relative flood peak water depthHp/H0decreases with the increases ofα. Moreover,Hp/H0decreases rapidly whenα＜1.0 and slowly whenα＞1.0, and theHp/H0finally approaches to 1.0 with the further increase ofα. In the channel behind the downstream dam, the flood peak water depthHpchanges little whenα＜1.0, andHpgradually decreases whenα＞1.0 and approaches a characteristic value, which is the flood peak water depth under the instantly complete collapse of the downstream dam only.

The influence of the dam spacing on the flood peak water depth of the downstream reservoir area and the stream channel behind the downstream dam appears insignificant. The curves ofHp/H0-αare substantially in an agreement with the variations of the dam spacing, so are the curves ofHp-α.

Due to the effect of the upstream dam-break flow, backwater occurs in the downstream reservoir area. It is an important reason for the differences of the characteristics of the dam-break flow between a single dam and cascade dams.

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March 7, 2011, Revised March 26, 2011)

* Project supported by the National Basic Research Program of China (973 Program, Grant No. 2007CB714105), the National Natural Science Foundation of China (Grant No. 50909067).

Biography: XUE Yang (1983-), Male, Ph. D. Candidate

XU Wei-lin,

E-mail: xuwl@scu.edu.cn

2011,23(4):491-497

10.1016/S1001-6058(10)60140-0