(1)
Huang Guobing Wang Caihuan
Yangtze
River Scientific Research Institute, Wuhan, 430010,China
Tel:
86-27-82829762 Fax: 86-27-82633828
Abstract: The energy dissipation effect of Cushion
pool and the stress characteristics ＆stability
of apron slab of high arch dam have been paid close attention in the field of
engineering construction. According to the
study results at home and abroad and the hydraulic model test data in Goupitan
Project, This paper illustrates the energy dissipation mechanism and the
yardstick for energy dissipation effect of cushion pool, analyses the stress and
stability against floatation of base slab. The flow pattern of cushion pool is
very complicated, which can be treated as the composite flow of submerged impact
jet and jump flow qualitatively. The
energy dissipation effect can be measured by the volume damping ratio impact
pressure of slab, the hydraulic characteristics of pool tail and subsidiary dam
crest, and the indices of downstream scour etc.
The stress characteristics and distribution of base slab are the
important basis of design and calculation for stability against floatation.
It is necessary to point out that the effective water stop, pump &
drainage and anchorage, and the rational slab size and thickness are the
guarantee of slab stability.
Keywords: high arch dam, cushion pool, time average pressure, pulsating pressure, stability of base slab, depth of cushion, energy dissipation effect
0 FOREWORD
Since the 1940s, the construction of high arch dam has been developed rapidly. According to the incomplete statistics, there are 13 thin arch dams more than 200m high existed and under construction worldwide, among which, the Injure arch dam in the former Soviet Union is the highest one, with the height of 272m, the second one is Wayiang arch dam of Italy, with the height of 262m, and the third one is Ertan dam of 240m high in China. The Goupitan dam of 234m high, Xiaowan dam of 285m and Xiluodu dam of 295m of the design stage occupy the first place of the world. Most of the existed projects at abroad belong to high dam with small flow, while the projects planned to build in China are the type of high dam with heavy flow, so the energy dissipation and erosion control are more formidable. In the process of flood discharge, due to the slow initial velocity on dam crest, the concentrated nappes in radial direction, and the short distance from deflected flow to dam toe, the measures for energy dissipation and erosion control such as cushion pool, subsidiary dam and bank revetment in the river bed behind dam are usually taken to avoid local erosion of river bed behind dam and ensure the safety of dam and mountains on both banks. According to the results of hydraulic model tests of energy dissipation in flood discharge in Goupitan Project of Wujiang River, and compared with Ertan and Xiaowan projects, this paper analyses the energy dissipation effect and the stress characteristics ＆ stability of base slab, which can be used for reference.
1 ENERGY DISSIPATION MECHANISM AND EFFECT OF CUSHION POOL IN HIGH ARCH DAM
Due to the high dam, large fall, heavy flood discharge and flood carrying capacity, and narrow valley of dam site, it is very difficult for high arch dam to carry out energy dissipation and erosion control. In Goupitan Project, the scheme of energy dissipation in flood discharge through dam body has been used, namely discharging layer by layer from surface and middle outlets, energy dissipating by collision in the air and arranging cushion pool. For this kind of cushion pool, the energy dissipation is mainly carried out through following three ways: overflow path, path and collision in the air and cushion pool. Usually, the energy loss in overflow path is smaller, the energy loss of jet flow in the air only accounts for 10%~20% of the total loss when no collision happens, and about 60%~80% of energy loss happens in cushion pool. The multiple outlets arranged layer by layer could increase the energy loss in overflow path. The mouth of surface outlet is expanded, where dentate piers with different height are arranged, then the deflected flow from middle outlets collides against the nappe from surface outlets to make the nappe scattered vertically as far as possible, therefore, the energy can be dissipated in the air and in the process of collision.
After falling into water, the nappe lashes the base slab to form an impact zone, spread along the slab to form a diving current zone and then roll upwards after spreading to a contain range to form a rolling zone, at last, a transition zone for the recovery of downstream water level is formed between the rolling zone and subsidiary dam. The comprehensive flow pattern of cushion pool can be treated as the composite pattern of oblique submerged impact jet and submerged hydraulic jump flow qualitatively. The strong turbulent diffusion and shear of jet in cushion pool, and the strong turbulent shear in jump rolling zone mainly dissipate the kinetic energy of jet flow. The collision and scattering of nappe can not only make the energy loss increase in the air, but improve the strong turbulent shear effect of jet in cushion pool.
Up to now, there have not been specifications or standards for the assessment of energy dissipation effect of cushion pool. For the cushion pool of high arch dam, the indices for assessing energy dissipation effect mainly include the volume ratio of damping, the hydrodynamic pressure in impact zone, the flow pattern, pressure and surface profile of pool tail and subsidiary dam crest, and downstream erosion etc.
1.2. 1 Volume damping ratio
The formula for calculating the volume damping ratio is as:
(1)
in which, Q is the total water discharge; hωis the head loss of unit volume;Vω is the water mass volume in energy dissipation. Due to the complicated composite flow pattern of cushion pool, in general, hω=H(water head of upstream and downstream), Vω is the total water mass in cushion pool, and η inflects the flood carrying capacity undertaken by water mass in cushion pool. The max damping ratio in Goupitan Project reaches 17.2kw/m3, 14.9kw/m3 in Xiaowan Project and 13.3kw/m3 in Ertan Project. In the preliminary design of cushion pool dimension, η value of similar project can be used for reference. Some experts consider that η value shall be controlled with 10kw/m3. But through the analysis of model test indices of Goupitan project, the author thinks that it is suitable to control η value within the range of 17kw/m3.
1. 2. 2 Max impact pressure of base slab
The max impact pressure △Pm of the base slab is a very important hydraulic parameter, its
expression is:
(2)
In which, Pmax is the maximum time average pressure in the jet impact zone, and ht is the depth of water cushion, i. e the difference between the downstream level and base slab elevation. △Pm is in direct proportion to the impulse of the deflected flow nappe, and in inverse proportion to the depth of water cushion. The protective standard put forwards by Japanese is △Pm≤30×9. 81kPa, while △Pm≤15×9. 81kPa are taken as the protective standard in China according to the results of Ertan Project. Through optimization of model test in Goupitan, the big differential sill dam with diversion dented sill is used in 6 surface outlets, and the combination deflecting bucket with different deflected angle (00~300) is adopted for 7 middle outlets. The nappe from surface and middle outlets collides in the air. Under the conditions of energy dissipation and erosion control design, △Pm is 8.7×9. 81kPa when the discharge is carried out only by surface outlets, and △Pm values are 0.5×9. 81kPa and –0.6×9. 81kPa separately when the discharge is carried out only by middle outlets and jointly by middle and surface outlets, all of them do not exceed 15×9.81kPa, which means the energy dissipation effect is better.
1. 2. 3
Pool tail and subsidiary dam crest
The energy dissipation effect of cushion pool also can be judged by the indices as flow pattern, surface profile and pressure distribution etc. If the water surface of pool tail is horizontal, the pressure is close to the hydrostatic pressure, the water is transparent without air bubble, and the water depth of subsidiary dam crest does not change with time, the energy dissipation effect will be the best, otherwise, the energy dissipation is not enough. In Goupitan Project, under the conditions of discharge through surface outlets and jointly through surface and middle outlets, the energy dissipation effect conforms to above mentioned rules; While under the condition of discharge only through middle outlets, it can be observed from model that some rolling water crosses subsidiary dam crest due to the far deflecting distance and the nearness of nappe to subsidiary dam. So in order to make energy dissipation carried out in cushion pool as far as possible, the measures such as changing the type of middle outlet mouth to short the deflecting distance etc. Shall be taken.
1. 2.
4 Downstream erosion
The downstream erosion of cushion pool is also an important index for judging the energy dissipation effect. In Goupitan Project, the deepest downstream erosion happens under the condition of discharge only by middle outlets, the second is joint discharge, and the third is the discharge only by surface outlets, which conforms to the regular of surface profile, pressure distribution and flow pattern of pool tail and subsidiary dam crest. Certainly, in order to reduce the construction cost of cushion pool, the complementary energy can be dissipated from the subsidiary dam if the erosion resisting capacity of downstream bed is strong.
In general, the energy dissipation effect of cushion pool shall be measured by the above mentioned factors. The opinion that the dimensionless number φexpressing (γ is the
(3)
water weight, z is the water head between upstream and downstream, and φ≥0. 0077 is proposed) the characteristics of submerged impact jet flow and hydraulic jump flow is take as the comprehensive evaluation index of energy dissipation effect is worthily to discuss.
The model tests of Goupitan Project show the progressive pressure distribution on base slab when discharging only by surface outlets: The pressure line goes gently in front of nappe impact zone, a peak pressure exists in the impact zone, and a low pressure zone occurs in the down stream of the peak pressure; after that the hydrostatic pressure distribution recovers gradually, and the pressure elevation of pool tail is close to the downstream level.
When the discharge is carried out only by middle outlets, there is no obvious peak pressure in the nappe falling zone; in the upper section of the zone, the pressure line is basically flat, which conforms to the regular of hydrostatic pressure distribution; behind the zone, the pressure line comes down slightly, and then goes up gradually; but the time average pressure is still lower than the maximum pressure of cushion pool in the downstream up to the pool tail, Which means the deflecting distance is too far and the link between upstream and downstream has not been carried out completely when the nappe goes through cushion pool. Due to the different deflected angles, far deflecting distance and scattered fall point of nappe, there is no peak value in falling zone.
Under the condition of joint discharge, the collision of nappe in the air makes some energy lost. Especially in the downstream, the level is high and the water cushion depth is enough, the time average pressure line goes gently in front of nappe falling zone, and comes down behind the falling zone, then goes up gradually. The piezometer head is lower than the downstream level.
The model tests of Goupitan Project show that: the pulsating pressure intensity of base slab is the biggest when discharging only through surface outlets, the pulsating pressure intensity comes second under the condition of joint discharge, and the pressure intensity is the smallest for the discharge only through middle outlets. The maximum pulsating pressure and the maximum time average pressure occur in the same place, with the maximum observed value of 5.4×9.81kPa. It is showed by multi-point. Observation that, the reoot-mean-, square value of pulsating pressure on base slab is only 1. 7%~6.0% of the water head between upstream and downstream; the skewness coefficient of pulsating pressure at every observation point is about 0.3, and the coefficient of excess is 2. 5~3. 3, which indicates the pulsating pressure accord with the normal probability distribution; the eddy of pulsating pressure is low frequency mainly, and the observed dominant frequency is 0.3~4.5Hz, which conforms to the turbulent theory.
Otherwise, the stress of pool base slab also includes uplift, anchor rod tension and dead weight of slab.
3.
1 Regardless of water stop, pump ＆
drainage and anchorage
The stability tests of cushion pool base slab in Goupitan Project indicate: the place where the unstable state happens first is the 1st or the 2nd apron slab behind the nappe impact zone, and the modes of unstability can be divided into tilting and floating. Behind the nappe impact zone, the pressure on the surface of apron slab becomes lower and a low pressure zone forms. Regardless of water stopping and pump & drainage, the pressure on the bottom of apron slab will be higher than that on the surface, thus the apron slab becomes unstable. The larger and faster the water discharge and flow velocity of impact flow and the shallower the downstream water are,
the lower the surface pressure is, then it is easier for apron slab to become unstable. The prerequisites for slab stability are:
(4)
(5)
(6)
(7)
in which, G is the concrete submerged weight; R is “lift”; K is the coefficient; h is the thickness of concrete plate; γ s is the concrete weight; A is the area of concrete plate;σup, σdown, Pup and Pdowe express the root-mean-square values of pulsating pressure and time averaged pressure elevation of slab surface and bottom respectively. Through calculation, K≈0. 9 in (4), namely, the prerequisites for slab stability is
(8)
Otherwise, the base slab thickness and foundation will produce effect on slab stability. The larger and thicker slab and indeformable foundation will be favorable for the slab stability; on the contrary, unreasonable slab size and thickness will make slab unstable partially.
If P1, P2, P3, P4 and P5 represent time average pressure, pulsating pressure, uplift, anchor rod tension and dead weight of slab respectively, the formula for stability against floatation is
(9)
It is indicated by the calculation of measured model data in Goupitan project, when encountering 100- year frequency flood, K=1.9, the maximum K is 2. 56;when encountering 500-year frequency flood, K=1.5, the max K is 3.0, All of them exceed 1.3, which means the design of base slab is safe. Under the condition of slab closure, the more the pool level with the maximum time average pressure exceeds the downstream level, the bigger the slab safety coefficient is. The less the min. time average pressure is, the smaller the safety coefficient is. Under the effect of the minimum time average pressure, if the safety coefficient against floatation meets the requirement, the maximum hydrodynamic pressure can not be limited within 15×9.81kPa.
The arrangement of layered multiple outlet to make the nappe of deflected flow and drop flow collide in the air and the installation of cushion pool are the trend of energy dissipation design for high arch dam. The flow pattern of cushion pool is very complicated, which can be treated as the composite flow of submerged impact jet and jump flow qualitatively. The energy dissipation effect can be measured by the volume damping ratio impact pressure of slab, the hydraulic characteristics of pool tail and subsidiary dam crest, and the indices of downstream scour etc. The stress characteristics and distribution of base slab are the important basis of design and calculation for stability against floatation. It is necessary to point out that the effective water stop, pump & drainage and anchorage, and the rational slab size and thickness are the guarantee of slab stability.
The southwest of China possesses more than 70% of the hydroelectric resources. After the development of the West, the superelevation dam of 200m or even above 300m high will be built successively in the 21st century. With the deepening of scientific research, we will have a better understanding of the hydraulic characteristics of cushion pool, and the design of cushion pool will be more advanced and perfect.
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[3] Liu Peiqing, Characteristics of Flow in Plunge Pool and Its Comprehensive Evaluation Index, Journal of Yangtze Rive Scientific Research Institute, 1,1997.
[4] Huang Guobing, Study on The Hydrodynamic Pressure Characteristic of Cushion Pool in Goupiton Project, Selected Works on Sluice Project and High Velocity Flow, 9,1994.