Shore Spillways

Abstract

A spillway is designed to conduct flood flows safely passing the dam, which plays an important role similar to a safety valve in hydraulic projects. Improperly designed spillways or spillways of insufficient capacity are responsible for many fatal accidents (e.g., failure) of dams. Therefore, spillways are, or should be, designed to accommodate flows during maximum flood period so as to prevent damage to the dam and appurtenant structures. Their size and location are determined by the size and type of dam, local topography, geology, and careful review of the stream flow history at the work site.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

12.1 General

A spillway is designed to conduct flood flows safely passing the dam, which plays an important role similar to a safety valve in hydraulic projects (Chen and Chen 2014; Golzé 1977; Grishin 1982; ICOLD 1987; Lin 2006; Novak et al. 1990). Improperly designed spillways or spillways of insufficient capacity are responsible for many fatal accidents (e.g., failure) of dams. Therefore, spillways are, or should be, designed to accommodate flows during maximum flood period so as to prevent damage to the dam and appurtenant structures. Their size and location are determined by the size and type of dam, local topography, geology, and careful review of the stream flow history at the work site.

Spillways may be built integrally with dam located within or on the downstream face of dam, which have been described in the Chaps. 7 and 8 of this book, or separately outside of dam and termed as shore (or river bank) spillways (State Economy and Trade Commission of the People’s Republic of China 2002; Ministry of Water Resources of the People’s Republic of China 2000), which will be presented in this chapter.

12.1.1 Types of Separate Spillways

Shore or river bank spillways may be on one side or both sides to the dam abutments (Fig. 12.1), or within the bank of reservoir where adequate topographic condition is available.

Fig. 12.1

The Tianshengqiao No. 1 Project (China, H = 178 m). 1 CFRD; 2 spillway; 3 chute; 4 intake of power tunnel; 5 power station; 6 flood release tunnel; 7 diversion tunnel; 8 upstream cofferdam; 9 downstream cofferdam; 10 the Nanpanjiang River

Shore spillways may be categorized by the purposes into normal and emergence spillways. The former is employed to release the flood stipulated by the design standard, while the latter is used to release the extreme flood of lower frequency.

Shore spillways may also be classified by the flow pattern into the types of chute, side channel, drop inlet, siphon, etc. (Golzé 1977; Zuo et al. 1987; USBR 1987).

• 1. Chute (proper open channel or trough) spillways

Proper open-channel spillway is one of the most prevalent type in which control weir is placed approximately perpendicular to the adjoining spillway discharge channel.

• 2. Side-channel spillways

Side-channel spillway is one in which control weir is placed along the side of and approximately parallel to the adjoining spillway discharge channel. Flow over the weir crest falls into a narrow trough along the weir, turns an approximate right angle, and then continues into the main discharge channel, inclined shaft, or tunnel.

• 3. Drop inlet (shaft or morning glory) spillways

Drop inlet or shaft spillway, as the name implies, is one in which the water enters over a horizontally positioned weir lip, drops through a vertical or sloping shaft, and then flows to the downstream river channel through a horizontal or near-horizontal conduit or tunnel. The spillway may be considered as being made up of three elements, namely an overflow control weir, a vertical transition, and a closed discharge conduit. Where the inlet is funnel-shaped, it is often termed as “morning-glory” or “glory hole” spillway (Bradley 1956; Peterkaon 1956).

• 4. Siphon spillways

A siphon spillway is a closed conduit system formed in an inverted shape, so that the interior of the bend of the upper pathway is at normal reservoir storage level. The initial discharges of the spillway, as the reservoir level rises above normal, are similar to that flow over a weir. Siphonic action takes place after the air in the bend over the crest has been exhausted. Continuous flow is maintained by the suction effect due to the gravity pull of the water in the lower leg of siphon (McBirney 1958).

12.1.2 Applicability of Separate Spillways

Shore spillways are usually employed with regard to the following situations:

• Flow over the dam is not permitted, e.g., where the embankment dam is erected as water-retaining structure in a hydraulic project (Fig. 12.1);

• Concrete arch dam is built in a narrow valley with large discharge requirement (Fig. 8.46);

• The space downstream of the dam is too limited to locate a dam-type spillway.

However, it should be emphasized that only expenditure and engineering function of all possible alternative designs can provide a basis for the consideration of shore spillway. For example, a natural saddle located near abutment with adequate elevation and competent rock is favorable to accommodate shore spillway.

12.2 Chute (Proper Open Channel or Trough) Spillways

Among all types of shore spillways, chute spillways have been exercised in embankment dam projects more often than any others. By the chute spillway, the flood discharge is conveyed from the reservoir to the downstream river reach through an open channel, placed either along a dam abutment or through a reservoir bank saddle, which might be called as chute-, open-channel-, or trough-type spillway. These designations can apply regardless of the control device used to regulate the flow. Thus, a spillway having a chute-type discharge channel, either controlled by an overflow crest, gated orifice, side-channel crest, or by some other control devices, might still be called as chute spillway. However, the name is most often employed when the spillway control is placed normal or nearly normal to the axis of an open channel, and where the streamlines of flow both above and below the control crest follow in the direction of the channel axis.

Factors in favor of the selection of chute spillways are the simplicity in their design and construction, their adaptability to almost any foundation condition, and their overall economy often attributable to the use of large amounts of spillway excavation in the embankment rockfill. Chute spillways have been constructed successfully on all types of foundation materials, ranging from hard rock to soft clay.

A chute spillway normally consists of an entrance (approaching) channel, a control structure, a discharge channel, a terminal structure, and an outlet channel (tail race channel) (Fig. 12.2).

Fig. 12.2

Layout of the chute spillway in an embankment dam project. 1 entrance channel; 2 control structure; 3 discharge channel (chute, trough); 4 terminal structure; 5 outlet channel; 6 emergency spillway; 7 embankment dam

The configuration of a chute spillway is usually dictated by the site topography and by the subsurface foundation conditions. The simplest form of chute spillway has a straight centerline and is of uniform width. Often, either the axis of entrance channel or that of discharge channel must be curved to fit the alignment entailed by the topography. Under such circumstances, the curvature segment is confined to the entrance channel with low approach velocities, if possible. Where the discharge channel must be curved, its floor is sometimes superelevated to guide the high-velocity flow around the bend, thus avoiding a piling up of flow toward the concave side of chute.

The control structure is generally placed in line with or upstream of the dam axis. Normally, the upper portion of the discharge channel is carried at minimum grade until it “daylights” along the downstream hillside to minimize excavation. The steep portion of the discharge channel then follows the slope along the abutment.

12.2.1 Entrance (Access or Approach) Channels

An entrance channel serves to draw water from the reservoir and convey it to the control structure. Where a spillway draws water immediately from the reservoir and diverts it directly back into river, as in the case with an overflow spillway on a concrete dam, entrance and outlet channels are not needed. However, in the case where the shore spillway is placed through abutment, saddle, or ridge, the entrance channel leading to the spillway control structure and away from the spillway terminal structure may be required. Where the entrance faces the reservoir directly or contacts with dam, a guide wall should be installed at the side of dam in a planar shape of morning-glory mouth, to avoid transverse current or vortex flow (Fig. 12.3).

Fig. 12.3

Entrance channels to open-channel spillways

Entrance velocity is generally v ≤ 4 m/s and head drop is smaller than 0.8 m, which should be greater than the non-deposit velocity of suspension load but smaller than scouring velocity. The channel curvatures and transitions should be made gradual. All these requirements are for the purposes to minimize head loss through the entrance channel and to obtain uniformity of flow passing the spillway crest. Effects of an uneven distribution of flow in the entrance channel might persist through the whole spillway structure to an extent that undesirable erosion could take place in the downstream river channel. Non-uniformity of head on the crest may also lead to a reduction in the discharge capacity. The longer of the channel, the larger of the head loss will be. Where the spillway is excavated in a steep mountain, larger velocity might be preferable to considerably reduce the excavation amount, such as the shore spillway in the Bikou Project (Fig. 9.3), whose velocity in entrance channel is 5.58 m/s for releasing design flood.

The approach velocity and the water depth below crest level have important influence on the discharge capacity through the overflow crest. The minimum depth below the crest level is 0.5H _d (H _d  = design head of weir shape). For a given head over the crest, a greater approach depth with the accompanying reduction in approach velocity will result in a larger discharge coefficient. Thus, a deeper approach depth will permit a shorter crest length for a given discharge. Therefore, a small reverse gradient for the channel bottom floor may be employed.

Within the limits demanded to secure satisfactory flow conditions and non-scouring velocities, the determination of the relationship of entrance channel depth to channel width is a matter of economics. The glory mouth transition section is usually installed to connect the entrance channel and control weir (Fig. 12.3), the length of guide wall along the flow direction should be greater than 2 times of the depth in front of crest, and the elevation of wall should be higher than the maximum reservoir level. The bottom of transition section should be lined using concrete of 0.2–0.3 m thick. The necessity of lining for the bottom and slope of entrance channel is dependent on the safety consideration with respect to stability, scouring resistance, and weathering resistance. The entrance channel is better to be layout in straight on plane to obtain good flow pattern. If bending is inevitable, the curvature radius should be larger than 4–6 times of the channel width in bottom.

Trapezoidal cross section is commonly adopted for entrance channel with a slope of 1:0–1:0.3 for fresh rock, 1:0.5–1:1.0 for weathered rock, and 1:1.5–1:3.0 for soil.

The water surface in the entrance channel may be solved using segmentation seeking algorithm by establish energy equation from the starting of the entrance channel until the section in front of crest at a distance 3–5 times of the head over crest.

Where restrained by the conditions of topography and geology, long entrance channel is inevitable (Fig. 12.1). Under such circumstances, the head loss in the channel should be taken into account in the computation of discharge capacity.

12.2.2 Control Structures

Consisting of weir, gates, piers, operative, and access bridges, etc., a control structure regulates and controls the outflows from the reservoir, which is a major component of the spillway. The control structure should be as close to the reservoir as possible to reduce head loss and should be built on competent foundation to bear large loads. The elevation of weir crest has very tight relation with the engineering amount; therefore, it should be determined by comprehensive studies taking into account of factors such as topographic condition in addition to rational specific flow discharge (Abecasis 1970). Usually, deep excavation leads to high and short weir, while shallow excavation gives rise to low and long weir.

Water should be prevented from seeping and leaking through the foundation in the spillway area. Generally, watertightness is provided by extending the grouting curtain of the dam adjacent to the spillway. Where the foundation rock under weir cannot be grouted, watertightness may be achieved by impervious blanketing.

• 1. Broad crested weir

With flat top and very small height, broad crested weir (Fig. 12.4a) has advantages of simplicity in structure and convenience in construction, but disadvantageous in lower discharge coefficient (approximately $m = 0.32 {-} 0.385$). It is suitable for low-headwater projects with a small crosshead (head difference of head- and tailwaters), or with soil foundation of low bearing capacity.

Fig. 12.4

Weirs of control structure. a Broad crested weir; b practical weir

• 2. Practical weir

Practical weir in a shape of ogee (e.g., WES) (Fig. 12.4b) may provide larger discharge coefficient than that of broad crested weir, which is advantageous in shortening the weir length, as a result the engineering expenditure could be saved and the layout of project may be facilitated. However, the construction of practical weir is more complicated. For large to medium projects, particularly where the bank slopes are steep, the practical weir is widely employed.

The most prevalent type of practical weir in the shape of ogee has a crest approximating the profile of the under nappe of a jet flowing over a sharp crested weir and provides the ideal form for obtaining optimum discharges. The design of ogee weir has been discussed in the Chap. 7 of this book. However, there are two main particularities in the ogee weir design for shore spillways:

• Since the ogee weir in spillways is often a low weir with high tailwater depth at downstream adjoined chute, large negative pressure and cavitation as well as vibration are unlikely occurred on the surface of weir; therefore, the smaller design head $H_{d}$ than that of high-gravity dams is preferable to obtain higher discharge coefficient, e.g., $H_{d}$ may be (0.65–0.85) times of the maximum head above the weir;

• The radius of bucket is larger than that of high dams, for the purpose of more smooth flow transition from weir to chute.

In the design of ogee weir for shore spillways, high attention should be called at that up- and downstream weir heights P ₁ and P ₂ (Fig. 12.4b) have great influence on the discharge coefficient. The definition of high and low weirs is based on the facts that:

• For sharp crested weirs with heights not lower than about one-fifth of the head, the coefficient of discharge remains fairly constant;

• For sharp crested weirs with heights lower than about one-fifth of the head, the contraction of the flow becomes increasingly suppressed, the velocity of approach is not negligible, and the discharge coefficient decreases significantly;

• When the weir height becomes zero, the contraction is entirely suppressed and the overflow weir becomes actually a channel or a broad crested weir.

With a relative height $P_{1} /H_{d} > 3$, the WES weir belongs to high weir placed in a channel, the velocity of approach is small and the under side of nappe flowing over the weir attains maximum vertical contraction. As a result, the discharge coefficient is nearly a constant. Nevertheless, many weirs on spillways are low weir entailed as $0.3 \le P_{1} /H_{d} \le 1$, whose discharge coefficient may be checked by Table 12.1.

Table 12.1 Variation of discharge coefficient $m$ versus $P_{1} /H_{d}$ for WES weirs

When the water depth downstream a WES weir is high enough to affect the discharge, the weir is said to be submerged. The altitude difference $P_{2}$ from the weir crest to the downstream apron and the depth of flow in the downstream channel, as they are related to the headwater level, are major factors altering the coefficient of discharge. Generally, five distinct flow types can occur below an overflow weir crest, depending on the relative positions of the apron and the downstream water surface:

• Flow will continue as supercritical flow;

• A partial or incomplete hydraulic jump will occur immediately downstream from the crest;

• A true hydraulic jump will occur;

• A drowned (submerged) jump will occur; and

• The jet will break away from the face of the overflow and ride along the surface for a short distance, and then, it erratically intermingles with the slow moving water underneath.

Where the downstream flow is of supercritical or where the hydraulic jump takes place, the reduction in the coefficient of discharge is due principally to the backpressure effect from the downstream apron and is independent on the submergence effect attributable to tailwater.

Based on the above considerations, $P_{1} > 0.3H_{d}$ and $P_{2} > 0.5H_{\hbox{max} }$ are both desirable for the low WES weir. In medium to small spillways, $P_{1} \ge (0.5{-}0.8)H_{d}$ and $P_{2} \ge (0.6{-}0.7)H_{\hbox{max} }$ may be demanded, where $H_{\hbox{max} }$ is the maximum head above the weir crest.

The low WES crest is continued tangent along a slope with a sufficient length; otherwise, the discharge coefficient $m$ will be reduced with the mechanism similar to the downstream water depth submergence. According to the data from physical model tests, the minimum slope where the crest tangent the straight line is 1:1.4. Therefore, a direct tangent linkage of the crest to the chute is very often impossible. Instead, a bucket tangentially connecting the chute to the straight weir slope steeper than or equal to 1:1.4 is ordinarily employed (Fig. 12.5).

Fig. 12.5

Connection of chute and low WES crest through a bucket. 1 curvilinear length of low WES crest; 2 rest portion of normal WES crest; 3 tangent points

• 3. Hump weir

Configured in a shape of multi-circular (Fig. 12.6), hump weir is a kind of low weirs developed in China with discharge coefficient above $m = 0.42.$ However, there is insofar no modular profile and the hydraulic experiments are indispensable to obtain discharge coefficient corresponding to a specific design. Table 12.2 lists the parameters of two typical hump weir profiles.

Fig. 12.6

Profile of a typical hump weir

Fig. 12.7

Longitudinal profile of the spillway (unit: m)—the Yuecheng Project (China, H = 55.5 m)

Table 12.2 Parameters of typical hump weir profiles

Hump weir has advantages of facilitation in construction, high discharge coefficient, and adaptability to weak foundation. The spillway in the Yuecheng Project (China) (Fig. 12.7) is one of the first batch using hump weir, the laboratory experiment showed that the discharge coefficient is around $m = 0.46.$ The prototype investigation carried out in 1971 showed that $m = 0.47$ when $H = 5.30\,{\text{m,}}$ and $m = 0.458$ when $H = 5.57\,{\text{m}} .$

• 4. Gate-controlled ogee crests

Water releasing from ogee crest with parapet, or from partial gate opening of gated crest, will exhibit orifice flow. If the ogee profile drops below the trajectory jet, gate operated with small opening under high-head manifests negative pressure along the crest in the region immediately below the gate. Experimental data show that for the ogee shaped to the ideal nappe profile with respect to maximum head $H_{\hbox{max} }$, such subatmospheric pressures would be equal to around one-fifth of the design head. Consequently, if subatmospheric pressures are to be avoided along the ogee crest, the profile downstream the gate sill must conform to the trajectory jet issuing from an orifice (Fig. 7.30). For a vertical orifice, the path of the jet can be expressed by Eq. (7.32).

However, the adoption of a trajectory jet rather than a nappe in the weir design will lead to a fatter ogee profile and reduced discharge efficiency under full gate opening. Where the discharge efficiency is not prime important and where a fat ogee shape is demanded for structural stability, the trajectory jet profile may be ideal for avoiding subatmospheric pressure. Otherwise, by placing the gate sill, a bit of lower at the downstream side of the crest apex, a slimmer orifice profile may be obtained which is inclined downstream for small gate opening and thus will produce a steeper trajectory jet more closely conforming to the nappe-shaped profile.

12.2.3 Chutes

The chute is that portion of the spillway which connects the weir to the terminal structure. Chutes installed in conjunction with embankment dams often must have a slope slightly steeper than critical. With critical velocity occurring, flows in the chute are ordinarily maintained at supercritical state over the weir, either at constant or accelerating rates, until the terminal structure is arrived.

• 1. Layout of chute

Figure 12.2 shows a conventional layout of chute, i.e., weir → convergence → chute → divergence. The purpose of convergence is to save the excavation and lining amount of chute, and the purpose of divergence is to reduce unit discharge for the energy dissipation and scouring protection of downstream river channel.

When the Froude number $F_{r}$ in chute is larger than 2, aeration and fluctuation start to manifest; when the average velocity reaches 15 m/s, cavitation and erosion are easy to take place; when the chute turns in plan, the high velocity will give rise to shock waves (ICOLD 1992). To obtain good hydraulic performance, abrupt vertical changes, sharp convex or concave curves in the vertical chute profile, should be avoided. Similarly, the convergence or divergence in plan should be gradual in order to avoid cross-waves, “ride-up” on the walls, excessive turbulence, or uneven distribution of flow at the terminal structure.

To avoid hydraulic jump, the discharged flow must remain in the supercritical state throughout the length of the chute. The flow in the chute may be uniform, accelerated, or decelerated, depending on the slopes and dimensions of the chute and on the total head drop. Where it is desired to minimize the slope to reduce excavation at the upstream portion of a chute, the flow might be uniform or decelerating in this portion, followed by accelerating flow in the steep drop leading to the downstream river channel. Flow along the chute will depend upon the specific energy available at the point concerned. This energy will be equal to the total drop from the reservoir water level to the floor of the chute at the point under consideration, subtracted by the intervening head losses (Bernoulli’s theorem concerning the conservation of energy). The velocities and depths of flow along the chute can be fixed by selecting its grade and the cross-sectional dimensions. The grade for chute ordinarily used is i ⁰ = 1–5 % but sometimes may be 10–30 %; in practices, the steepest slope even may be reached up to 1:1 for the chute on high-quality rock.

The longitudinal profile of a chute in the form of open channel is usually so selected to conform to the site conditions related to topography and geology. It is generally configured as straight segments joined by transition curves. Sharp convex and concave curves should be avoided to prevent adverse flows in the channel. Where it is inevitable, convex curves should be flat enough with regard to the trajectory of a free-discharging jet as it enters the curve, to maintain positive pressures and thus avoid the tendency for separation and spring away of the flow from the floor. Concave curves should have a sufficient radius of curvature to minimize the dynamic actions on the floor brought about by the centrifugal force attributable to the change in the direction of flow. The pressure will drive the water penetrating into and under the lined floor to build up high uplift if the drain condition does not work well, which may result in the damage to floor lining. The conventionally used radius may be selected among $5 < R/h < 10.$

The spillway chute of the Liujiaxia Project (China) is composed of six segments of different grades. In 1969, the accumulated flood releasing time was 324 h during flood season, the maximum discharge and velocity were 2350 m³/s and 30 m/s, respectively. The examination after the flood season revealed three serious damage portions in the chute, which all happened at the concave portions: The lining was flushed away, and the deepest scouring pit was 13 m.

Fig. 12.8

Spillway layout—the Yunlong Project (China, H = 77 m). a Plan. b longitudinal profile

Convex and concave transition curves in the longitudinal profile should be avoided where the chute varies in plan. Sometimes, restricted by the conditions of topography, geology and layout requirements, longitudinal convex and concave curves and planar bending may not be avoided to be configured simultaneously, such as the spillway of the Yunlong Project (Yunnan, China) shown in Fig. 12.8. In this case, comprehensive studies should be carried out to mitigate the detrimental hydraulic phenomena for the safety of the project.

The type of cross section of chute (open channel or trough) is dependent on the geologic conditions and lining. For the trough excavated in bedrock and with lining, rectangular or steep trapezoidal cross section is commonly adopted (1:0.1–1:0.3); for the trough excavated in soil, flat trapezoidal cross section is commonly employed (1:1–1:2).

The height of side walls should be sufficient to retain the water, which is estimated by adding freeboard to the aerated and fluctuated water depth, the former is normally 0.5–1.5 m according to the SL253-2000 “Design code for spillway”.

The water surface in the chute may be solved using segmentation seeking method by establishing energy equation as follows:

$$\Delta l_{1 - 2} = \frac{{\left( {h_{2} \cos \theta + \frac{{\alpha_{2} v_{2}^{2} }}{2g}} \right) - \left( {h_{1} \cos \theta + \frac{{\alpha_{1} v_{1}^{2} }}{2g}} \right)}}{{i - \overline{J} }}$$

(12.1)

$$\overline{J} = \frac{{n^{2} \overline{v}^{2} }}{{\overline{R}^{4/3} }}$$

(12.2)

where $\Delta l_{1 - 2}$ = length of the segment, m; $h_{1} ,h_{2}$ = depth at the starting and ending of the segment, m; $v_{1} ,v_{2}$ = average velocity at the starting and ending of the segment, m/s; $\alpha_{1} ,\alpha_{2}$ = non-uniform velocity distribution coefficient at the starting and ending of the segment (usually 1.05); $\theta$ = inclining angle of the trough bottom, (°); $i$ = grade of the trough bottom; $\overline{J}$ = average hydraulic gradient in the segment; $n$ = roughness coefficient of the trough selected according to design code; $\overline{v} = (v_{1} + v_{2} )/2$ = average velocity, m/s; $\overline{R} = (R_{1} + R_{2} )/2$ = average hydraulic radius of the segment, m.

• 2. Design of convergence and divergence

The best hydraulic performance in a discharge chute is obtained by uniform flow. However, economy may dictate a chute section narrower or wider than either the crest or the terminal structure, thus requiring converging or diverging transitions in plan to fit the various components together.

The paramount phenomenon attributable to transitions and to be aware of is shock waves (cross-waves) of positive and/or negative. On the outer side of an angular bend, a positive shock wave (piling up) will take place leading to a rise of the water surface. The wave is stationary and across to the inside of the chute, continues to reflect back and forth repeatedly. Where the flow passes the inner side of an angular bend, a separation will take place which results in negative shock wave (drop in the water surface). This stationary negative shock wave will cross to the outside of the chute. Both the aforementioned positive and negative shock waves will continue to reflect off the walls, forming a very disturbed flow pattern.

• (a) Convergent transition

Laboratory and field tests help to stipulate design criteria and guidance applicable to spillway chutes with convergence, by which an optimum flow conditions will prevail in the chute.

The commonly used symmetric sidewall convergence is shown in Fig. 12.9. It must be made gradual to avoid cross-waves, “ride ups” on the walls, and uneven distribution of flow across the chute trough. The maximum height of cross-wave is dependent on the deflection angle $\theta$ but has no relation with the curvature radii of the sidewalls. Since the deflection angle $\theta_{1}$ of a curved side wall is always larger than that $\theta_{2}$ of a straight side wall, straight side walls for convergence transition section are customarily employed subject to local round off.

Fig. 12.9

Convergent transitions and cross-waves. a Curved; b straight

• (b) Divergent transition

When site or economic conditions indicate that a short crest length and a widened terminal structure are desirable, diverging chute walls may be employed. Similarly, the rate of divergence of the sidewalls must be limited or else the flow will not spread to occupy the entire width of the chute uniformly, which will lead to undesirable flow conditions in the terminal structure.

Experiments have shown that an angular deflection $\theta$ of the flow boundaries with respect to the trough centerline not exceeding that entailed by Eq. (12.3) will provide an acceptable transition for a divergent chute.

$$tg\theta \le \frac{1}{{KF_{r} }}$$

(12.3)

where $F_{r}$ = Froude number at the initiation or end of the divergence; $K$ = 1.5–3.0, revision coefficient (inferior bound for horizontal trough bottom, whereas upper bound for steeply inclined trough bottom).

In divergent transition, $F_{r}$ varies along the flow; therefore, the angle $\theta$ theoretically varies according to Eq. (12.3). In practice, however, a uniform $\theta$ smaller than 6°–8° is commonly adopted for simplicity.

• 3. Design of curved transition

Curved transition may be desirable in case with limitation of topographic and geologic conditions, which should be located at the portion of lower velocity. To eliminate or to reduce the interference of shock waves, the requirements for curved transition are explained hereinafter.

• (a) Curvature radii

Usually 6–10 times of the width of rectangular trough is adopted as the curvature radii of transition.

• (b) Complex curve

Using of transition curve segments at the two ends of circular transition.

• (c) Over height of trough bottom

Influenced by the centrifugal force, the flow pattern in a curved transition is complex: The water will be piled up at outside and dropped down inside, which in turn, results in non-uniform distribution of velocity in the transition (Fig. 12.10a). Over height $\Delta Z$ of trough bottom at outside may create a transverse slope as shown in Fig. 12.10b, to counter balance the centrifugal force. However, such an over height of trough bottom may only be applied to the trough with rectangular cross section.

Fig. 12.10

Curved transitions of trough. a No measures; b over height of trough bottom at outside only; c over height of trough bottom at both sides; d sloping sill

$\Delta Z$ may be estimated using the formula of centrifugal force as follows:

$$\Delta Z = C\frac{{v^{2} b}}{{gr_{c} }}$$

(12.4)

where $v$ = average velocity at the starting section of curved transition, m/s; $b$ = surface width of water in trough, m; g = gravity acceleration, m/s²; $r_{c}$ = curvature radius of the axis of transition curve, m; $C$ = coefficient depending on the Froude number, geometry of the cross section and transition curve (rectangular cross section and simple circular transition: $C$ = 2.0 for supercritical flow, $C$ = 1.0 for subcritical flow).

Customarily, to facilitate the construction by keeping the elevation of chute axis unchanged, the inside of chute is brought down by $0.5\Delta Z$ and the outside is raised up by $0.5\Delta Z$, with respect to the axis, as shown in Fig. 12.10c.

It also should be emphasized that the over height of trough bottom should be varied gradually, as the spillway in the Bikou Project (China) shown in Fig. 12.11.

Fig. 12.11

Trough with over height bottom of the spillway (unit: m)—the Bikou Project (China, H = 80 m)

• (d) Guide plate

The whole transition is divided into narrower subsections by circular guide plates of overlapped center, within which the water surface piling up and flow fluctuation is reduced.

• (e) Sloping sill

This is customarily employed as a remedy measure for the constructed spillways, as shown in Fig. 12.10d.

• 4. Prevention of cavitation-induced damage to concrete trough

The damage potentiality resulted from cavitation is dependent upon the boundary configuration, the damage resistance of the concrete, the flow velocity and depth, the elevation of the structure above mean sea level, and the time duration of cavitation actions. Cavitation damage or erosion to the trough could happen where the pressure is lower or irregularity is too large, which might be derived from inaccurate construction setting-out and frame distortion, poor concrete quality, abrasion by sand to the flow boundary, and even the outcrops of reinforcing steel bar (Vide Chap. 4). The commonly encountered unevenness of concrete surfaces are illustrated in Fig. 12.12, and the corresponding cavitation and damage zones are shown in Fig. 12.13.

Fig. 12.12

Commonly encountered unevenness on concrete surface

Fig. 12.13

Flow states and cavitation damage zones on uneven surfaces

Damage to concrete surfaces can take place at velocities significantly lower than 25 m/s provided the adverse combination of cavitation parameters exists. As a rule of thumb, cavitation should be investigated whenever flow velocities are in excess of 9 m/s. The spillway tunnel in the Liujiaxia Project (China) is converted from the diversion tunnel by reuse it as the downstream leg conduit. In 1972, it was operated for flood releasing with a duration of about 315 h. The crosshead of the reservoir water level and the elevation on elbow part was 104.64 m with corresponding velocity about 40 m/s and discharge of 260–287 m³/s. Serious damages were found on the elbow part and adjacent downstream floor. There were three main damaged zones: two scouring pits were found in the first zone with depth of 0.3–0.5 m; a larger scouring pit with depth of 3.5 m was found in the second zone; the third zone was damaged very serious—a 190-m-long floor of concrete line was nearly all washed away. The construction irregularity was mainly blamed for these damages.

Cavitation-induced damage can be prevented by a number of methods, such as by increasing the cavitation index to ensure $\sigma > \sigma_{i}$, by providing a smoother boundary configuration, by improving the damage resistance of the boundary materials. A relatively new and very effective method is to disperse a quantity of air along the flow boundary. This is achieved by passing the water over aeration devices (e.g., aeration slot) specially designed to entrain air along the boundary (DeFazio and Wei 1983; ICOLD 1992), which may be particularly demanded when flow velocity is higher than 20 m/s and must be installed when velocity is over 35 m/s. An air duct or slot is the most prevalent form on steep chute or tunnel and easy to trap air, whose variants are

• Deflector ramp (Fig. 12.14a);

  Fig. 12.14

  

  Artificial aeration devices. a Deflector ramp; b slot; c sill

• Slot (Fig. 12.14b);

• Sill (Fig. 12.14c).

The configuration and location of aeration slot must be tailor-designed for the specific application. Until further experiences, data, and design guidelines, are significantly accumulated and developed, physical experimental studies for aeration slot design are strongly recommended insofar.

• 5. Lining structure of trough

When a spillway is working, the trough floor is subjected to the hydrostatic forces due to the weight of the water in the chute, to the boundary drag forces due to the frictional resistance along the surface, to the dynamic forces due to the flow impingement, and to the uplift forces due to the leakage through joints or cracks. When there are no spills, the trough floor is subject to the actions including thermal expansion and contraction, freezing/thawing, weathering and chemical deterioration, settlement and buckling, as well as uplift pressures brought about by under seepage or high groundwater table.

Purposes for lining chutes are to create a reasonable watertight surface over the channel to protect the trough structure from abrasion, erosion, and weathering (Bauer and Beck 1969). Whether, or not, the spillway has to be lined is one of the first questions in the design related to geologic conditions and velocity of the spillway discharge. For example, earths and soft sedimentary rocks that may be easily eroded need to be lined unquestionably. However, the decision on the need for lining is more difficult in hard sedimentary rocks and in crystalline rocks where rock structures are the important consideration. If the rock exhibits laminate structures with unfavorable trends (e.g., volcanic flow or thinly bedded sandstone), it will be susceptible to eroding by the rush of water. Scouring also can manifest in closely jointed or fractured rock where the rock blocks are small. Massive, hard crystalline rock generally does not have to be lined, but, unfortunately, this kind of rock is seldom encountered in the spillway construction.

Since it is not always possible to exactly evaluate the various forces which might occur nor to make the lining heavy enough to resist them, the thickness of the lining is most often established on the conditions of specific work site with regard to flow and construction. Based on which type of lining is selected, countermeasures such as under drains, anchors, cutoffs are utilized to stabilize the floor.

• (a) Lining on rock foundation

When a spillway trough is excavated in rock, the lining may be accomplished by concrete cast, cement–rubble masonry, or lime mortar–rubble masonry, etc., if necessary.

Lime mortar–rubble masonry lining may be applicable to the spillways in small reservoirs with flow velocity below 10 m/s.

Cement–rubble masonry lining may be employed for the spillways in small to medium reservoirs with flow velocity below 15 m/s. If the smoothness and joint seals as well as the under drains may be secured, the higher velocity up to 20 m/s may be allowable, such as the spillway of the Shibi Reservoir (China, H = 48.19 m). The thickness of cement–rubble masonry lining is generally 0.3–0.6 m. Composite lining with dry rubble masonry at bottom and cement–rubble masonry or concrete paving on surface also may be employed.

For medium to large projects, cast-in-place concrete lining around 0.3 m in thickness is customarily necessitated. The transverse and longitudinal joints are installed for thermal cracking control. The planar joint is conventionally used (Fig. 12.15a), whereas semi-overlapped (Fig. 12.15c), overlapped (Fig. 12.15d), or keyed joints (Fig. 12.15b) might be adopted where significant differential settlement is anticipated. Contraction joints are generally spaced 10–15 m apart in both the floor and walls, depending on the lining thickness and temperature variation. Reinforcement must be provided in both the transverse and longitudinal directions, with reinforcement ratio of 0.2 % in bidirections. These steel bars should not penetrate the contraction joints. Transverse joints over which flow velocities are high are arranged by lowering the upstream edge of downstream lower slab a certain depth, to prevent it from the building up of dynamic head beneath lining through the joints (Fig. 12.15c, d). Metal or rubber water stops are installed to seal the joints and to prevent high-pressured exterior water from penetrating into the foundation.

Fig. 12.15

Types of slab joints. a Planar; b keyed; c, d overlapped

A grid work of under drains laid beneath transverse and longitudinal joints is demanded, by which seeping water is gathered into longitudinal drains and delivered into downstream. The longitudinal drains is usually formed by excavating ditches, in which earthenware pipes of 0.1–0.2 m in diameter depending on the seepage discharge are installed. Gravel envelope is used to cover the pipes; on the top of gravel envelope, it is covered by concrete plate or bituminous felt, to prevent the block from cementing during the lining placement. Where the seepage discharge is small, the ditch may be filled only by gravels which is covered by concrete plate or bituminous felt. Transverse drains are also formed by excavated ditches on rock foundation whose size is ordinarily 0.3 m × 0.3 m depending on the seepage discharge. To be on the safe side, at least two rows of longitudinal drains should be installed.

Lining pavement also may be employed for side walls if the rock quality is competent. To facilitate the construction, the thickness of side wall lining is not smaller than 0.3 m, which should be back tied to the rock by bolts. The transverse joints of side walls are identical to that of floor lining slab, and a longitudinal joint is installed between the side wall and the floor. Where the rock is weak, the gravity-type retaining wall may be adopted. Drains also should be installed behind side walls, which link with the transverse drains under the floor lining slab. To ensure the draining, air vent is installed on the top of the side wall drain, which is located at near the top of the wall and above the maximum water surface. Berms should be installed on the top of the side wall to provide access pathway.

Fractured and weathered rocks should be cleared. In case with large uplift and pressure fluctuation from flow, anchorage using rock bolts may raise the effective weight of the slab against the displacement by a certain volume of foundation rock to which the bolts are tied. Depth and spacing of bolts depend on the nature of the bedrock such as stratification, jointing, and weathering. Conventionally, 1 cm² in cross-sectional area of bolt would be expected for 1 m² of slab, the diameter d and spacing are usually 25 mm or more and 1.5–3.0 m, respectively, the bolting depth into bedrock is 40–60d.

• (b) Floor paving on earth foundation

Figure 12.16 shows typical structures of floor paving on earth foundation. When a spillway chute channel is excavated through earth, the paving slab might be cast directly on the excavated surface. An intervening pervious blanket of approximately 30 cm thick may be laid, depending on the nature of the foundation soil as related to its permeability, susceptibility to the damage due to freezing/thawing action, and heterogeneity as it may give rise to differential settlement. A thicker slab of at least 0.3–0.5 m should be provided, to forestall slab from moving, cracking or buckling due to expansion and contraction.

Fig. 12.16

Typical structures of floor paving on earth foundation. a Transverse joint; b longitudinal joint. 1 water stop; 2 draining pipe; 3 mortar pad; 4 cutoff wall; 5 pervious blanket; 6 longitudinal draining pipe; 7 transverse draining pipe

For a better bonding of the floor slab to the foundation, it is advisable to install reinforced concrete cutoff wall at the upstream end of each slab. Bulb anchors are sometimes employed for very important project.

Attributable to the fact that the slab is not strongly restrained by the foundation, the spacing of thermal contraction joints of the slab on earth foundation may be larger than 15 m. However, a reinforcement ratio 0.2 % in bidirections is still demanded to prevent thermal cracking.

A pervious gravel blanket is often provided between the slab and the foundation where the foundation soil is sufficiently impervious. The blanket serves not only as a free-draining layer but also aids to insulate the foundation from freezing/thawing action. The thickness of the blanket thus depends on the climate at the site and on the susceptibility of the foundation to FT heaving. A grid work of under drains is provided as a collecting system for seeping water. It is laid with open joints within gravel and embedded on a mortar pad to prevent the foundation material from being leached into draining pipes. The network of draining pipes links one or more trunk drains which carry the seepage flows to the outlets through the floor or side walls. For gravel pervious foundation, only network draining system is necessary. Filter should be installed around draining pipes.

12.2.4 Terminal Structures and Outlet Channels

When released outflow falls from reservoir pool level to downstream river level, the static head is converted into kinetic energy. The energy manifests itself in the form of high velocities which, if impeded, give rise to large pressure. Terminal structure provides means of returning the flow to the river without serious scouring to the dam toe or damage to the adjacent structures. The design principles of terminal structures with energy dissipation are similar to that of overflow gravity dams (Vide Chap. 7).

In case with good bedrock, the upturned deflectors, cantilevered extensions, or flip buckets can be employed to deliver high-velocity flow directly to the main river stream where the energy is absorbed along the streambed by impact, turbulence, and friction. Often, scouring in the streambed at the plunge point can be minimized by fanning the jet horizontally by the use of a flaring deflector or vertically by slit bucket into a thin sheet. The stability and strength of the flip bucket should be calibrated taking into account of its self-weight, the weight of water in bucket, the centrifugal force of flow, the fluctuation pressure, and uplift. In such arrangements, an adequate cutoff or other protection must be installed at the end of the bucket to prevent it from being undermined retrogressively (Fig. 12.17). The depth of the cutoff wall is ordinarily 5–8 m which depending on the depth, distance, and shape of the scouring pit. Rock bolts are commonly employed to back tie the bucket with the bedrock. To prevent scouring near the bucket at lower flow discharge, a short bottom lining of riprap or concrete is usually installed downstream the flip bucket. The measures such as air vent or expansion excavation of outlet channel are demanded to forestall the vacuum under the jet nappe, to ensure the jet impingement distance (Fig. 12.17c).

Fig. 12.17

Types and structures of flip bucket. a Gravity type; b reinforced thin lining type; c draining and air vent. 1 face slab; 2 cutoff wall; 3 concrete apron; 4 steel bar; 5 air vent; 6 drainage hole (Φ15); 7 rock bolt

Where serious streambed scouring is anticipated to endanger the dam or other important appurtenance structures, the alternatives of energy dissipation devices such as stilling basin and roller bucket should be taken into account (Bradley and Peterka 1957a, b).

Outlet channel conveys the flow from the terminal structure to the river stream. In some instance, only a pilot channel is provided, on the assumption that scouring action will enlarge the channel during major flood releasing. However, where the channel is in a relatively non-erodible material, it should be excavated to an adequate size to pass the anticipated flow without affecting the tailwater.

Although energy dissipation devices are provided, yet it might be impossible to reduce the outflow velocity below the natural velocity in the original stream, and certain scouring of the riverbed, therefore, cannot be avoided.

Under natural conditions, the beds of many streams are scoured during the rise stage of a flood and silted during the falling stage by the deposition of material carried in the flow. After the creation of a reservoir, the spillway will normally release clear water, and the materials scoured by the clear current of high velocity will not be replaced by deposition. Consequently, there will be a gradual retrogression of the downstream riverbed, which will bring down the tailwater level. On the contrary where only a pilot channel is installed, scouring may build up islands downstream, thereby effecting a degradation of the downstream river channel which will raise the tailwater level. The outlet channel dimensions and its need for protection by lining or riprap should be decided by all these considerations.

12.3 Spillways of Other Types

12.3.1 Side-Channel Spillways

Where a long overflow crest is desired in order to limit the surcharge head, and the abutment are steep and precipitous, or where the control structure must be connected to a narrow discharge channel or tunnel, side-channel spillway (Fig. 12.18) is often a good choice. Flow from the side channel can be directed into an open discharge channel (chute) or into a closed conduit or inclined tunnel.

Fig. 12.18

An embankment project with side-channel spillway

The design of side-channel spillway is concerned particularly with the hydraulic action in the upstream reach of the discharge channel and is more or less independent of the details selected for the other spillway components (Farney and Markus 1962; Hinds 1926).

• 1. Layout and work conditions of side-channel spillways

Side-channel spillway possesses control weir placed alongside and approximately parallel to the upper portion of the discharge channel. Flow into the side channel might enter on only one side of the trough in the case of a steep hillside location, or on both sides and over the end of the trough if it is located on a knoll or gently sloping abutment (Fig. 12.19).

Fig. 12.19

Intake types of side-channel spillway. a Standard; b T-type; c Y-type; d contour-type; e, f labyrinth-type; g L-type; h circular type. 1 weir crest; 2 intake tower; 3 management bridge; 4 partition wall; 5 side channel

Although side-channel spillways are generally ungated, there is no reason why gates cannot be installed.

Modifications to the conventional side-channel spillway include the addition of a short crest length perpendicular to the channel at the upstream end forming an L-shaped crest as illustrated in Fig. 12.19g. The labyrinth spillway (Darvas 1971; Hay and Taylor 1970) is also may be looked at as a modification of side-channel spillway characterized by a broken axis of crest in plan in order to create a greater crest length compared to a conventional spillway crest occupying the same lateral space (Fig. 12.19e, f). The broken axis forms a series of interconnected V-shaped weirs. Each of the V-shapes is termed as a cycle. The labyrinth spillway is particularly well-suited for rehabilitation of existing spillways and for providing a large capacity spillway in a site with restricted width, whose hydraulic characteristics are extremely sensitive to approach flow conditions. This requires sitting the crest configuration in the direction of upstream as far as possible into the reservoir, in order to achieve approach flow nearly perpendicular to the axis. Serious consideration of this type of spillway will require verification of the design by a physical model study. The other modifications of side-channel spillways are also shown in Fig. 12.19.

Because of turbulence and vibration inherent in side-channel flow, a side-channel design is ordinarily not considered except where a competent foundation (e.g., rock) exists.

• 2. Design features of side-channel spillways

A side-channel spillway is composed of control weir, side channel, chute (trough or tunnel), terminal structure, and outlet. Preliminary design of a side-channel spillway can be accomplished with respect to discharge ability, flow pattern, and water surface. In view of the complex nature of flow, physical hydraulic modeling is normally undertaken to ensure adequate and economical details for the final design.

Discharge characteristics of a side-channel spillway are similar to those of an ordinary overflow and are dependent on the selected profile of the weir crest (Fig. 12.20). However, for maximum discharges the side-channel flow may differ from that of the proper open-channel spillway in that the flow in the trough may be restrained and the flow over the crest may be partially submerged. Under such circumstances, the flow will be controlled by the downstream trough. The constriction may be resulted from a point of critical flow in the channel, an orifice control, or a conduit or tunnel flowing full. In the design of weir crest, its position and size are selected together with the side channel.

Fig. 12.20

Overflow weir and cross section of side channel. a Plan; b longitudinal section; c transverse section

The water in side channel is spatially varied flow with strong lateral inflow whose flow pattern is restrained by both the weir and side-channel trough, which dictates the hydraulic design requirements as follows:

• ① The water level in the side-channel trough should not influence the flow discharge passing the weir, i.e., the flow is free over the weir. According to experiences $h_{s} = 0.5H_{d}$ may be used as the minimum value, in which h _s is the water depth over the weir at the starting of side-channel trough (m) (Fig. 12.21); H _d is the design head over weir corresponding to the design flow discharge Q _d , usually being equal to the maximum discharge Q _max.

  Fig. 12.21

  

  Diagram to the water surface computation of side-channel trough. a Longitudinal; b plan

• ② The assumption is made that the energy of flow over the crest is totally dissipated by turbulence as it turns and mixes with the side-channel flow and that the only force driving longitudinal motion in the side channel is attributable to the gravity. It is also assumed that the frictional resistance of the side channel is sufficiently small and may be neglected without seriously affecting the accuracy of the computations. A longitudinal grade smaller than 0.1 and usually varies between 0.01 and 0.05 is necessary for the channel floor to keep the movement of the flow along the side-channel trough.

• ③ The downstream end of side-channel trough should not be influenced by the connected open channel; therefore, it is demanded that:

  • The floor grade $i > i_{k}$, i _k is critical slope.

  • No hydraulic jump should occur in the side-channel trough. If the channel floor grade is small, i.e., the water depth all over the side-channel trough is larger than critical depth h _k , and at the end of trough $h_{l} > h_{k}$, a horizontal adjustment segment is installed between the end of the side-channel trough and the starting of open-channel chute (Fig. 12.21), whose length is l ≈ (2–3) h _k . This enables the end of adjustment segment to be a control section with critical depth.

  • Usually, divergence or bending transition is avoided near the end of side-channel trough.

  • A trapezoidal cross section is prevalent for the side-channel trough. The sectional width ratio $b_{0} /b_{l}$ may be 0.25–1.0. The slope of the trapezoid side may be selected around 1:0.5–1:0.9 on the weir side and 1:0.3–1:0.5 on the hillside, depending on the rock properties (Fig. 12.20).

  • The lateral difference of water in the side-channel trough should be limited. Usually, the raising of water level on the hillside $\Delta h$ (Fig. 12.20c) is 10–25 % of the average depth ($h$), which is subject to hydraulic model verification.

  • The crest length by the conventional computation must be corrected with regard to the loss in effective crest length caused by angularity of flow at the junction of the crest sections.

• 3. Open-channel chute, terminal structure, and outlet channel

Their design is identical to open-channel spillways.

• 4. Hydraulic computation of side-channel trough

The purpose of hydraulic computation of side-channel trough is to decide the water surface and corresponding floor elevation of side-channel through, according to the conjunction relationship among weir, side-channel trough, and open-channel chute.

The starting section for computation is usually located at the downstream end of the side-channel trough (Fig. 12.21), at which the water depth $h_{l}$ termed as “economical depth” is commonly 1.20–1.35 time of the critical depth $h_{k}$ of the starting section of the adjoining open-channel section (control section). The flow in the side-channel trough is a gradually varied flow whose surface may be computed using differential Eq. (12.5) based on the momentum principle, in which the item $\overline{J}\Delta s$ may be neglected if the flow segment is short.

$$\Delta y = \frac{{Q_{1} }}{g}\frac{{\left( {v_{1} + v_{2} } \right)}}{{\left( {Q_{1} + Q_{2} } \right)}}\left[ {\left( {v_{2} - v_{1} } \right) + \frac{{v_{2} \left( {Q_{2} - Q_{1} } \right)}}{{Q_{1} }}} \right] + \overline{J}\Delta s$$

(12.5)

where $\Delta y$ = water-level difference of up- and downstream computation sections, m; $\Delta s$ = length of the segment; $Q_{1}$ and $Q_{2}$ = the flow discharges of the up- and downstream computation sections of the segment concerned, respectively, m³/s; $v_{1}$ and $v_{2}$ = the averaged flow velocities of the up- and downstream computation sections of the segment concerned, respectively, m/s; $\overline{J}$ = averaged hydraulic gradient of the computed segment [Eq. (12.2)]; $\overline{R}$ = averaged hydraulic radius of the computed segment, m.

• 5. Design procedure for side-channel spillways

• ① According to the outflow discharge related to the design flood, topographic and geologic conditions, and construction conditions, several layout schemes are contemplated. The schemes are specified as combinations concerning the length of weir $L$, side-channel trough width $b_{0}$ and $b_{l}$, as well as the floor grade $i$.

• ② For each scheme, the critical depth h _k at the control section and the exit depth $h_{l}$ of the side-channel trough are computed, which are subject to comparison with the design criteria. Unqualified schemes are abandoned.

• ③ For the selected weir and side-channel scheme, the water surface in relation to outflow discharge is calculated.

• Where the floor slope $i$ is small, the depth in side trough is higher than critical depth. The latter may be regarded as occurring at the conjunction of the horizontal adjustment section with the open-channel chute. A rising deflector may be added to the end of the horizontal adjustment section (Fig. 12.21a). Make use of the energy equation between the end section of side trough and control section, the height d of the deflector at control section floor may be obtained:

  $$d = \left( {h_{l} + \frac{{v_{l}^{2} }}{2g}} \right) - \left[ {h_{k} + \frac{{v_{k}^{2} }}{2g} + \xi \left( {\frac{{v_{k}^{2} - v_{l}^{2} }}{2g}} \right)} \right]$$

  (12.6)

  where $h_{k} ,v_{k}$ = the critical depth and velocity at the control section, respectively; $h_{l} ,v_{l}$ = the depth and velocity at the exit end of side-channel trough, respectively; $\xi$ = 0.2, the local drag coefficient.

Height of deflector sill $d$ also may be estimated by 0.1–0.2 times of critical depth h _k at the control section.

• Use the exit end of side-channel trough as the first computation section, the water surface and corresponding depth of the side-channel trough is calculated retrogressively section by section according to Eq. (12.5). By parity of reasoning, until the whole water surface and depth are obtained.

• ④ The hydraulic design for the open-channel trough is carried out, which is identical to that of the proper open-channel chute.

12.3.2 Drop Inlet (Shaft or Morning Glory) Spillways

A drop inlet spillway, as the name implies, is one in which the water enters over a horizontally positioned lip, drops through a vertical or inclined shaft, and then flows to the downstream river stream through a horizontal or near-horizontal conduit (e.g., tunnel).

A drop inlet spillway can be used advantageously at the dam site in narrow valley where the abutments rise steeply or where a diversion tunnel/conduit is available for reuse as the downstream leg (Fig. 12.22). Another advantage of drop inlet spillway is that near maximum release capacity may be achieved at an early flood period with low surcharge heads, which makes the spillway ideal for use where the maximum outflow is rigorously limited. However, the accompanied disadvantage is that there is little increase in capacity beyond the designed surcharge heads, should a flood larger than the design flood occur. Anyway, this disadvantage may be compensated for if the spillway is used as a main service spillway in conjunction with an auxiliary or emergency spillway.

Fig. 12.22

A drop inlet spillway. 1 crest of morning glory; 2 shaft; 3 diversion tunnel; 4 concrete plug; 5 flood release tunnel; 6 outlet; 7 bending transition

• 1. Layout of drop inlet spillways

The spillway may be considered as consisting of four elements, namely diversion and anti-swirl facilities, an overflow control weir, a vertical transition, and a closed discharge channel in form of vertical or inclined shaft, which is often linked with diversion tunnel. Where the inlet is funnel-shaped, this type of structure is often termed as “morning-glory” or “glory hole” spillway.

• 2. Hydraulics and structure of drop inlet spillways

As the heads increase on a drop inlet spillway, the control will shift from the weir flow over the crest to the tube flow in the transition and then to the full pipe flow in the downstream portion. Full pipe flow design for drop inlet spillways except those with extremely low drops is not recommended.

The inflow discharge is dependent on the head over crest, type, and circular length of the morning glory. The capacity of inflow being diverted through tunnel is depending on the section size and effective head within tunnel.

There are two common profile types for the weir section: the ogee profile using parabolic curve, and the board crested profile with flat cone-shape (Fig. 12.23), of which the former is more prevalent. Gate may be installed on the crest of morning-glory entrance. Problems frequently encountered in this type of structure involve vortex action, unstable flow, and cavitation. Local topography may initiate vortex trends in the adjoining approach flow to the spillway, resulting in reduced capacity, flow instability, and surges in the shaft and tunnel. Laboratory studies indicate that the vortex over a submerged circular orifice may reduce the discharge by as much as 75 %. Piers, fins, vanes, and curtain walls may be installed to suppress vortex actions. However, physical model studies are imperative to verify their effectiveness. When the flow control shifts from the crest to the conduit and vice versa, violent surging originating in the shaft can induce severe pressure and flow pulsations throughout the structure. Deflectors and vents in the shaft have been exercised to prevent these surges and pulsations. The need for deflectors and vents and verification of their design must be established by hydraulic physical models. The likelihood of cavitation near the tangency of the curve connecting shaft to horizontal conduit should be explored.

Fig. 12.23

A drop inlet spillway with board crested weir and radial gates (unit: m)

• 3. Hydraulic design

The discharge ability of morning-glory entrance is computed by

$$Q = \varepsilon m\left( {2\pi R - n_{0} s} \right)\sqrt {2g} H^{3/2}$$

(12.7)

where $m$ = discharge coefficient ($m = 0.48$ for ogee crest, $m$ = 0.32–0.38 for broad crested weir); $\varepsilon$ = contraction coefficient (usually $\varepsilon = 0.9$); $R$ = radius of morning-glory entrance, m; $H$ = head over the crest, m; $n_{0}$ = number of piers; $s$ = width of pier, m.

Usually, $R = (2{-} 5)H$ for the ogee crest and $R = (5{-} 7)H$ for the broad crest.

Beneath the morning glory, the inflow becomes full. A transition section is necessary to compress the flow gradually into a smaller section of pressure shaft or tunnel. In the transition section, the free drop of flow increases its velocity, but keeps its pressure identical to atmospheric pressure. Pressure flow is started in the shaft section, from there until the exit of the tunnel, the diameter $d_{r}$ of the whole flow conduit and velocity is kept unchanged. The head difference $h$ is used to overcome the friction drag and local drag of this pressure conduit; therefore, the suitable diameter $d_{r}$ is selected in the design to secure a good balance between head difference $h$ and the head loss resulted from the friction drag and local drag.

• 4. Countermeasures for improving the flow pattern in drop inlet spillways

Unstable flow in the transition from the crest control to the conduit control, which would take place over an extended period of time, is blamed for unacceptable noise, rapid pressure fluctuations, and strong vibrations. To improve the flow condition, air vent is installed around the shaft whose total cross-sectional area is around (10–15) % that of shaft (Fig. 12.24). In small to medium projects, guide piers or still walls may be employed for the same purpose.

Fig. 12.24

Aerator installations for shaft spillways

Drop inlet spillways are more commonly exercised in France and Italy than the other counties. It was rarely used in China in the past time by the reason of large inlet structure of morning glory, complex flow state, tiny increase in capacity beyond the design heads, rapid pressure fluctuations, and strong vibrations under small overflow discharge. However, a new version of drop inlet spillway has been studied and placed in the Shapai Project (China, H = 132 m) successfully that consists of a short length of pressure intake, approaching tunnel, vortex chamber, vertical shaft, and original diversion tunnel. The maximum head is 88 m and maximum flow discharge is 248 m³/s.

12.3.3 Siphon Spillways

A siphon spillway is a closed conduit system in the shape of an inverted U tube and so positioned that the interior of the bending upper conduit (Fig. 12.25a) is at the normal storage level. The siphon spillway may be integrated into the dam or located at bank (Fig. 12.25b).

Fig. 12.25

Siphon spillways. 1 top cover; 2 siphon-breaker air vent; 3 deflector sill

Most siphon spillways consist of five elements including an inlet, an upper leg, a throat or control section, a lower leg, and an outlet. A siphon-breaker air vent is also provided to control the siphonic action of the spillway so that it will cease operation when the reservoir water surface is drawn down to the normal level. The inlet is generally placed below the normal reservoir water surface to prevent entrance of ice and debris. The upper leg is formed as a bending convergent transition adjoining the inlet to a vertical throat section. The throat or control section is generally rectangular in cross section and is located at the crest of the upper bend of the siphon. The upper bend then continues to join a vertical or inclined tube which forms the lower leg of the siphon. Often the lower leg is placed on an adverse slope, to provide a more positive priming action by forming a flow curtain which seals across the leg. The lower leg can be so terminated as to discharge vertically or along the face of a concrete dam, or it may be provided with a lower bend and diverging outlet tube to release the flow in a horizontal direction. The outlet flow can be free discharging or submerged, depending on the arrangement of the lower leg and on the tailwater conditions.

Due to the negative pressure prevailing in the siphon, the conduit should be sufficiently rigid to withstand the collapsing forces. Joints must be made watertight, and countermeasures must be taken to avoid cracking of the conduit.

The principal advantage of a siphon spillway is its ability to pass full-capacity discharges with narrow limits of headwater rise. A further advantage is its automatic operation without mechanical devices or moving parts.

In addition to its higher cost, as compared to other types, the siphon spillway has a number of disadvantages as follows:

• The inability of passing ice and debris;

• The possibility of clogging the siphon conduits and siphon-breaker air vents with debris or leaves;

• The possibility of water freezing in the inlet legs and air vents before the reservoir rises to the crest level of the spillway, thus preventing flow through the siphon;

• The occurrence of sudden surges and stoppages of outflow as a result of the erratic make-and-break action of the siphon, thus giving rise to radical fluctuations in the downstream river flow;

• Vibration disturbance is more pronounced than in other types of control structures.

As is the case with other types of closed conduit structures, a principal disadvantage of the siphon spillway is its inability to release flows greater than designed capacity although the reservoir head exceeds the design level. Consequently, the siphon spillway is best suited as a main service spillway in conjunction with an auxiliary or emergency spillway.

12.3.4 Baffled Apron Drop Spillways

Baffled aprons or chutes are used in spillways where it is desirable to avoid a stilling basin. The baffle piers partially obstruct the flow, dissipating energy as the water flows down the chute so that the flow velocities entering the downstream channel are relatively low. Advantages of baffled aprons are low expenditure, low terminal velocity of the flows regardless of the height of the drop, downstream degradation does not affect the spillway operation, and there are no requirements for initial tailwater depth in order for the stilling basin to be effective.

The chute is normally constructed on a slope of 2:l or more flat, extending below the outlet channel floor. Chutes with slopes steeper than 2:l should be model-tested and their structural stability should be checked. The lower end of the chute should be constructed far enough below the channel floor to prevent damage from degradation or scour.

12.3.5 Culvert Spillways

Culvert spillway is a special adaptation of the conduit or tunnel spillway. It is distinguished from the drop inlet and other conduit types in that its upstream or downstream inlet is placed either vertically or inclined, and its profile grade is made uniform or near uniform of any slope. The spillway inlet might be sharp edged or rounded, and the approach to the conduit might have flared or tapered sidewalls with a horizontal or sloping floor. If it is desired that the conduit flow partially full for all conditions of discharge, special precautions are taken to prevent the conduit from flowing full; if full flow is desired, bell mouth or streamlined inlet are provided.

Culvert spillways operating with the inlet unsubmerged will perform similarly to an open-channel spillway. Those who operate with the inlet submerged, but with the inlet orifice arranged so that full conduit flow is prevented, will perform similarly to an orifice-controlled drop inlet spillway, or to an orifice-controlled chute spillway. Where priming action is induced and the conduit flows full, the operation will be similar to that of a siphon spillway. When the culvert spillway is arranged to operate as a siphon, recognition must be taken of the disadvantages of siphon flow.

As is the case with a drop inlet or siphon spillway, a principal disadvantage of culvert spillway is that because its capacity does not substantially raised with the increase in head, it does not provide high safety margin against the emergencies due to the improper or varying hydrologic data with regard to the design flood. This disadvantage would be compensated for where the culvert type is used as a main service spillway in conjunction with an auxiliary or emergency spillway.

When culvert spillways placed on steep slopes flow full, reduced or negative pressures manifest along the boundaries of the conduit. Where negative pressures are large, there is a danger of conduit collapse or cavitation to the conduit surfaces. Where cracks or joints appear along the low-pressure regions, there is the potentiality of drawing in soil surrounding the conduit. Culvert spillways, therefore, should not be used for high-head installations where large negative pressures are very likely manifested. Further, the transition flow phenomenon, when the flow pattern changes from partially full to full, is attended by rather severe pulsations and vibrations. With regard to these reasons, culvert spillways should not be employed where the head drops exceed 6 m.

For head drops not exceeding 6 m, culvert spillways offer advantages over similar types due to their adaptability for either partially full or full flow operation and due to their simplicity and economy in construction. They might be placed on a bench excavation along the abutment of steep side hill location, or they can be placed through the dam to discharge directly into the downstream river channel.

12.4 Emergency Spillways

Emergency spillway is a kind of auxiliary spillways performing as fuse plugs for additional safety, should emergencies not contemplated by normal design assumption, arise. Figure 12.26 shows the layout of the Tarbela Project (Pakistan, H = 105 m), at its right bank there is an auxiliary spillway.

Fig. 12.26

The Tarbela Project with auxiliary spillway—Pakistan, H = 143 m

Where conditions occur that have not been anticipated and considered in the design of the main spillway, they may lead to following emergency situations:

• The actual flood exceeds the design flood;

• There is an enforced shutdown of the outlets;

• There is a malfunctioning of spillway gates;

• There is damage or failure of the main spillway;

• A high flood occurs before the previous flood has been evacuated by the main spillway.

An emergency spillway is usually positioned in a saddle or depression along the reservoir rim or by excavating a channel through abutment/ridge. Because an emergency spillway is not needed to function under normal reservoir operations, its crest is placed at or slightly above the design maximum reservoir level. Thus, an encroachment on the minimum free board is usually permitted for the design of an emergency spillway. The emergency spillway is washed out as soon as the water level in the reservoir reaches a predetermined elevation. The breaching section is sometimes called as “fuse plug.” Although it may take many months to restore the fuse plug and channel after an emergency operation, the total damage and cost to repair is less than if the main water-retaining structures had been overtopped.

The following requirements in the design of emergency spillways should be observed:

• The structural safety standard could be suitably lower, for its lower operation chance;

• The total discharge of spillways in a project should not be excess the maximum inflow discharge;

• Fully preparation for the released flow passage and downstream area should be made;

• If there are two or more emergency spillways, they are applied in sequence, for control the downstream flood;

• Emergency spillways should be located on the stratum with good geologic conditions, to prevent unexpected scouring to the foundation and unexpected downstream flood;

• The foundation of control section should be protected, to avoid scouring of saddle into deep groove, which in turn, leads to large reservoir draw down and difficulties associated with rehabilitation.

The fuse plug may be sparked by manner of overtopping, natural washout (or flushing), and blast washout.

12.4.1 Overtopping Emergency Spillways

With a crest near the water level at which the emergence operation is anticipated, overtopping emergency spillway is similar to the open-channel spillway. Where the water level is higher than the crest, a free flow commences. Since the initial outflow depth is shallow, it usually possesses long crest located at a wide saddle, for the reduction of excavation amount. The Dahuofang Project added a 150-m-long emergence spillway of this type in 1977, to help release MPF only.

12.4.2 Flushing Embankment Emergency Spillways

Flushing embankment emergency spillway consists of flushing dyke, concrete weir (or bottom sill), and chute. The flushing dyke may be either natural washout (or flushing) or blast washout.

An conventional emergency spillway with natural washout is shown in Fig. 12.27. The embankment and foundation should meet the requirements for the stability and seepage of permanent structures. Figure 12.28 shows another emergency spillway with natural washout flushing, at its middle portion fuse ditches are installed, as a result the washout of the whole dyke may be expedited.

Fig. 12.27

An emergency spillway with natural wash out flushing embankment (unit: m)

Fig. 12.28

Upstream elevations of a natural wash out flushing embankment with fuse ditches (unit: m)

Where the emergence spillway is long, separation walls may be installed to divide it into several segments with small difference in their crest elevations, this may stagger the operative time between segments, in this manner to prevent a sudden increase of discharge flood for downstream reaches. This design is implemented in the Dahuofang Project (China, H = 49.2 m).

12.4.3 Blast Washout Emergency Spillways

A blast washout emergency spillway also comprises the embankment and foundation satisfying the requirements for the stability and seepage of permanent structures, but it uses dynamite to form blasting cone as fuse ditches, as shown in Fig. 12.29.

Fig. 12.29

A blast wash out emergency spillway

12.5 Type Selection and Layout of Spillways

There are two basic ways to release flood through bank: chute spillway (or ski jump spillway) and spillway tunnel. Large flood flow can only be discharged through bank structures for earth- and rockfill dams. This arrangement also can be exercised for concrete dams where there is additional flood flow to be discharged and geologic and topographic conditions on abutments are available.

The bank-side or shore spillways can send the flow far away from dam and will not affect dam safety and power plant operation. Where an angle will be formed between the chute spillway (or spillway tunnel) and the river, it should be as small as possible in order to reduce the erosion to the opposite bank and the strength of return current. For a chute spillway with high crosshead, a curved channel is normally designed in approach channel and various kinds of flip bucket can be used to adjust flow direction.

Topographic condition influences the excavation amount of spillway greatly. Open-channel spillway would be the first choice where there is a saddle whose elevation is near the reservoir level, and whose downstream gully enables the released flood back to the mainstream easily. For a dam site of steep valley, two open-channel spillways may be layout on both river sides, or the side-channel spillway may be employed. Under very steep topographic condition, tunnel spillways using side-channel entrance or morning-glory entrance may be indicated.

Geologic condition also significantly influences on the spillway design. The excavated slopes should be stable. The unstable bank slopes after the reservoir impounding, the large faults, and potential land sliding are to be shunned. Deep excavation is avoided as far as possible, to facilitate the treatment of cut slopes. Stable bedrock is desirable for accommodating the spillway. The open-channel spillway may be constructed on non-rock foundation, if the slope is quite steep along the trough, step energy dissipation of multi-level head drop could be contemplated.

The composite design of spillway can be prepared by properly considering the various factors related to the other structures (e.g., dam, hydropower station, and ship lock) which influence the spillway size and type, location, and correlating alternatively selected components. In this way to achieve competent design of tech-economically reasonable, the entrance of spillway is so located to obtain a stream flow as smooth as possible and to keep the embankment dam at a safe distance, for preventing the lateral current scouring the upstream dam slope; otherwise, the guide wall should be installed to separate the spillway and dam. The control weir of the spillway would be better near the reservoir, to shorten the entrance channel and corresponding head loss. The released water fluctuation should have minor influence on the normal operation of power plant and ship lock.

Regarding the flood discharge ability, open-channel spillway performs well in the increase of discharge along with the rise of head over crest (since Q ∝ H ^3/2); the side channel in front of the chute or non-pressure tunnel has similar advantage. On the contrary, the drop inlet and siphon inlet spillways have slow increase of the discharge ability governed by Q ∝ H ^1/2.

In the engineering practice, auxiliary spillway may be provided which should be separately layout with the main spillway. In suspicious of larger flood than that of the design and check ones, it is wise to provide an emergence spillway.

For the spillway located far away from the other main structures in the project, the construction is less interfered, but the operation management is inconvenient. On the contrary, for the spillway tightly combined with the other main structures in the project, the construction interference could be magnificent, but the excavated materials from spillway may be easily hauled for the embankment fill. Therefore, the slag line and slag dump should be carefully designed in the construction organization and layout, to obtain better inter-coordination and less interference in the project construction.