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In this article we will discuss about how to control gully erosion.

#### Introduction to Gully Control:

Permanent gully control structures are constructed with the help of permanent materials such as cement, masonry, reinforce, concrete or earth. These structures are used for gully control works, where temporary measures are either inadequate or impractical.

These are most suitable for the gullies with large contributing watershed area and those which are to be retained as permanent waterway. The main function of permanent structures is to check the advance of vertical over fall of concentrated run-off at the gully head; so that grade of the gully bank may get stabilized and can also be changed into a regular waterway.

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In gully control practices, primarily the use of permanent type of structures should be avoided as far as possible, but when safety of the structures etc., are involved, then construction of permanent structure may be preferred. These structures are generally feasible for medium to large size gullies with medium to large watershed areas, respectively. The construction of permanent structures requires a careful study of the area, and development of appropriate plan, accordingly.

Although, the vegetative control measures are very efficient and productive, but they are not completely appropriate for all types of erosion control. In advance phase of gully erosion, where mass washing is very active as in the case of gully formation, the vegetative measures are meaningless, but mechanical structures play an effective role to control them. Normally, the permanent structures are necessary to use, particularly in those areas where vegetations cannot be established, immediately.

**The following three permanent structures are commonly used for stabilizing the gully: **

1. Drop spillways

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2. Chute spillways; and

3. Drop inlet spillways.

**Design of Permanent Structures: **

In general, the hydraulic structures are mainly become failed due to their insufficient capacity and lack of provisions for dissipating the energy of falling water into the structure. Because of this reason, the design of these structures is done by considering not only the sufficient discharge handling capacity, but also for dissipating the kinetic energy of falling discharge within the structure in such a manner and to such a limit at which the structure and downstream channel remain safe from the erosion.

**The gully control structures perform the following functions: **

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1. Soil Erosion Control – Specially to control the development of gullies.

2. Sediment Control – The design of these structures is based on the consideration to dissipate the kinetic energy of flowing water. This reduces the outgoing flow velocity to a great limit, which results into deposition of sediments.

3. Water Harvesting – It is performed by storing the run-off water, as found in case of drop inlet spillway.

4. Flood control; and

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5. Drainage of land.

**Design Steps for Gully Control: **

**The design of permanent gully control structures is completed under following three design steps: **

1. Hydrologic design

2. Hydraulic design; and

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3. Structural design.

**1. ****Hydrologic Design:**

The hydrologic design is concerned, it involves the estimation of design runoff rate which the structures have to handle, safely. The estimation of runoff rate depends on several factors associated to the watershed and climatic characteristics. The rainfall characteristics are mainly the rainfall amount, intensity and its distribution pattern. Similarly, the watershed characteristics such as shape, size and land use pattern affect the runoff rate, greatly.

The hydrologic design of permanent gully control structures is done by computing the runoff rate for 25 to 30 years return period, which indicates that the heaviest rain has occurred once in 25 to 30 years period.

In order to perform the design of flood storage structures (drop inlet spillway) the informations about total runoff volume, inflow-outflow hydrograph and reservoir stage-storage characteristics are also required. These are also determined under hydrologic design.

**2. ****Hydraulic Design:**

Hydraulic design consists of determining the dimension of different components of the structure on the basis of expected maximum runoff rate that has been determined under hydrologic design. The dimension of structure should be such that the flowing runoff through this should not overtop and can dissipate the kinetic energy of discharge falling towards down-stream face of the structure to a great extent. This effect helps in controlling the erosion below the structure.

**3. ****Structural Design:**

It involves the determination of strength and stability of different parts of the structure. The forces which act on the structure are mainly, the water pressure, force due to overflow and effect of water flow below the structure (i.e. seepage and sub-surface flow). All these forces are analysed under structural design. The structure must be stable against these forces.

In addition, the dimension of structure should also be such that, the internal stress developed in the structure, must be resisted by the construction materials. It is achieved in that condition when internal stress becomes equal to the external stress.

**Design Components of Permanent Gully Control Structures: **

**The basic components of gully control structures (i.e., permanent gully control structure) are given as below: **

1. Inlet

2. Conduit; and

3. Outlet.

Basically, the structures are classified and named in accordance with the features of above components. In addition to the above hydraulic components, the structure also consists of suitable wing walls, side walls, head wall extension and toe walls for checking the seepage loss, both from under and around the structure.

**The above three components are described as under: **

**1. Inlet: **

It is that part, through which water enters the structure. It may be either in the form of box or weir, constructed either in front or in the head wall, respectively. The head wall has two sub walls, i.e., the cutoff wall and headwall extension. The vertical wall is known as cutoff wall which is extended into the gully bed, to prevent the flow below the structure, and also provide strength to the structure. Similarly, another wall called as head wall extension, is extended into the soil of gully bank, which prevents the flow of water around the structure.

**2. Conduit: **

It is that part of the structure, which receives the flow from the inlet and delivers the same to the outlet. The conduits used in drop structures are mainly in two forms, one is in closed form that is box type channel; and other is in open form, i.e., the rectangular channel. In order to control the seepage loss from the area adjacent to the conduit and also to provide a greater stability, the conduit is supported by cutoff walls or antiseep collars, from below.

**3. Outlet: **

It is the component, which discharges the flow into the gully down-stream side with a safe velocity. The design and construction of outlet is performed in such a way that, it can dissipate the maximum kinetic energy of falling discharge within the structure in such a manner and to a limit that the outgoing discharge cannot erode the down-stream channel and structure, both.

The permanent gully control structure also requires a firm foundation. As far as possible, the wet foundation should be avoided, but in case if it is not avoidable, then there must be made a provision of adequate drainage system. For maintaining a good bond between the structure and foundation, the organic matters and surface soils should be removed from the construction site.

#### Design of Drop Spillway:

The construction of drop structure is usually limited up to the drop height of 3 to 4m only. It is not economical to construct, when drop height exceeds 4 m. The drop structures are used over the bed at suitable intervals to stabilize the gully by changing its profile from a higher slope to a gentle slope length.

**The design of straight drop structure is done under following steps: **

**1. Inlet Design: **

Straight drop spillway consists of straight type inlet that is why its name become as straight drop spillway. This type of inlet is most suitable for wide and shallow gullies to handle small to medium flows.

**To calculate the inflow capacity of straight drop spillway, the following weir formula can be used: **

Where,

Q = peak discharge rate which is to be handled by the structure.

g = acceleration due to gravity (9.81 m/s^{2}).

L = length of crest

H = head of the crest

C_{d} = coefficient of discharge. Its value varies considerably with the entrance conditions. However, the value of C_{d} as 0.6 is commonly used. Thus, substituting the values of C_{d} and ‘g’ in above equation and after simplification, the equation (5.1) is reduced to–

Q = 0.017 LH^{3/2} … (5.2)

This equation computes the value of peak discharge in m^{3}/s, if L and H are expressed in m. By above equation, the L and H are determined using hit and trial method by satisfying the Q value. A free board ranging from 15 to 30 cm is also added to H.

**2. Outlet Design: **

Outlet design is performed with the consideration that the kinetic energy gained by the sheet of flowing water when falls from crest of the gully head to the down-stream side of the structure, must be dissipated and/or converted into potential energy.

**The preliminary calculations to design the outlet, are performed by following two terms: **

**Froud Number: **

It may be calculated by using the following formula –

F = V/√gd

Where,

F = froud number, is a dimensionless term.

V = velocity of flow entering the jump

d = depth of flow at entrance.

When F = 1, then V = √gd, under this condition the flow is said to be in critical state.

If F < 1 or V < √gd, then flow is known as sub-critical flow. In this case, the gravity force is most dominating which results into reduction of flow velocity. Similarly, if F > 1 or V > √gd, the flow is called super critical flow. In this state, the internal forces become more effective than the gravity force, causing increase in flow velocity. In outlet design, the attempts are made to bring the d/s flow velocity in sub-critical range by creating hydraulic jump inside the outlet.

**3. Hydraulic Jump: **

Super critical flow in a channel of small slope is unstable, because slope of channel is unable to sustain it; therefore, super critical flow tends to change in sub-critical flow. In super-critical state, the depth of flow is less than the critical depth while in sub-critical condition, it is greater than the critical depth.

Thus, when flow changes from super-critical state to sub-critical state, then depth of flow gets increase. This increase in depth of flow is effective for a shorter length, is known as hydraulic jump. In hydraulic jump, a high degree of turbulence is created, which is responsible for dissipating the energy to a very high range.

**The amount of energy lost in hydraulic jump is described below: **

Loss of Energy in Hydraulic Jump. The loss of energy in hydraulic jump is the difference between specific energies before and after the jump, being taken place.

It is given by –

Where,

E = loss of energy in hydraulic jump

Y_{1} = depth of flow before the jump

Y_{2} = depth of flow in the jump

V_{1} = flow velocity before the jump

V_{2} = flow velocity after the jump.

Using the continuity equation, i.e. q = V_{1}.Y_{1} = V_{2}.Y_{2}

Thus, equation 5.4 becomes as –

This is the desired equation for computing the amount of energy lost in hydraulic jump.

**Applications of Hydraulic Jump: **

**The practical applications of hydraulic jump are mainly as under: **

1. Used to dissipate the energy of flowing water over the weirs, dams and other hydraulic structures. The energy dissipation of flowing water is helpful to prevent soil scouring at down-stream section of the hydraulic structure, in significant way.

2. To raise the water level on d/s side of the measuring flume, this property is beneficial to create high water level in the irrigation channels, and thus to make easy water distribution at every corners of the field.

3. It is used to increase the water weight on apron section; and thus to reduce the uplift pressure below masonry structure by raising the water depth within the apron section. The uplift pressure can be estimated with the help of water depth existing over the hydraulic structure.

4. Also, used to increase the discharge of a sluice by hiding the back tail water, because the effective head gets reduce, when tail water is permitted to drown the jump. Based on this property of hydraulic jump a device called ‘fall increaser’ has been developed which increases the effective head in a water- power plant during flood occurrence by holding back tail water from the outlet of the draft tube.

5. Hydraulic jump is employed for locating the gauging station, as it creates the special flow conditions such as existence of super critical flow or the presence of control sections in the stream.

6. For domestic/city water supply it is used to aerate the water.

7. For water purification the hydraulic jump makes a complete mixing of chemicals in the water.

8. It is also applied to remove the air pockets from the water supply lines; and thus removing the problem of air locking from there.

**Types of Hydraulic Jump: **

**U.S. Bureau of Reclamation classified the hydraulic jumps occurring on horizontal floor in following distinct types, based on the Froude number (F = v/****√gd)**** of incoming flow: **

i. At F = 1, the flow is said to be critical; in this flow no hydraulic jump forms.

ii. At F = 1 to 1.7, the water surface includes some undulation i.e., jump occurs, called as undular jump.

iii. At F = 1.7 to 2.5, a weak jump forms which is characterized by having a series of small rollers on the surface of jump, while d/s water surface remains smooth or plane. The flow velocity is fairly uniform, throughout. And loss of energy is very low.

iv. At F = 2.5 to 4.5, an oscillating type hydraulic jump takes place. The oscillation produces a large wave of irregular period. This type of jump formation is more common in canals. Since, it generates wave, so can damage the canal banks or rip-rap provided there.

v. At F = 4.5 to 9.0, a steady jump forms. This type of hydraulic jumps are least sensitive to change the tail water depth. They are always in well-balanced condition and have performance at their best. About 45 to 70% energy is dissipated.

vi. At F ≥ 9.0, a strong hydraulic jump takes place. In this type of jump, a high velocity jet grabs intermittent slugs of water rolling down the front face of the jump and generating the waves at downstream side, as result a rough surface is prevailed, there. Its action is rough, but more effective to dissipate the energy. The energy dissipation may reach up to 85%.

**Height of Hydraulic jump:**

It is the difference of water flow depths after and before the jump. If depth of water flow before jump is Y_{1} and Y_{2} after the jump, then height (h_{j}) is given as h_{j} = Y_{2} – Y_{1}. This height can also be expressed in terms of ratio with respect to the initial specific energy, which is given as under –

In which, h_{j}/E_{1} is denoted as the relative height, Y_{2}/E_{1} is relative sequent depth and Y_{1}/E_{1} is the relative initial depth.

The equation 5.6 can also be shown in dimensionless term as the function of F, which is –

**Hydraulic Jump as Energy Dissipator: **

The hydraulic jump is a useful means of dissipating the kinetic energy of water flow in super critical range. This merit provides a guideline to install spillways, chutes or sluices at d/s end to prevent the erosion. The energy dissipation of flow results into the reduction of flow velocity, causing the d/s flow becomes incapable to scour the soil particles.

For energy dissipation the hydraulic jump is required to form in channel reach, i.e., the stilling basin. The bed of basin is paved to make it stable against scouring. The stilling basins are seldom designed to confine the entire jump on the paved bed (i.e., apron), as such basins are more costlier to construct. Therefore, for this purpose some accessories are installed in the basin to form the jump within the basin. These accessories may be the floor blocks etc.

**For design of stilling basin, which could be best to dissipate the energy of falling water by creating hydraulic jump, the following three features are always counted: **

1. Position of Jump.

2. Conditions of Tail Water.

3. Jump types.

**1. Position of Jump: **

A hydraulic jump can be formed in following three alternate patterns that allow a jump to form a down-stream end of the sources like an overflow spillway, a chute or a sluice.

(a) When tail water depth Y^{1}_{2} is equal to the depth Y_{2} sequent to Y_{1}.

(b)* *When tail water depth Y^{1}_{2} is less than Y_{2}.

(c)* *When tail water depth Y^{1}_{2} is greater than Y_{2}.

All these cases are illustrated in Fig. 5.1.

**Case (a):**

In this case, the hydraulic jump will occur on a solid apron, immediately ahead of the depth y_{1}; and the values of F_{1}, y_{1} and y^{1}_{2} (= y_{1}) will satisfy the following equation –

This position of hydraulic jump is ideal for scour protection. But has a big objection that, at this position of jump, there is a little difference between the actual and assumed values of the relevant hydraulic coefficients, which cause to move the jump towards d/s face from its predicted position. Due to this reason, it is always required to install some devices to control the position of jump formation. This position of jump formation is shown in Fig. 5.1 (a).

**Case (b): **

This case of jump position is shown in Fig. 5.1 (b). In this case the tail water depth (y^{1}_{2}) is less than y_{2}, indicates that the tail water depth in first case is decreased, causing the jump gets recede downstream to a point where equation 5.8 is satisfied.

This position of jump formation is avoided for design of stilling basin, because the jump is repelled from the scour-resisting apron to either on loose rubble bed or in unprotected channel section, which causes generation of severe erosion problem. However, it can be overcome by providing a control at the channel bottom favouring to increase the tail water depth, and thus to arrive at the position of jump as in case (a).

**Case (c): **

In this case, tail water depth (y^{1}_{2}) is greater than the depth y_{2}, indicates that the tail water depth in case (a) is increased. In this position, the jump is shifted towards upstream side and it may finally be drowned out at the source, causing to submerge the jump.

This position of jump formation is assumed to be a safest case for design, because in this case the position of submerged jump is very readily fixed, but there a little energy is dissipated under this condition of jump formation. This position of jump formation is illustrated in Fig. 5.1 (c).

**2. Conditions of Tail Water: **

In previous case, the position of hydraulic jump formation was described by assuming that the tail water has certain fixed position whether its depth position Y^{1}_{2 }is equal to, greater than or lesser than the sequent depth Y_{2}. But in real situation it is never so; always tends to fluctuate according to the variation of the channel discharge. Leliavsky (1955) has suggested following five classes of tail water conditions for taking into consideration to design scour-protection structure (i.e., stilling basin).

**Class (I): **

The jump rating curve and tail water rating curves always coincide, which indicates that at all times the tail water depth y^{1}_{2} is being equal to the depth y_{2 }sequent to y_{1}, causing the formation of hydraulic jump on protective apron at all discharges. This is an ideal condition, but rarely takes place in natural condition. This class of tail water condition is shown in Fig. 5.2.

**Class (II): **

In this class, the jump rating curve is always at higher stage than the tail water rating curve, i.e., it satisfies the case (b) in which tail water depth Y^{1}_{2} is less than y_{2}. The hydraulic jumps are formed at a certain place away from the downstream; it may be beyond the apron reach. In order to ensure the jump formation within the apron section, there is required to provide sills in the stilling basin. This class of tail water condition is shown in Fig. 5.2.

**Class (III): **

It refers the condition when jump rating curve is at lower stage than the tail water rating curve, which shows that the tail water is higher than the sequent depth; under which the jump moves to upstream and probably be drowned at the source. In this condition of jump formation, a provision is made to ensure the jump within the apron section.

Normally, a sloping apron above the channel-bed is constructed for this purpose, provided that the apron slope must be in proper range to form the jump on the apron at all discharges. Besides sloppy apron, a drop can also be constructed at the channel bottom to lower the depth of tail water; and thus to form the jump within the apron.

**Class (IV): **

It is opposite condition of class III, i.e., jump rating curve is at higher stage than the tail water rating curve at lower discharge, but a lower jump stage at high discharge rate. In this situation, a stilling basin is constructed to ensure the jump formation at low discharge; similarly, a basin is constructed along with a sloppy apron for forming the jump at high discharge rates.

**Class (V): **

Refers the situation, in which jump rating curve is at lower stage at low discharge, but at a higher stage than the tail water, at high discharge. At this specific condition, the formation of jump to dissipate the maximum energy of stream water is ensured by providing a stilling pool.

**3. Jump Types:**

**U.S.B.R. has suggested following points for different types of jump: **

i. In design of stilling basin all types of jump are taken into consideration.

ii. The baffles or other special considerations are not required for weak jumps.

iii. The oscillating type jumps are very difficult to handle, if possible should be avoided to consider for design of stilling basins. However, if it is not avoidable then jump formation can be ensured by altering the dimension of apron in such a way, as to form the jump into desirable range.

iv. In case of formation of steady jumps, the length of stilling basin can be shortened by providing baffles and sills.

v. As the froude number gets increase, the jump becomes more sensitive to the tail water depth. For froude number as low as 8, the tail water depth is found greater than the sequent depth. In this condition, it is suggested to confirm the formation of jump over the apron section, exactly.

vi. If froude number exceeds 10, then a Bucket type energy dissipater can be constructed. However, in this case the energy dissipation can also be achieved by constructing a deep stilling basin, along with high retaining wall. It involves more cost that may not be commensurate with the obtained result. Actually, in this case the difference of initial and sequent depth is more, as result a deep basin is required to handle this character of discharge.

In straight drop spillway the dissipation and conversion of energy of falling water is achieved by creating the hydraulic jump either in straight apron or in stilling basin. The stilling basin is used in the large size structures as hydraulic jump is induced in smaller apron. Therefore, for confining the jump an end sill is provided at the toe of structure.

**Design of Straight Drop Spillway Stilling Basin:**

A straight-drop spillway stilling basin completely prevents the soil scour in the down-stream channel. The stilling basins are normally used, when d/s channel is more erodible in nature or when flows are approaching the design value and occur frequently for longer duration.

**Design Steps: **

**It is completed under following steps: **

**1. Minimum Length of Stilling Basin: **

It is given –

L_{B} = x_{a} + x_{b} + x_{c} … (5.9)

Where,

L_{B} = minimum length of stilling basin

x_{a} = distance between head wall and the point where surface of upper nappe strikes the floor of stilling basin.

x_{b} = distance between the point where surface of upper nappe strikes the basin floor and u/s face of the floor blocks. It is approximated equal to 0.8 d_{c} (d_{c} is the critical depth of flow)

x_{c} = distance between the u/s face of the floor block and the end of stilling basin. It is given by = 1.75 d_{c}

Thus, substituting the values of x_{b}, and x_{c} in equation 5.9 we have –

L_{B} = x_{a} + 0.8 d_{c} + 1.75 d_{c}

= x_{a} + 2.55 d_{c} … (5.10)

**2. Floor Blocks: **

**Different parameters of floor blocks are given as under: **

(i) Height of floor blocks = 0.8 d_{c}

(ii) Width and spacing of floor block = 0.4 d_{c}, however a variation of ± 0.15 d_{c} from the above is also permitted.

(iii) The plan of floor blocks should be square.

(iv) The floor blocks should occupy the space between 50 to 60% of the width of stilling basin.

**3.** Height of End Sill – It is approximately 0.4 d_{c}.

**4.** **Longitudinal Sills:**

These are provided to increase the structural strength of the structure. Their width is kept less than the floor blocks, and height is kept equal to the end sill. One point should also be kept in view that, they should pass through the blocks, but not between them.

**5.** Height of Sidewalls above Tail-water Level – It is given by 0.85 d_{c}.

**6.** The wing-walls should be placed at 45° with the outer centre line; and should have 1:1 as top slope.

**7.** Minimum height of tail-water surface above the floor of stilling basin should be 2.15 d_{c}.

**8. Approach channel: **

**It should accomplish the following features: **

(i) Should be in the level of crest of spillway.

(ii) The approach channel should have the bottom width equal to the notch of spillway at the head wall.

(iii) The toe of the dyke or toe of the side slope should intersect the floor of approach channel at the end of spillway notch.

(iv) The approach channel must be protected by using stone revetment or rip-rap, for the distance 2 times of the notch depth.

**9.** The provision of aeration space is not required, if approach channel has been constructed as per above points.

**Design of Box-Type and Inlet Drop Spillway:**

This type of drop structure consists of box type inlet, which is a rectangular box. It is opened, both from its top and down-stream end. The flow passes in the inlet through dyke and head wall.

The box-inlet drop spillways are particularly useful, where –

1. A long crest length is required to keep the head on the crest, low.

2. The down-stream channel is so narrow, that a straight drop spillway of equivalent crest length cannot be constructed.

3. Drops ranging from 0.60 to 3.5 m.

They are also useful to serve as a tile outlet structure in case of drainage works, which permit the surface water to enter the drainage ditch without eroding the head end or the adjacent bank.

**However, it is described as under: **

**A. Inlet Design: **

The box-inlet controls the head-discharge relationship at low flows. When approach channel is level with the crest then following head-discharge relationship can be used for inlet design –

Q = 3.43 LH^{3/2} … (5.10)

In which, Q is the discharge (cfs) L is indicated as crest length (feet) equal to 2B + W, the B and W are explained in Fig 5.5 and H is the head on crest (feet). The discharge used in above equation should be multiplied by the correction factor for head, shape of box-inlet, width of approach- channel and dike proximity to obtain true capacity.

The head-discharge relationship for higher flows is controlled by the opening made through the headwall.

**In this condition the head-discharge relationship is given as under: **

Q = C_{2 }.W (H – H_{0.2})^{3/2} … (5.11)

Where,

W = head wall opening (ft)

C_{2} = coefficient of discharge

H_{0}_{.}_{2} = head correction

The discharge should be computed by both the equations; the smaller discharge value between them should be counted as actual discharge.

In spite above corrections, the discharge should also be modified based on the submergence condition, if tail water depth is close to or above the crest of the box-inlet.

**B. Outlet Design: **

The outlet design of box-inlet drop spillway is based on the critical depth of flow in the straight section and at the end sill.

**The design procedure is described below: **

Eq. (5.15) is suitable for the value B/W ≥ 0.25; however, a longer length of stilling basin can also be used, but it will require less material if straight section is lengthened to secure the same over the outlet length.

5. Calculate the tail water depth –

d_{2 }= dce + 0.052 We

This equation is applicable in that condition, when width of stilling basin is more than 11.5 dce at exit point. At the width of stilling basin equal to 11.5 dce it does not predict the correct value of d_{2}. For this purpose a greater tail water depth may be used. And, when width of stilling basin is less than 11.5 dce at exit, then minimum tail water depth over the basin floor is given by –

d_{2 }=_{ }1.6 dce

6. Calculate the height of end sill –

*f* = d_{2}/6 … (5.17)

7. Height of longitudinal sills is the same to the height of end sill.

**The other details of it, are also mentioned below: **

(a) They should not be provided, when side walls of stilling basin are parallel.

(b) The centre pair of longitudinal sills should originate at the exit of the box-inlet and extend through the straight section of stilling basin to the end sill.

(c) When W_{e} is less than 2.5 W, then only two longitudinal sills should be provided, which should be at a distance ‘p’ varying from W/6 to W/4 each side of the centre line.

(d)* *When W_{e} exceeds 2.5 W, then two additional sills are needed, which should be located parallel to the outlet centre line, and in the midway between the centre sills and the side walls at the exit of stilling basin.

8. Find out the minimum height of side walls above the water surface, at the exit point of stilling basin.

t = d_{2}/3 … (5.18)

However, this value can be kept more, depending on the height of water existing in the stilling basin.

9. The wing wall should be constructed triangular in elevation; and have 45° slope with the horizontal. The construction of wing wall parallel to the centre line of the structure is not suitable.

**Various notations used in the above formulae of design steps are explained as under: **

d_{c} = critical depth of flow in straight section

Q = design runoff rate

W = width of box type inlet

B = length of box type inlet

W_{e} = width of end sill

L_{B} = length of stiling basin

L_{S} = minimum length of straight section

d_{2} = minimum tail water depth over the basin floor

dce = critical depth of flow at the end sill

*f *= height of end sill

**The design of this type of drop spillway is described under the following steps: **

**1. ****Computation of Peak Runoff: **

The peak runoff to be handled by the spillway is calculated by using the Rational formula. Normally, for design of drop structures 25 to 50 years return period is used. If area of watershed contributing the runoff to the gully (A); rainfall intensity for the duration equal to time of concentration (I) during a specified return period and runoff coefficient (C) which is determined based on the land use and soil types, are known then peak runoff rate, using Rational formula is given as under –

Q_{peak }= CIA/36 m^{3}/s …(5.19)

**2. ****Computation of Length and Depth of Weir:**

It is performed on the basis of peak runoff, estimated. The weir is used as inlet of the drop spillway.

**For computation of ‘L’ (length of weir) and ‘h’, (depth of weir) the following steps are followed: **

(i) Select an arbitrary values of ‘L’, and substitute in following formula to compute the value of ‘h’.

In which, Q is the peak discharge (m^{3}/s) and F is the net drop from the top of the transverse sill to the crest (m). In this formula, the value of Q is known and L and H are unknown. To determine L and H values, a set of L and h combinations to suit the discharge Q is prepared.

(ii) Compute L/h ratio for each set of L and h combinations.

(iii) Compute h/F ratio for each set of L and h combinations.

(iv) Select that combination of L & h, which h/F ratio is less than 0.50. In this way the values of L and h are determined.

**3. Computation of Hydraulic Components: **

**4. Apron Thickness: **

The apron thickness is decided on the basic of overfall height (F) and materials used for its construction. If apron is to be constructed using cement-concrete materials then its thickness can be have from the Table 5.1 for different values of (F). But if apron is to be constructed with masonry and gabion, then the thickness given in table should be increased by 1.5 and 2.0 times, respectively.

**5. Wall Thickness: **

**The minimum top widths of head wall, side wall, wing wall and head wall extension are given as below: **

Head Wall – 0.45 m

Side Wall – 0.30 m

Wing Wall and – 0.30 m

head wall extension

The base width of above components is dependent on the height of head wall. The base widths of head wall, side wall, wing wall and head wall extension for different heights of wall, constructed with masonry materials are cited in Table 5.2.

**Structural Design of Drop Spillway:**

The stability of any hydraulic structure depends on the construction materials, used. Reinforce, concrete, brick and masonry (stone) are the most common materials used for the construction. In addition to the above, the dimensional proportions of different components of the structure, other than those determined hydraulically, also affect the stability of the structure; this consideration should also be counted during design, to make the structure stable.

**For structural design the entire structure is assumed as one unit for computing structural strength against following causes of failures: **

**1. Check against Overturning:**

The structure should be safe against overturning about the toe. It is predicted by computing a factor known as overturning factor, which is defined as the ratio of restoring moment (R.M.) to the turning moment (T.M.), i.e.-

If the value of factor of safety against overturning (FS_{0}) is more than 1.2 (for concrete), then structure is assumed to be safe.

Restoring moment is due to weight of structure; and turning moment is because of water and uplift pressure. The turning moment also depends on the condition or nature of the sub-soil strata. The uplift pressure is generally considered equal to the depth of water in the structure (towards u/s side).

It is zero at the down-stream side, while at u/s side it is to be maximum. Its line of action is vertically upward from the centre of the structure. For safety point of view, the restoring moment should always be greater than the turning moment.

**2. Check against Sliding: **

Any structure may be failed due to sliding, when horizontal forces acting on the structure are greater than the resisting forces. The resisting forces are concerned, there are mainly two types of forces; one is frictional resistance of the foundation and other is cohesion force of the soil and foundation, both. The sum of all horizontal forces (ΣH) should always be less than the resisting forces of the structure, for making the structure safe against sliding action.

It is expressed as –

where,

*f *= coefficient of friction (tan θ) of the soil

θ = angle of repose of the soil

ΣV = total vertical forces

C = cohesion force of the foundation material

A = area of plane sliding.

To ensure the safety of structure against sliding, the value of sum of all resisting forces must be equal to 1.5 times the sum of horizontal forces (i.e. *f*. ΣV + C.A. = 1.5 ΣH). In case, if it is not satisfied, then the cutoff wall and toe of the wall should be constructed for greater depth. This develops more cohesive force. In addition, the base of structure should also be constructed uneven to increase the frictional resistance of the structure.

Sliding of the structure can also be predicted by a factor, known as factor of safety against sliding.

It is given as –

Where,

F.S_{s} = factor of safety against sliding

ΣH = sum of all horizontal forces which tend to slide the structure

ΣV = sum of all vertical forces

u = uplift force

The value of factor of safety against sliding should not exceed 0.8 and 0.75 in case of concrete and masonry structures, respectively.

**3. Check against Piping: **

The piping type failure in hydraulic structure takes place due to removal of materials from the foundation by flow of seepage water. Conceptually, there are two basic thoughts about piping phenomenon, in which one is concerned with the flow of water through the foundation and other is related to the line of creep. The line of creep is the contact surface between the structure and the soil at the base of the foundation.

After an intensive investigation, it has been reported that most of the hydraulic structures are failed due to piping, mainly along the line of creeps. Lane (USDA 1957) suggested the weighted line of creep as the sum of all steep contacts and one third of all those contacts which are flatter than 46°, between the head and tail water along the contact surface of the structure. The value of safe weighted creep ratio (C_{W}) of different soil types can be calculated, using the following formula; and can be have an idea about the failure of structure due to piping.

**The formula is given as under: **

Where,

C_{w} = weighted creep ratio

ΣL_{H} = sum of all horizontal or flat contact surfaces

ΣL_{V} = sum of all vertical or steep contact surfaces

H = head between head and tail water depths.

The recommended values of weighted creep ratio for different types of materials are also given in Table 5.3. The computed values of C_{w} should always be either equal to or greater than the table values to have stable structure. By the way, if it does not satisfy, then the depth of cutoff or toe wall should be suitably increased.

**4. Check against Tension:**

When structure is constructed with the bricks or stone masonries, then it should be ensured that no tension should be developed at the base of head wall, as these materials are not capable to bear the tensile stress. This is achieved by passing the resultant force acting on the head wall through middle third of the base of the structure.

**The position of resultant force can be calculated by using the following formula: **

Where,

Z = position at which resultant force is acting, i.e., horizontal distance measured from the wall to the point of action of vertical force.

ΣM = sum of all horizontal forces

ΣV = sum of all vertical forces

The eccentricity (e) is given as –

e = (d/2) – z

It should not be more than d/6, in which d is the base length (Fig. 5.7).

**5. Check for Compression: **

It is performed by determining the direction of resultant force acting on the structure. It is satisfied in the condition when resultant force of all horizontal and vertical forces is acting on the structure, vertically downward, i.e., in compressive nature. This makes the structure stable against floating.

The compression of structure is also expressed by the contact pressure, which is equal to the total load transmitted to the foundation caused by all horizontal and vertical forces acting on the structure. The contact pressure can be calculated, using the following formula –

Where,

P = contact pressure

ΣV = sum of all vertical forces including uplift force

A = base area of the structure

e = eccentricity (i.e., longitudinal distance from the centroid of the base area to the point of application of the resultant vertical force)

d = base length of the structure.

**Design of Apron Thickness: **

The apron thickness is determined on the basis of uplift pressure acting on it. The thickness should be such that the own weight of the apron must be greater than the uplift pressure. The magnitude of uplift pressure may be obtained by multiplying the depth of water to its density in terms of weight per unit area.

**Design of Side Wall: **

The side walls are designed to counteract the lateral pressure caused by the filled materials behind the wall, and at the same time pressure exerted by the head wall and apron which contributes stability to the side wall. The lateral pressure exerted by the earth fill on side walls can be calculated by using the following formula –

Where,

P_{s }= lateral earth pressure acting in horizontal direction

W = vertical pressure is given as –

= γ_{s}H

γ_{s}_{ }= density of earth fill or soil

H = height of earth fill

θ = internal friction angle of the soil

After substitution of W = γ_{s}H, the above equation is given by –

#### Design of Drop Inlet Spillway:

The drop inlet spillways are ideally located in the gullies towards down-stream side of the depressed spot for making storage of water. The water stored in such storages, can be used for irrigation or other farm’s use purposes. In addition, this structure is also found suitable for stabilizing and controlling the advancement of gully head, when its depth is being more than 3 m.

The drop inlet spillways are frequently used for controlling the flood water in gullies, and as an outlet in farm ponds, reservoirs, silt detention tanks and settling basins. A series of this structure on gully bed produces a retarding effect on water flow, which results into sedimentation at up-stream side of the structure, in the gully.

Under hydraulic design, it involves the design of earth dam and pipe spillway, as these two components are the main in drop inlet spillway.

**Design of Earth Dam: **

The design of earth dam is also performed by considering all the design steps, i.e., hydrologic, hydraulic and structural design as in other hydraulic structures. The hydrologic design determines the peak runoff rate and its total amount of flow coming to face the structure.

**The design of earth dam suitable to drop inlet spillway is described as below: **

1. The side slopes which are commonly used in earth dams are 3:1 and 2:1 towards upstream and downstream sides, respectively.

2. Top width of dam varies with its height. The minimum top width should be equal to 1.8 m for the dam height of 3.5 m. If top width of dam is to be used as a road, then it should be kept between 2.5 to 3.0 m. In addition, there should also be added 30 cm additional top width for each 60 cm dam height.

3. In order to make the dam safe against overtopping, there must be added 5% of theoretical dam height or more to the dam height as the settling allowance and 60 cm as freeboard.

4. Bottom width of dam is calculated on the basis of side slopes and its height, used. The bottom width of dam should match the length of conduit, used.

The side slopes of dam should be protected against erosion. This is performed by making rip-rap, using heavy gravels or rocks when upstream side slope is expected to get badly eroded by the wave action. The d/s side slope is not affected by wave action, so vegetations can be grown to protect this side.

**Design of Pipe Spillway: **

Use this type of spillway for gully control, depends on the size of watershed producing the runoff and condition of proposed site. However, the choice of spillways depending on watershed size, is given in Table 5.4.

In drop inlet structure, the pipe spillway has vertical section towards upstream face of the dam, is called riser, which is connected to the conduit passing through the dam. The top of the riser can be raised up to desired height for providing grade to the conduit. The flow rate of pipe spillway is controlled by the inlet and conduit, both. To follow the hydraulic design of this type of spillway, the types of flow occurring in conduit should be considered.

A typical discharge characteristics curve of drop inlet spillway is shown in Fig. 5.9. The flow through conduit is governed by the slope provided to it. There is also some head loss due to friction of the pipe, which should be fully taken into consideration for design purpose.

**The head loss due to friction is given as: **

Where,

H_{f}_{ }= head loss due to pipe friction

L = length of pipe

K_{c} = head loss coefficient

V = flow velocity

g = acceleration due to gravity

In drop inlet spillway design two types of pipe slope are considered, i.e., natural slope and conduit slope.

**The natural slope of pipe can be computed by using the following formula: **

**On the basis of natural slope, the conduit capacity for different flow conditions as shown in Fig. 5.10, can be computed, which is as follows: **

**Case (A): **

When conduit slope is less than the natural slope and outlet is under submerged condition, then discharge capacity of spillway is given as –

Where,

a = cross-sectional area of the conduit

K_{e} = coefficient of entrance loss.

**Case (B): **

When conduit slope is greater than the natural slope and outlet is not submerged. In this case, the discharge of spillway can be calculated as –

In which, C is the coefficient of orifice.

**Construction of Drop Inlet Spillway: **

**The constructional features of these components are described as under: **

**1. ****Installation of Antiseep Collars: **

In drop inlet spillway it is done to check the flow of seepage water along the conduit pipe. The antiseep collars are made of concrete and masonry materials. The length of collar is kept about 30% of the total seepage length. These collars are constructed in the size of atleast 2.5 m width and 2 m in height, centered around the conduit pipe.

The thickness should be equal to 25 cm in case of concrete collars. The concrete collars are also reinforced with 1.2 cm diameter steel rods at 30 cm interval, horizontally and vertically, both, when they are used to clay or concrete conduit pipes. The number of collars to be required, depends on the length of conduit used in the spillway. If length of conduit exceeds 18 m, then two antiseep collars are sufficient.

There should also be made an arrangement to prevent uneven settlement, causing development of heap stress in the conduit. This arrangement is known as ‘cradle’. It is made of masonry or concrete materials, because these materials have sufficient capacity to bear the heavy load, when heap stress is formed in the conduit.

**2. Location of Emergency Spillway: **

The use of emergency spillway is essential when volume of inflow runoff exceeds the design runoff volume. In this condition if such arrangements are not made, then there is created problem of overtopping through the embankment, thereby rises a position to get failure of the structure. To overcome this bad happening, the use of emergency spillway is desirable.

The location of emergency spillway should be fixed at appropriate place in the earthen embankment. It should also lead to the downstream end of the structure. The emergency spillway should be taken care against water erosion; for this purpose stone pitching or grass growing is done in the section of emergency spillway.

**3. Protection of Earthen Embankment: **

The protection work is followed on both the sides of earthen embankment. The upstream side slope is protected against wave action of stored water; and downstream side slope needs protection against rainfall etc. For this purpose, stone pitching is recommended both on the upstream and downstream side slopes. Towards downstream side, the stone pitching should be done above outlet of the embankment. However, stone pitching is not used as general protection measure for d/s side slopes, but vegetation is always preferable.

**4. Drainage System in Earthen Embankment:**

Filter zones are invariably used in earthen embankments to solve the drainage problem. They are constructed with those materials, which are more pervious than the embankment materials.

**The provision of filter zone in earthen embankments serves following two purposes: **

i. It reduces the pore water pressure at downstream side of the dam, causing to increase the dam stability, and

ii. By checking the migration of soil particles, it also prevents the piping action which takes place through the foundation.

**The drainage systems, which are commonly provided in earthen embankments include following three types of drain: **

i.. Toe drains

ii. Horizontal blanket drains; and

iii. Chimney drains.

#### Design of Chute Spillway:

Chute spillways are constructed at the gully head to convey the runoff discharge from u/s area into the gully through a concrete or masonry open channel. They are better preferred than the drop spillways, particularly when drop height exceeds the economic limit of drop structure. In addition, they are also preferred more than the drop spillway, when a large runoff volume is required to discharge from the area.

The chute spillways are used at gully head for disposing the runoff from upstream land to the gully bed, very safely. Furthermore, these are also used in earth dam to dispose the stored water from a greater drop, which is not feasible with the drop structures. The chute spillway usually requires less construction material than the drop inlet structure for the same capacity and drop.

Chute spillways are more susceptible to get failure due to overturning, settling and sometimes by undermining also, caused by rodents. These failure reasons can be easily controlled by providing proper drainage system, proper compaction in controlled conditions and by constructing the structure on a firm ground surface. The materials such as reinforce, concrete, brick and masonry are commonly used for constructing the chute spillway.

**Design Components: **

**The chute spillway consists of following three design components: **

**1. Inlet Design: **

The most common type of inlets used in chute spillways are the straight inlet, box type inlet and sometimes, the side channel inlet, also. The box type inlet is generally used in that condition, when straight inlet is not sufficient to pass the runoff at desired drop.

The design procedure of the inlet used in chute spillway is the same to the inlet of drop spillway, which is usually done on the basis of design runoff required to handle by the structure. In chute spillway, the discharge capacity of structure is governed by the size of inlet section. The inlet also controls the flow of water through piping action under and around the open channel.

**2. Design of Channel Section: **

In chute spillway, the rectangular open conduits or channels are most common. The side walls of conduit confine the flow rate and discharge distribution, too, within the conduit section. The top of side wall is constructed in such a way, that it is flushed with the embankment slope. Design of channel cross-section is similar to the design of open channel, in which bottom width, top width, side slope and depth are determined for the given discharge rate. For design purpose the Manning’s formula can be used.

**3. Outlet Design: **

Cantilever type outlet is most suitable to use in the chute spillway, especially where channel grade below the structure is being unstable. The straight apron type outlet does not dissipate sufficient energy; and therefore, it is not commonly used. Normally, straight apron type outlets are used in small gully control structures. The SAF stilling basin type outlet provides adequate result on dissipating kinetic energy of falling water, and is described herewith.

The design principle of outlet of chute spillway is similar to the design of outlet of drop structure, i.e., outlet should be such that the hydraulic jump must be occurred within its boundary. For outlet design using hydraulic jump concept, the froud number (F) of incoming flow into outlet and corresponding downstream water depth (d_{2}) should satisfy the following equation-

Where,

d_{1} = depth of flow before hydraulic jump

d_{2} = depth of flow after hydraulic jump

F = Froud number, given by the equation, as-

=V_{1}/√gd_{1}_{}

In which, V_{1} is the flow velocity before occurrence of hydraulic jump and g is the acceleration due to gravity.

**Design of SAF Stilling Basin: **

**Referring Fig. 5.12, the dimensions of different components of SAF stilling basin are given as under: **

1. Length of stilling basin (L_{B}) –

This equation is valid for the Froud number less than 3 and more than 300. The Froud number can be calculated by the equation, F = V^{2}/√gd_{1}, in which d_{1} represents the height of chutes & floor blocks.

2. Width and spacing of the chutes as well as floor blocks = 0.75 d_{1}.

3. Spacing of floor blocks from upstream end of the stilling basin = L_{B}/3.

4. The floor blocks should not be closer than 3/8 d_{1} from the side walls of the basin.

5. The location of floor blocks should be fixed at downstream side from the openings between the chute blocks.

6. The height of end sill should be equal to 0.07 d_{2}, in which d_{2} strands for theoretical tail water depth, corresponding to flow depth d_{1}.

7. The actual depth of tail water above the stilling basin can be computed by the equation-

d_{2}’ = 1.4F^{0.45 }.d_{1} … (5.42)

8. The height of side wall above the maximum tail water depth is given by –

J = (d_{2}/3) + d_{2}’

9. Height of wing wall should be equal to the height of stilling basin’s side wall.

10. The wing wall should be inclined at 1:1 slope.

11. Length of wing wall should be equal to d_{1}’ + J.

12. The wing wall may be inclined at the angle of 45° from the centre line of the outlet.

13. The width of stilling basin at the downstream end is given by –

In which, D_{1}‘ is the slope of flare given to the side wall.

14. In order to make the structure safe against sliding, a cutoff wall of nominal depth should be provided at the end of stilling basin.

15. In the design of stilling basin the effect of entrained air should be neglected.

**Structural Design: **

Under structural design of chute spillway, the thickness of stable chute floor is determined. For this purpose, the thickness of floor is initially assumed, and stability is checked at every section of the floor for the assumed thickness. The structure is assumed to be stable, when Δ W is being greater than Δ u (i.e. Δ W > Δ u) in which Δ W is the weight of structure and Δ u is the uplift pressure due to water.

The uplift pressure over structure is calculated by drawing the pressure diagram, assuming that the pressure at the beginning of structure is equal to the depth of flow, and at the outlet end it is zero. The pressure diagram is then divided into several equal parts and area of each part is calculated. The uplift pressure is obtained by multiplying the density of water to the area of pressure diagram. For stability point of view, the value of Δ W should be greater than Δ u at all the sections.

**Check against Piping: **

Piping type failure is very common in chute spillway. It can be checked by providing the cutoff walls. Apart from above, there can also be made an additional arrangement to control piping by providing a layer of coarse sand below the structure to facilitate the drainage through the structure.

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