Scour depth Calculations

yogendra borse

Scouring is the process by which flowing water erodes sediment from the bed and banks of a river channel. The process can occur in response to changes in flow velocity, water depth, or sediment supply, among other factors. As the water flows over the bed, it exerts a shear stress on the sediment particles, which can cause them to move or be picked up and carried downstream.

Over time, the repeated erosion of sediment from the bed and banks of the river can cause the channel to deepen and widen. This can lead to changes in the flow velocity and patterns of the river, which can in turn affect the sediment transport and scouring processes.

In some cases, the scouring can lead to the formation of deep holes or pits in the river bed, known as scour holes. These can pose a hazard to navigation, as they can cause boats and other vessels to become grounded or capsized.

The appearance of scouring in a river can vary depending on a number of factors, including the type and size of sediment, the flow velocity, and the slope of the channel bed. In general, scouring can result in the exposure of bare bedrock, the formation of steep banks, and the deposition of sediment downstream of the scour hole. In extreme cases, scouring can even result in the formation of new channels or channels that deviate from their original course.

There are several methods available for calculating scour depth in open channel flow, including:

Empirical formulas: These are equations that have been developed based on experimental data and are commonly used in practice. Examples of empirical formulas include Lacey's formula, HEC-18, Froehlich's formula,and Hager's formula.

Hydraulic model tests: This involves building a physical model of the channel and testing different flow conditions to measure the scour depth. The results from the model can then be extrapolated to the actual channel.

Computational fluid dynamics (CFD): This involves using computer simulations to model the flow conditions in the channel and predict the scour depth.

Field measurements: Scour depth can also be measured directly in the field using various techniques, such as using sonar equipment, measuring sediment deposits, or conducting underwater surveys.

Semi-empirical formulas: These are equations that combine empirical data with theoretical principles, such as sediment transport theory, to predict the scour depth. Examples of semi-empirical formulas include the Briaud and Chen formula and the Melville and Coleman formula.

Empirical formulas:

Lacy's formula:- This formula is based on the principle of conservation of energy, and uses the energy dissipation rate and hydraulic geometry to predict scour depth.

In current practice in India, Lacey regime scour depth is given by equation-

$$d = 1.35\left(\frac{q^2}{f}\right)^{\frac{1}{3}}$$

Where,

f = Silt factor

q = Discharge (m3/s)

Silt factor can be evaluated using equation-

$$f = 1.76\times \sqrt{d_{mm}}$$

d_mm = dia in mm

Link for the Calculator of Silt factor

In general Lacy's formula is an empirical formula for estimating scour depth around bridge piers. It was developed by Lacy in 1934 and is based on laboratory and field data. The formula has the following form:

$$d = K_s\cdot\left(\frac{Q}{g\cdot D^{2/3}}\right)^{1/2}\cdot\left(\frac{d_{50}}{\Delta}\right)^{1/6}$$

Where,

d is the scour depth (m)

K_s is a dimensionless constant that depends on the properties of the sediment and the flow conditions

Q is the flow rate (m^3/s)

g is the acceleration due to gravity (m/s^2)

D is the depth of flow (m)

d_{50} is the median sediment grain size (m)

Δ is the size of the largest sediment that can be moved by the flow (m)

K_1, K_2, and K_3 are empirical coefficients that depend on the pier shape, sediment properties, and flow conditions.

Lacy's formula is a relatively simple formula that is easy to use and apply. However, like other empirical formulas, it has some limitations. One limitation is that it assumes that the sediment transport is dominated by bedload transport, which may not be the case in some situations. It also assumes that the flow is one-dimensional and uniform, which may not be the case in natural channels.

Additionally, the formula may not be applicable to all bridge piers, sediment types, and flow conditions, and it may require calibration based on local experience and conditions. The coefficients K_1, K_2, and K_3 may need to be adjusted for specific situations, and the formula should be validated with field measurements to ensure its accuracy.

In summary, Lacy's formula is a useful tool for estimating scour depth around bridge piers, but it should be used with caution and calibrated based on local conditions and experience. It is recommended to use it in conjunction with other methods and field measurements to ensure its accuracy.

Hager's formula:- Hager's formula: This formula uses the ratio of the sediment size to the hydraulic radius of the channel, along with other parameters, to predict scour depth.

is an empirical formula for estimating scour depth around bridge piers, and it is derived from laboratory experiments. The formula is given by:

$$d = K_s\cdot\left(\frac{Q}{g\cdot D}\right)^{0.5}\cdot\left(\frac{d_{50}}{b}\right)^{0.33}$$

where:

d is the scour depth (m)

K_s is a dimensionless coefficient that depends on the sediment properties and flow conditions (typically in the range of 1 to 3)

Q is the flow rate (m^3/s)

g is the acceleration due to gravity (m/s^2)

D is the flow depth (m)

d_{50} is the median sediment grain size (m)

b is the width of the bridge pier (m)

Hager's formula has been shown to provide reasonably accurate estimates of scour depth for a wide range of flow and sediment conditions. However, like other empirical formulas, it may not be accurate for all situations, and it should be used with caution and calibrated based on local experience and conditions.

HEC-18 formula:-

HEC-18 formula is an empirical formula for estimating scour depth around bridge piers. It was developed by the US Army Corps of Engineers and is based on laboratory and field data. The formula has the following form:

$$d = K_1\cdot\left(\frac{Q}{g\cdot D^{2/3}}\right)^{K_2}\cdot\left(\frac{d_{50}}{\Delta}\right)^{K_3}$$

K_1, K_2, and K_3 are empirical coefficients that depend on the pier shape, sediment properties, and flow conditions.

The HEC-18 formula is more complex than some other empirical formulas and takes into account more factors that can affect scour depth. However, like other empirical formulas, it has some limitations. One limitation is that it assumes that the flow is one-dimensional and uniform, which may not be the case in some situations. It also assumes that the sediment transport is dominated by bedload transport and does not account for suspended sediment transport.

In summary, the HEC-18 formula is a useful tool for estimating scour depth around bridge piers, but it should be used with caution and calibrated based on local conditions and experience. It is recommended to use it in conjunction with other methods and field measurements to ensure its accuracy.

Froehlich's formula:-This formula is based on the conservation of momentum principle, and uses the flow depth and velocity, as well as the sediment size and hydraulic geometry, to predict scour depth.

Froehlich's formula is an empirical formula for estimating scour depth around bridge piers. It was developed based on experimental data and is derived from dimensional analysis. The formula has the following form:

$$d = 0.33\cdot\left(\frac{Q}{g\cdot D}\right)^{0.5}$$

The formula assumes that the sediment transport is dominated by bedload transport, which is when sediment moves along the bed of the channel due to the force of the flowing water. It also assumes that the sediment particles are uniform and that the flow velocity is constant. These assumptions make the formula suitable for a limited range of sediment and flow conditions.

One of the limitations of Froehlich's formula is that it only considers bedload transport, whereas suspended sediment transport can also contribute significantly to scour depth in some situations. Additionally, the formula does not account for the effects of pier shape, bridge alignment, and other factors that can affect scour depth. Therefore, it should be used with caution and should not be relied upon exclusively for predicting scour depths.

Despite its limitations, Froehlich's formula can be a useful tool for providing a rough estimate of scour depth around bridge piers under certain conditions. However, it should be used in conjunction with other methods and validated with field measurements to ensure its accuracy.

Einstein's formula: This formula is based on the equilibrium between the erosive shear stress and the resisting bed material strength, and uses the sediment size and flow velocity to predict scour depth.

$$d = K_s \left(\frac{\tau}{\gamma_s - \gamma} \right)^{1/2}$$

where:

d is the maximum scour depth

K_s is a dimensionless coefficient that depends on the sediment size and shape

て is the bed shear stress

⋎_s is the specific weight of sediment particles

⋎ is the specific weight of water

The bed shear stress can be calculated using the following formula:

$$\tau = \rho g Hf$$

where:

ρ is the density of water

g is the acceleration due to gravity

H is the flow depth

f is the Darcy-Weisbach friction factor

Einstein's formula is often used to predict scour depth around bridge piers and other hydraulic structures. It is a semi-empirical formula that combines theoretical principles with empirical data to estimate scour depth. The formula has some limitations, such as the assumption that the bed material is uniform and that the flow is steady and uniform. Field measurements and physical modeling should be used to validate the predictions of Einstein's formula.

Hydraulic Model Tests:

Hydraulic model tests are physical experiments that simulate the behavior of water in a scaled-down physical model of a hydraulic structure or system. They are commonly used in engineering and design to investigate the performance of hydraulic structures such as dams, spillways, river channels, and bridge piers.

The hydraulic model is constructed to scale, meaning that its dimensions are reduced proportionally from those of the full-scale structure. The model is then placed in a hydraulic laboratory or testing facility, where water is pumped through it to simulate the flow conditions that the structure will be subjected to in real-world situations. Data is collected through instruments and sensors that measure various hydraulic parameters such as water levels, velocities, and pressures.

Hydraulic model tests can provide valuable information for the design and operation of hydraulic structures. They can help engineers to identify potential problems and optimize the design of the structure before it is constructed at full scale. Model tests can also be used to evaluate the effectiveness of various design alternatives and to verify the accuracy of computer simulations.

However, hydraulic model tests also have some limitations. The main limitation is that the behavior of water in the model may not perfectly replicate the behavior of water in the full-scale structure due to scale effects. Scale effects arise from the fact that the physical properties of water and the laws of physics do not always behave the same way at different scales. Therefore, the results of hydraulic model tests must be carefully extrapolated to full-scale conditions and validated with field measurements.

Overall, hydraulic model tests are an important tool for the design and operation of hydraulic structures, but they should be used in conjunction with other methods and approaches, and their limitations and uncertainties must be carefully considered.

Computational fluid dynamics (CFD):

Computational fluid dynamics (CFD) is a branch of engineering and science that uses numerical analysis and algorithms to simulate and solve problems related to the behavior of fluids. CFD is based on the fundamental equations that govern fluid motion, including the Navier-Stokes equations and the continuity equation, and uses computational methods to discretize these equations and solve them numerically.

CFD has become a widely used tool for simulating fluid dynamics in a variety of applications, including aerospace, automotive, energy, environmental engineering, and biomedical engineering. Some examples of CFD applications include aerodynamic simulations of aircraft, combustion modeling in engines, ocean current modeling, and blood flow simulations in human organs.

One of the main advantages of CFD is its ability to provide detailed information on complex fluid behavior that may be difficult or impossible to measure experimentally. CFD simulations can provide insights into flow patterns, turbulence, pressure distributions, and other fluid properties that can help to optimize the design of hydraulic structures, improve the performance of industrial processes, and enhance our understanding of fluid dynamics in natural systems.

However, CFD also has some limitations and challenges. The accuracy and reliability of CFD simulations depend on several factors, including the accuracy of the underlying mathematical models, the quality of the numerical methods used to solve the equations, and the accuracy and completeness of the input data. CFD simulations can also be computationally expensive and require significant computational resources and expertise.

Overall, CFD is a powerful tool for simulating fluid dynamics and has a wide range of applications in engineering and science. However, it should be used with caution and validated with experimental data when possible to ensure its accuracy and reliability.

Field measurements:

Field measurements for scour depth involve collecting data from an existing hydraulic structure or system, such as a bridge or a river channel, to determine the depth of scour that has occurred at the structure's foundation. These measurements are important for assessing the stability and safety of the structure and for designing appropriate mitigation measures to prevent further scour.

There are several methods for measuring scour depth in the field, including:

Bathymetric surveys: This involves using sonar or other instruments to measure the depth of the water and the topography of the river bed. The data collected can be used to create a three-dimensional map of the river bed and identify areas of scour.

Acoustic Doppler Current Profilers (ADCP): This involves using an instrument that measures the velocity of the water and can detect changes in the river bed caused by scour.

Sediment probes: These are probes that can be inserted into the river bed to measure the depth of sediment layers and the depth of the scour hole.

Divers: In some cases, divers can be used to physically inspect the foundation of the structure and measure the depth of the scour hole.

Remote sensing: This involves using aerial photography, satellite imagery, or LiDAR to detect changes in the topography of the river bed and identify areas of scour.

Field measurements for scour depth can provide valuable information for assessing the safety and stability of hydraulic structures and for designing appropriate mitigation measures. However, these measurements can also be challenging and require specialized equipment and expertise. They should be conducted with caution to ensure accurate and reliable data is collected.

Semi-Empirical formulas:

Briaud and Chen formula:- This formula is based on the energy approach and uses the hydraulic geometry of the channel, flow velocity, and sediment size to predict scour depth. The formula is expressed as:

$$d = K_b \frac{Q^{2/3}}{g^{1/3}b^{4/3}}D_{50}^{1/3}$$

where:

d is the maximum scour depth

K_b is a dimensionless coefficient that depends on the channel geometry

Q is the flow discharge

g is the acceleration due to gravity

b is the width of the channel

D_{50} is the median grain size of the bed material

Melville and Coleman formula: This formula is based on the conservation of momentum principle and uses the flow velocity, flow depth, and sediment size to predict scour depth. The formula is expressed as:

$$d = K_m \left(\frac{V^2D_{50}}{g}\right)^{1/3} D_{50}$$

where:

d is the maximum scour depth

K_m is a dimensionless coefficient that depends on the flow conditions and sediment properties

V is the flow velocity

D_{50} is the median grain size of the bed material

g is the acceleration due to gravity

Both Briaud and Chen formula and Melville and Coleman formula have been shown to be effective in predicting scour depth around hydraulic structures, but they also have some limitations and assumptions that should be taken into consideration when using them. Field measurements and physical modeling should be used to validate the predictions of these formulas.

Median sediment grain size (D50)

Sieve analysis is a commonly used method for determining the particle size distribution of a sediment sample. It involves passing the sediment through a series of sieves with progressively smaller mesh sizes, and measuring the weight of sediment retained on each sieve.

To find the median sediment grain size (D50), the cumulative weight percentage of sediment retained on each sieve is plotted against the logarithm of the sieve opening size. The resulting curve is called a grain-size distribution curve or a cumulative particle-size distribution curve.

The median grain size (D50) is the size at which 50% of the sediment is finer and 50% is coarser. It can be read directly from the grain-size distribution curve by locating the point at which the cumulative percentage passing is 50%.

Alternatively, the median grain size can be calculated using the following formula:

$$D_{50} = 2^{\frac{\sum_{i=1}^n w_i \log_2 d_i}{\sum_{i=1}^n w_i}}$$

where:

n is the number of sieve sizes

w_i is the weight of sediment retained on the i-th sieve

d_i is the diameter of the i-th sieve opening

Sieve analysis is a relatively simple and inexpensive method for determining the median grain size of a sediment sample, and it is widely used in both laboratory and field settings. However, it does have some limitations, such as the assumption of spherical particle shapes and the potential for particle breakage during sieving. Other methods, such as laser diffraction and sedimentation analysis, may be used in conjunction with sieve analysis to obtain a more complete picture of the particle size distribution.

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Scour depth Calculations