Free Essay On Hydrostatic Equilibrium And Its Application In Civil Engineering
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Fluid mechanics involves the application of the principles of forces and motions to liquids and gases (fluids).Based on the laws of motions we have two distinct categories of fluid mechanics which are hydrostatics and fluid dynamics. In hydrostatics the study involves the characteristics of the fluid at rest and the resultant pressure exerted by a body that is introduced into the fluid by immersion. Numerical models form a very integral part in dam construction modeling and design. Concrete dams rely mainly on their weight for stability and are categorized as gravity dams. The most common material used in the construction of the gravity dams was cement-concrete. There are important considerations to make when constructing gravity dams such as design, foundation and the structural integrity. This article examines the application of hydrostatic equilibrium in the design and construction of concrete gravity dams. The forces that are existent in the dam are considered in the design of the dams. There are forces that arise from the fluid on one hand and forces that are due to the dam and its composite structure. The walls of gravity dams are triangular in nature and are thickest at the bottom. The pressure due to the water head in the reservoir is highest at the bottom since pressure is directly proportional to the height of water column. Pressures due to the upward and downward streams are also factored into the dam design. In addition to the forces design and analysis, this article looks at dam failure (example of Austin Dam) and failure mitigation.
Gravity dams are mostly concrete dams. The dams are built to store water for electricity generation, irrigation or domestic use. Hydrostatic Pressure is the measure of force resisted by the structures against some hydraulic forces. The stability and reliability of the dam structures depends on the ability of the structures to resist the externally applied hydrostatic pressure. In the design of concrete dams, consideration of various construction materials is done in the primary stages. Material availability and suitability needs to be ascertained. For stability of the dam, the following criteria need to be ensured: that it is safe against overturning at the base or below the base, ensure that the structure is sliding-averse against any forces and that tolerable stresses are not exceeded. The specific areas to be carefully examined are the gates, upstream and downstream slope transitions. The major surmise is the hydraulic principle that pressure from the fluid at a specific point acts in all directions and that the pressure needs to be resolved normally to the surface of the plane.
There are several forces that act on the membrane of the concrete gravity dam under hydrostatic conditions which include: internal water pressure, both the upstream and downstream pressure, and the weight of the material with which the dam was constructed. The pressure resultant from the water in the reservoir may be calculated by the law of hydrostatics. This means that the pressure at any depth h is given by γh kN/m² and is perpendicular to the surface.
P= γh kN/m; where h is the water height measured from the bottom.
The other consideration in modeling is the uplift pressure. Uplift forces result from internal pressure in cracks and seams in the body of the dam. The pressure is considered in both upstream and downstream as:
P= γhu; for upstream pressure and hu is the depth of water above the plane
P= γhd; for downstream pressure and hd is the depth of water above the plane
It is advisable not to ignore the non-hydrostatic pressure while carrying out the hydrostatic modeling. The main fluid dynamics in consideration in the gravity dams is the wave pressure which is produced by the shearing action of wind blowing over the water surface. The magnitude of the force relies mainly on the size of the waves and the speed of the wind. The other consideration is the possibility of occurrence of earthquakes and how the dam materials may stand against the seismic forces. The linear dynamic equation for the dam is given as:
MÜ + CŮ + KU = P (t)
While, the linear dynamic equation for the water is given as,
GÜ + LŮ + HU = R (t)
In which case M, C, K, Ü, Ů, U, and P (t) are the mass, damping, stiffness, acceleration, velocity, displacement and exciting force on the dam. G, L, H, Ü, Ů, U, and P (t) are the mass, damping, stiffness, acceleration, velocity, displacement and exciting force on the reservoir. (Adedeji, 2004)
There are several forces that act on the dam structure namely: water pressure, earthquake (seismic) forces, Silt Pressure, Waves pressure, ice pressure and dam’s own weight. The most important consideration and analysis is focused on water pressure and the dam’s weight. Seismic forces result in waves that may move in any direction and hence in design, they are resolved into the vertical and horizontal directions. Silt pressure is the pressure which results due to the amount of silt deposited at the bed of the dam. It is usually very minimal in terms of impact and magnitude. Another type of pressure consideration is ice pressure which is minimal in design impact. Ice pressures occur in extremely cold countries where ice may be formed in dams. The blocks of ice may release pressures in the dam and is dependent on temperature variations. The weight of dam and its component structures is a major force.
An example of how a failure to accurately determine and design for the forces can result in disaster is the Austin Dam Failure of 1900s where several people lost their lives as a result of dam failure. This was an example of sliding failure. The pressures that resulted from the increasing water heights resulting in the overturning of the walls of the dam. Just like the case of Austin Dam, there several causes of gravity dam failures. The causes include hydraulic failures, seepage, stresses and earthquakes. Failures could occur when foundations of the dams deteriorate. Failures due to operations of the dam are rare. Most failures are due to poor material or underestimation of forces that could result from water heights and flooding. According to the US Association of Dam Safety, 34% of dam failures result from overtopping resulting from poor design, 30% failures result from foundation defects while 20% of failures are accounted for by internal erosion (seepage). The other causes of dam failures include mechanical structure failure and inadequate maintenance.
Failures can be mitigated by the employment of experienced dam contractors and material testing as well as computerized simulations and modeling. Mathematical and scientific calculations can be used to analyze the possible impact of forces on the dam structures. The calculations can be used to give recommendations on inward and outward flow speeds, retention levels of water, the size of the dam walls from top to bottom, the type of materials and their mechanical properties and the probabilities of failures. With such knowledge, the dams can today be constructed with high degrees of operational and mechanical accuracy.
Gravity dams are good examples of how hydrostatic analysis can be applied in Civil Engineering. The forces that act on the dam at static conditions are diagnosed and analyzed to ensure that the resultant dam is stable and strong against both the static and dynamic forces that may occur. The dam construction considers several factors such as both hydrostatic and non-hydrostatic forces. Non-hydrostatic forces originate from waves and water movement in the reservoir. Under hydrostatic conditions the dam’s construction and behavior considerations need to take care of the shape, height and cross-sectional area. High pressures can result in deformation of rigid dams. The tension in the dam increases with the increase in dam height and the perimeter length. Numerical models form a very integral part in dam construction modeling. Concrete dams rely mainly on their weight for stability and the important considerations to make when constructing gravity dams are design, foundation and the structural integrity. When the forces are not properly factored in dam failures such as breakages and overturning could occur as with the case of Austin Dam. Proper consideration for the dam materials needs to be made. The materials’ resistances to hydraulic and thermal stresses are key factors to be considered.
Ferziger, Joel H. & Perić, Milovan. Computational Methods for Fluid Mechanics. Berlin: Springer, 2002. Print.
Garg, Santosh K. Irrigation Engineering and Hydraulic Structures. New Delhi: Khanna Publishers, 2010. Print.
Kundu, Pijush K. & Cohen, Ira M. Fluid Mechanics. New York: Academic Press, 2002. Print.
Kreyszig, Erwin, (1999). Advanced Engineering Mathematics. New York: John Wiley & Sons, Inc., 1999. Print.
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