A dam is a barrier that is constructed across a river or stream so the water can be held back or impounded to supply water for drinking or irrigation, to control flooding, and to generate power. The main kinds of dams are earth fill, rock fill, concrete gravity, concrete arch, and arch gravity. The last three types are all made of concrete, reinforced concrete, or masonry. (The term masonry can mean concrete, bricks, or blocks of excavated rock). Fill dams include all dams made of earth materials (soil and rock) that are compacted together. One type of fill dam called a tailings dam is constructed of fine waste that results from processing rock during mining; at mine sites, this soil-like waste is compacted to form an embankment that holds water for the mining and milling processes or to retain the tailing themselves in water. Gravity dams are solid concrete structures that maintain their stability against design loads from the geometric shape and the mass and strength of the concrete. Generally, they are constructed on a straight axis, but may be slightly curved or angled to accommodate the specific site conditions. Gravity dams typically consist of a non-overflow section and an overflow section or spill- way. Earthquakes have affected several large concrete dams in the past. Although no catastrophic failure has yet been reported unless a dam crossed a fault, historical events have shown that severe seismic damage could be imparted to concrete dams. Gravity dams are structures that rely on their own weight for resistance against sliding and overturning to maintain stability.
A gravity dam should be constructed of concrete that will meet the design criteria for strength, durability, permeability, and other required properties. Because of the sustained loading generally associated with them, the concrete properties used for the analyses of static loading conditions should include the effect of creep. Properties of concrete vary with age, the type of cement, aggregates, and other ingredients as well as their proportions in the mix. Since different concretes gain strength at different rates, measurements must be made of specimens of sufficient age to permit evaluation of ultimate strengths. Although the concrete mix is usually designed for only compressive strength, appropriate tests should be made to determine the tensile and shear strength values (Dowdell, 2004).
Poisson’s ratio, the sustained modulus of elasticity of the concrete, and the latter’s ratio to the deformation modulus of the foundation have significant effects on stress distribution in the structure. Values of the modulus of elasticity, although not directly proportional to concrete strength, do follow the same trend, with the higher strength concretes having a higher value for modulus of elasticity. As with the strength properties, the elastic modulus is influenced by mix proportions, cement, aggregate, admixtures, and age. The deformation that occurs immediately with application of load depends on the instantaneous elastic modulus. The increase in deformation which occurs over a period of time with a constant load is the result of creep or plastic flow in the concrete. The effects of creep are generally accounted for by determining a sustained modulus of elasticity of the concrete for use in the analyses of static loadings. Instantaneous moduli of elasticity and Poisson’s ratios should be determined for the different ages of concrete when the cylinders are initially loaded. The sustained modulus of elasticity should be determined from these cylinders after specific periods of time under constant sustained load. These periods of loading often 365 and 730 days. The cylinders to be tested should be of the same size and cured in the same manner as those used for the compressive strength tests.
The effects of temperature change in gravity dams are not as important in the design as those in arch dams. However, during construction, the temperature change of the concrete in the dam should be controlled to avoid undesirable cracking. Thermal properties necessary for the evaluation of temperature changes are the coefficient of thermal expansion, thermal conductivity, specific heat, and diffusivity. The coefficient of thermal expansion is the length change per unit length for 1 degree temperature change. Thermal conductivity is the rate of heat conduction through a unit thickness over a unit area of the material subjected to a unit temperature difference between faces. The specific heat is defined as the amount of heat required to raise the temperature of a unit mass of the material by 1 degree. Diffusivity of concrete is an index of the facility with which concrete will undergo temperature change. The diffusivity is calculated from the values of specific heat, thermal conductivity, and density. Appropriate laboratory tests should be made of the design mix to determine all concrete properties.
No data are yet available to indicate what the strength characteristics are under dynamic loading.
Until dynamic modulus information is available, the instantaneous modulus of elasticity determined for concrete specimens at the time of initial loading should be the value used for analyses of dynamic effects.
Necessary values of concrete properties may be estimated from published data for preliminary studies until laboratory test data are available. Until long-term tests are made to determine the effects of creep, the sustained modulus of elasticity should be taken as 60 to 70 percent of the laboratory value for the instantaneous modulus of elasticity. Criteria-If no tests or published data are available, the following average values for concrete properties may be used for preliminary designs until test data are available for better results
Foundation deformations caused by loads from the dam affect the stress distributions within the dam. Conversely, response of the dam to external loading and foundation deformability determines the stresses within the foundation. Proper evaluation of the dam and foundation interaction requires as accurate a determination of foundation deformation characteristics as possible. Although the dam is considered to be homogeneous, elastic, and isotropic, its foundation is generally heterogeneous, inelastic, and anisotropic. These characteristics of the foundation have significant effects on the deformation moduli of the foundation. The analysis of a gravity dam should include the effective deformation modulus and its variation over the entire contact area of the dam with the foundation. The deformation modulus is defined as the ratio of applied stress to elastic strain plus inelastic strain and should be determined for each foundation material. The effective deformation modulus is a composite of deformation moduli for all materials within a particular segment of the foundation. Good compositional description of the zone tested for deformation modulus and adequate geologic logging of the drill cores permit extrapolation of results to untested zones of similar material (Pataki, 1885).
Criteria- The following foundation data should be obtained for the analysis of a gravity dam:
Resistance to shear within the foundation and between the dam and its foundation depends upon the cohesion and internal friction inherent in the foundation materials and in the bond between concrete and rock at the contact with the dam. These properties are determined from laboratory and in situ tests. The results of laboratory triaxial and direct shear tests, as well as in situ shear tests, are generally reported in the form of the Coulomb equation:
R = C.A + N. tan φ
(Shear resistance) = (unit cohesion times area) +
(Effective normal force times coefficient of internal friction)
Analysis of a dam foundation requires knowledge of the hydrostatic pressure distribution in the foundation. Permeability is controlled by the characteristics of the rock type, the jointing systems, the shears and fissures, fault zones, and, at some dam sites, by solution cavities in the rock. The exit gradient for shear zone materials that surface near the downstream toe of the dam should also be determined to check against the possibility of piping. Laboratory values for permeability of sample specimens are applicable only to the portion or portions of the foundation that they represent. Permeability of the aforementioned geologic features can best be determined by in situ testing. The permeability obtained is used in the determination of pore pressures for analyses of stresses, stability, and piping. Such a determination may be made by several methods including two- and three dimensional physical models, two- and three-dimensional finite element models, and electric analogs (Xie, 2011).
Compressive strength of the foundation rock can be an important factor in determining thickness requirements for a dam at its contact with the foundation. Where the foundation rock is non-homogeneous, tests to obtain compressive strength values should be made for each type of rock in the loaded portion of the foundation. A determination of tensile strength of the rock is seldom required because unhealed joints, shears, etc., cannot transmit tensile stress within the foundation.
During the recent years, the seismic behavior of concrete gravity dams was in the centre of Consideration of dam engineers. Numerous researches have been conducted in order to determine how the dams behave against the seismic loads. Many achievements were obtained in the process of analysis and design of concrete dams including dam-reservoir-foundation interaction during an earthquake. The earthquake response of concrete gravity dam-reservoir-foundation system has been addressed to study the effect of foundation flexibility and reservoir water body on the seismic response of concrete gravity dams. Safety evaluation of dynamic response of dams is important for most of researchers. When such system is subjected to an earthquake, hydrodynamic pressures are developed on upstream face of the dam due to the vibration of the dam and reservoir water. Consequently, the prediction of the dynamic response of dam to earthquake loadings is a complicated problem and depends on several factors, such as interaction of the dam with rock foundation and reservoir, the computer modelling and material properties used in the analysis (Edward, 1908).
Gravity dams are very important structures. The collapse of a gravity dam due to earthquake ground motion may cause an extensive damage to property and life losses. Therefore, the proper design of gravity dams is an important issue in dam engineering. An integral part of this procedure is to accurately estimate the dam earthquake response. The prediction of the actual response of a gravity dam subjected to earthquake is a very complicated problem. It depends on several factors such as dam-foundation interaction, dam-water interaction, material model used and the analytical model employed. In fluid-structure interaction one of the main problems is the identification of the hydrodynamic pressure applied on the dam body during earthquake excitation. The analysis of dam reservoir system is complicated more than that of the dam itself due to the difference between the characteristics of fluid and dam’s concrete on one side and the interaction between reservoir and dam on the other side.
The earthquake response of concrete gravity dam-reservoir-foundation system has been addressed to study the effect of foundation flexibility and reservoir water body on the seismic response of concrete gravity dams. Safety evaluation of dynamic response of dams is important for most of researchers. When such system is subjected to an earthquake, hydrodynamic pressures are developed on upstream face of the dam due to the vibration of the dam and reservoir water. Consequently, the prediction of the dynamic response of dam to earthquake loadings is a complicated problem and depends on several factors, such as interaction of the dam with rock foundation and reservoir, the computer modeling and material properties used in the analysis.
FEM modeling of concrete gravity dams is a method with a lot of advantages compared to traditional structural dynamics and scale modeling. Compared to scale modeling the time and cost issue is the main factor, it is a lot cheaper to construct a virtual model than a physical one. Also the convenience of computer based models compared to the location and rarity of scale models provide a significant advantage. Compared to structural mechanics FEM has a big advantage in the alteration of both construction and external loads. Once a dam has been modeled in FEM it is possible to experiment and change details about it without the need to restart the whole process.
This is still just an analysis of a single section in a static state of a dam; a lot of aspect is because of that limitation not dealt with at all. Examples of these aspects are: discharge capacity, temperature changes, cracks, earthquakes and fatigue of the concrete. FEM means Finite Element Method and it is a way of turning real life objects, such as a dam construction, to a computable model. In the FEM the object is divided into smaller elements which are calculated separately, preferably by a computer. It is the density and shapes of these elements that determines the accuracy of the FEM-model. From advanced mathematical models to simple models made of for example clay, they are still just models. Models can be more or less accurate, but they will never behave exactly as reality would.
The size and shape of elements is utterly important, and some basic standards have been set up to make it easier to create well-functioning elements. The two most common types of two-dimensional elements are quad and tri elements. Tri elements are made from three different nodes and contain only one integration point while quads, as implied by their name, are made of four nodes and contain four integration points. The height-width relation should not exceed three to one, for the quad elements, and no interior angle should be less than 45 degrees. In practice the limit may be reduced to 30 degrees and the result will still be acceptable. According to the two shape standards above, the most precise element has the height-width ratio of one to one and all interior angles 90 degrees, the perfect square. Usually, fitting all elements into these standards is impossible and not even that important, a small percentage of the elements may remain distorted. The element standards in critical regions of the model where the mesh may also possibly be denser. Minor alteration in the model’s geometry can be made, in such a way that they generate no significant difference in the results.
Selection of the method of analysis should be governed by the type and configuration of the structure being considered. The gravity method will generally be sufficient for the analysis of most structures; however, more sophisticated methods may be required for structures that are curved in plan, or structures with unusual configurations.
The gravity method assumes that the dam is a 2 dimensional rigid block. The foundation pressure distribution is assumed to be linear. It is usually prudent to perform gravity analysis before doing more rigorous studies. In most cases, if gravity analysis indicates that the dam is stable, no further analyses need be done. A Stability criteria and required factors of safety for sliding are required.
In most cases, the gravity analysis method discussed above will be sufficient for the determination of stability. However, dams with irregular geometries or spillway sections with long aprons may require more rigorous analysis. The Finite Element Method (FEM) permits the engineer to closely model the actual geometry of the structure and account for its interaction with the foundation. Note that the thinning spillway that forms the toe of the dam is not stiff enough to produce the foundation stress distribution assumed in the gravity method. In this case, gravity analysis alone would have under-predicted base cracking.
However, it is implicitly assumed that shear stress is distributed uniformly across the base. This assumption is arbitrary and not very accurate. Finite element modeling can give some insight into the distribution of base contact stress. Shear stress is at a maximum at the tip of the propagating base crack. In this area, normal stress is zero, thus all shear resistance must come from cohesion. Also, the peak shear stress is about twice the average shear stress. An un-zipping failure mode can be seen here, as local shear strength is exceeded near the crack tip, the crack propagates causing shear stress to increase in the area still in contact.
Dynamic analysis refers to analysis of loads whose duration is short with the first period of vibration of the structure. Such loads include seismic, blast, and impact. Dynamic methods are appropriate to seismic loading. Because of the oscillatory nature of earthquakes, and the subsequent structural responses, conventional moment equilibrium and sliding stability criteria are not valid when dynamic and pseudo dynamic methods are used. The purpose of these investigations is not to determine dam stability in a conventional sense, but rather to determine what damage will be caused during the earthquake, and then to determine if the dam can continue to resist the applied static loads in a damaged condition with possible loading changes due to increased uplift or silt liquefaction. It is usually preferable to use simple dynamic analysis methods such as the pseudo dynamic method or the response spectrum method (described below), rather than the more rigorous sophisticated methods.
The model includes all the nodes, elements, material properties, real constants, boundary conditions and other features that are used to represent the physical system. First model will be generated then specific boundary conditions will be applied on the specific nodes then final analysis will be conducted.
In the present work two types of opening shapes are considered, one is square and second is circular. Different sizes of the openings are also considered in the present work. Two different sizes for square opening and different sizes of circular opening are considered. Table below shows the dimensions of the openings.
Table 1 Openings dimension
|
Dimensions: square opening (m) |
Dimensions: circular opening (m) |
||
|
W × H |
3.5 × 3.5 |
R |
2 |
|
W × H |
5.3 × 5.3 |
R |
3 |
To analyses the effect of opening two shapes of openings are considered circular and square. Dimension of the opening are also varied to study its effect on the stress and deformation generated on the dam.
Deformation and Equivalent stress for 2mm radius circular opening
Above figures show deformation and stress results for 2mm circular opening radius. Red colour shows the regions where highest values of stress and deformation generated while blue colour shows regions where least values of stress and deformation generated. It can be observed from the figures that at the centre of the dam maximum amount of deformation is generating and it gradually decreasing towards the corner of the dam. Below figures shows the comparison of the deflection and stress generated in the dam for different size of circular and square openings.
Below figures shows the comparison of the circular and square opening for same area of hole in the dam. Comparison of stress and deflection generated is conducted.
Conclusion
References
Dowdell, D.J., & Benedict H. F., (2004), Practical Aspects of Engineering Seismic Dam Safety Case Study of A Concrete Gravity Dam, 13th World Conference on Earthquake Engineering, 1-6.
Pataki, G.E., & Cahill, J. P., (1885), Guidelines for Design of Dams, New York State Department of Environmental Conservation, 1-24.
Xie, K-Z., Meng, F-C, Zhang. J-S, & Zhou, R-Y., (2011), Seismic response analysis of concrete arch dam in consideration of water compressibility, Electric Technology and Civil Engineering, 6850-6853.
Edward W. C. E., (1908), “The Design and Construction of Dams”, “New York John Wiley & Sons”.
Khosravi, S, & Heydari, M.M., (2015), Design and Modal Analysis of Gravity Dams by Ansys Parametric Design Language, Engineering and Physical Science, 12(2).
Mohsin, A.Z., Omran, H.A, & Al-Shukur A.B., (2015), Optimum Design of Low Concrete Gravity Dam on Random Soil Subjected to Earthquake Excitation, International Journal of Innovative Research in Science, Engineering and Technology, 8961-8973.
Zeng, C., Hao, D., Hou, L., Pan, W., & Su, H., (2015), Seismic Performance of Non-overflow Gravity Dam Considering Dam-rock Coupling Effect, AASRI International Conference on Industrial Electronics and Applications, 171-174.
Ajaya D., Girija K. & Raj, A., (2015), Static Analysis and Safety Evaluation of an Arch Dam, International Journal of Innovative Research in Science, Engineering and Technology, 8369-8372.
Patil, S.V., (2015), Effect of Soil Structure Interaction on Gravity Dam, International Journal of Science, Engineering and Technology Research, 1046-1053.
Al-Suhaili, R.H.S., Ali, A.M., & Behaya, S.A.K., (2014), Artificial Neural Network Modeling for Dynamic Analysis of a Dam-Reservoir-Foundation System, International Journal of Engineering Research and Applications, 121-143.
Ferdousi, A., Gharabaghi, A.R.M., Ahmadi, M.T., Chenaghlou, M.R., & Tabrizi, M.E., (2014) Earthquake Analysis of Arch Dams Including the Effects of Foundation Discontinuities and Proper Boundary Conditions, Journal of Theoretical and Applied Mechanics, 579-594.
Gupta, V., Waghmare, V., Dhadse, G., Hate, A., Ghumde A., & Uttarwar, A., (2014), Study of Structural Behaviour of Gravity Dam with Various Features of Gallery by FEM, ACEE International Journal on Civil and Environmental Engineering, 7-14.
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