The Optimization of Section of Embankment Dams with Multiple Platforms and Rock Foundation through Bee Colony Optimization Method

Transcription

1 J. Appl. Environ. Biol. Sci., 5(9)6-6, 05 05, TextRoad Publication ISSN: Journal of Applied Environmental and Biological Sciences The Optimization of Section of Embankment Dams with Multiple Platforms and Rock Foundation through Bee Colony Optimization Method Nader Barahmand, Ebrahim Dini Assistant Professor, Department of Civil Engineering, Larestan Branch, Islamic Azad University, Iran M.S Student, Department Of Civil Engineering, Larestan Branch, Islamic Azad University, Iran Received: May, 05 Accepted: July, 05 ABSTRACT The embankment dams are one the most significant and costliest civil structures to which a major portion of national budget are assigned. The cost of constructing embankment dams is directly proportional to the size of earthworks needed to build them the latter of which depends upon the cross-section of embankment dams. As a result, the smaller sections of embankment dams are proportionally associated with less earthworks and less construction costs. On one hand, attaining the most optimal section for embankment dams to satisfy stability and executive requirements and minimize the size of earthworks is highly difficult and somehow impossible through the traditional methods of designing embankment dams.in the present study, the main problem is to study the effects of using the bee colony algorithm in optimization of the size of earthworks for embankment dams. In this regard, different platforms were constructed to develop distinctive cases in designing the section of the dam which significantly reduced the size of earthworks. In addition, the collection of obtained results and representing them as linear diagrams will satisfy the designing requirements of different types of embankment dams along with considering the predominant conditions of the problem. For instance, one can observe the size of earthworks needed in different heights of the dam lake by reference to the associated diagrams and determine the levels of confidence in different normal heights. One can also extract the necessary information based on the types of materials used in the dam body through reference to associated diagrams. KEYWORDS: embankment dam, slope stability, stability, clone bee algorithm, stone foundation, optimization INTRODUCTION In the present study, the main objective is to find a section of embankment dams which satisfy the stability conditions and executive aspects while demanding the least size of earthworks. This can be done by constructing platforms of different widths and various levels of the body of embankment dams. This issue has been schematically represented in figure (). Therefore, the application of normal methods of designing embankment dams makes the achievement of an optimal section with proper arrangement of platforms a difficult and time-consuming task. As a result, the solution of this problem and attaining more optimal sections for embankment dams demand the application of optimization methods. On the other hand, the large number of existing variables in this problem doesn t provide the possibility of using classic optimization methods and one has to metaheuristic methods which may not develop and absolute optimal solution but a near-absolution optimal one. These methods are used in solving complicated optimization problems, especially different optimization problems in different fields of engineering, although they are not widely applied in Geotechnics and its associated problems.[],[],[3],[4] In the present study, the optimization instrument of bee colony algorithm used by artificial bees to find the shortest path as modeled from nature is used to solve the problem of optimizing the determination of optimal section of embankment dams. [5],[6],[7],[8]. *Corresponding Author: Ebrahim Dini, M.S Student, Department Of Civil Engineering, Larestan Branch, Islamic Azad University, Iran. 6

2 Barahmand and Dini, 05 Figure.-A View of Platform Effect upon Reduction of Size of Earthworks It should be noted that the present study is a constrained optimization problem the objective of which is quantification, namely finding a section with the least cross-section. First, the problem graph is developed based on figure (). As a search field for artificial bees to find the shortest path, this graph is made of a number of decision points which are the geometrical parameters of the problem introduced later on. Each decision point is made of a number of decision choices developed by discretization of the values of each variable which refers to the variation range of geometrical parameters. After preparing the problem graph, the artificial bees are directed towards this graph and pass some ways toward the graph in a randomized manner. It should be noted that each pathway represents the geometrical characteristics of one of the possible cases of the section of embankment bank which might be in the upstream or downstream of the dam without considering any platform or by considering a definite number of platforms. Then, a bee dance is done on passed-across points of the pathways for each bee based on the quality of that pathway (calculation of the level of cross section in objective function). In this regard, the pathways with higher quality (lower cross-section) have a higher level of dance and as a result, higher possibility in the next iterations. [],[9] Figure.-A General View of Applied Graph in Bee Colony Optimization Algorithm It should be noted that the pathways which do not satisfy the secondary conditions of the problem are excluded by defining heavy fines. Then, in the second iteration, the artificial bees are directed toward the graph but they select some pathways in a randomized manner. Of course, the second iteration is accompanied by higher possibility of selecting more optimal pathway points crossed compared with the first iteration. This process continues until all bees are inclined toward the more optimal pathway (i.e. the least obtained value in the objective function along with satisfying all primary and secondary conditions). As a result, the most optimal solution is 7

3 J. Appl. Environ. Biol. Sci., 5(9)6-6, 05 determined for the problem of defining the least size of earthworks for the embankment dam with considering the design and engineering requirements in addition to maintaining structural stability against the applied loads and prevention of structural collapse based on the levels of confidence.[0],[5],[9].characteristics of Parameters for Model of Optimal Section Determination The necessary data for the problem which should be collected by the user are called primary information which include the height of lake behind the dam, mechanical properties and type of earth materials used in the body of the dam as well as the climatic conditions of the region and coefficient of friction between the interface of the foundation and body of the dam. The height of the lake behind the dam is measured in meter and represented by letter h. It is inserted by the user as the primary information of the project. The addition of free water height represented as FB (i.e. abbreviation of free board) to it leads to obtaining the basis of final height of the dam represented by letter H. The specific gravity of different earth materials used in the dam body (kg.m 3 ) represented by γ is the second variable included in primary information. The coefficient of cohesion (kg.m 3 ) represented by letter C, repose angle of the soil (based on degree) represented by Ø, the wind speed (km. h) represented by letter V, the wind runup (km) represented by letter F, and dimensionless coefficient of friction in stationary state represented by μare the other associated variables included in the primary information.[] The problem of optimizing the section of embankment dams is the objective function A (the sectional area of embankment dam) which is represented as a function of the vector of problem variables described in the following. In the problem of defining the optimal section of embankment dam, the objective function is the area of the section of embankment dam and the objective is quantification, namely finding a cross-section for an embankment dam which satisfies the conditions of dam s stability, the least cross-section and the least size of earthworks. The variables of this problem include n, bi s, hi s, ai s and H as represented in figure (3.3).[3] n: number of upstream and downstream platforms (due to symmetry in reverse counting of platforms, each level is only counted once. bi: the width of i th platform in upstream or downstream slope (m) hi: the height of i th platform in upstream slope from level on previous platform (m) iα: the slope of i th region of embankment dam in upstream or downstream (degree) Figure.3-Representation of Sectional Variables of Embankment Dam with Three Upstream Platforms and Three Downstream Platforms Based on the existence of these variables, the graph represented in figure (3) is developed for the intended section. The transmission of artificial means on this graph and identification of graph node leads to determination of parameters of optimal section of embankment dam in a section with three upstream and downstream platforms. In regard to search field (i.e. variation range of parameters), one should prevent from ranges in which it is impossible to find possible solutions. For the intended problem, the range of bi variable representing the width of upstream and downstream platform is selection between 4 to 0 meters. It should be noted that the least width of platforms based on defined executive problems is determined based on the maximum normal width of the platforms in Iran. In 8

4 Barahmand and Dini, 05 addition, the range of hi s representing the height of upstream and downstream platforms from previous one was selected to be from 5 meters to H. It is noteworthy that H denotes the height of crest of embankment dam. The variation range of a angle was from the placement angle of shell materials to 30 degrees. [3] Figure.4-Graph of Sections in Embankment Dam with Three Upstream and Downstream Platforms Therefore, the above-mentioned set of limitations are called geometrical conditions which play the main role in determining the problem parameters. In addition, some other conditions could be added to the above set to increase the accuracy of problem solution. [4] - The sum of all hi s should be equal with total height of dam. hi H, 5 m < hi < H - The width of lower base of dam section in cases with platform should be less than those with platform.[] n hi+ bi + tgα i= i+ H tgα In the following, some of the essential parameters for the problem such as calculation of the width of the dam crust, the free height of wave, the height of lake water behind the dam are discussed based on the introduced expressions of designing embankment dams. Now, the objective function of the problem which is the area of the section of embankment dam (m per length) and equivalent with the volume of earthworks for m length of embankment dam is discussed. As shown in the following figure, the dam section was divided into three zones. The developed polynomial as the objective function consists of three parts. The first part represents the calculated areas of white triangles. The second part refers to the function red rectangulars and the third part is associated with green rectangular. Figure.5-Division of Section of Dam to Formulate Volume Function A= n+ i= hi + tgα i n i i+ hj bi + i= j= tgαi+ h + B n+ i= h i 9

5 J. Appl. Environ. Biol. Sci., 5(9)6-6, 05 The second category is conditional constrains which generate distinction between possible and impossible solutions. In this regard, facing with impossible solutions (for which constrains do not apply) is responded by applying fines on deviation from constrains to neglect the solutions. In this regard, instead of assigning dance to these pathways to develop the dance of bees based on the value of objective function, a fine is applied to prevent the following of other bees in those pathways. This problem is based on conditional and geometrical constrains of stability. Therefore, the forces applied on the structure are discussed and then the conditions of stability are implemented as secondary conditions. [6],[7] The reversal stability by defining the moment of all forces at the intersectional /3 zone as shown in the following. n+ n+ h n n ( ) n+ h + h iγ w B hi j hi ( ) B hi j ( + ) bj hj bi γ w bi bj i= tgαi tgαi j= tgα j+ i= j= i+ tgαi tgαi j= tgα j+ FS ( ) = >.5 Fh h+ Fw h 3 To better understand the above expression, the forces applied on dam are described in the following. [] A- Dam Weight: The force of dam weight refers to all elements of the dam crossing from its center of gravity. In the present study, symmetry of dam section makes its anchoring effect in the center of mid one third zone equivalent with zero.[8] B- Hydrostatic Pressure of Water: The hydrostatic force of upstream of the dam is composed of a horizontal factor (FH) and vertical factor (FV) the values of which can be calculated in the following.[8] γ w h Fh = F j n+ n n hi v = ( + i tgα = i i= = i+ h i hj bi γ w tgα + ) i It should be noted that based on the pressure prism method, the Fh force is equivalent with the volume of pressure prism in which is the special gravity of water usually considered as 000 kg.m 3 and h is the height of free reservoir level to the bottom. The effect point of this force relative to height is /3 of the free height of the reservoir to the bottom and the effect point of FV force at the gravity center of water is above the level of sloped body of dam.[8] C-Wave Force: The force applied by the wave upon the body of dam is calculate from the following relation (Rahimi, 0)[8] γ w( hw) Fwv= In the above relation, hw is the significant wave height (m). The significant wave height refers to the mean height of the highest one third of the waves which can be calculated from the following relation: V Fe hw= 0.53 g In the above relation, V refers to wind speed (ms), Fe is the length of fetch (m) and g is the gravity. The length of Fe fetch represents the length of maximum movement of the wave in reservoir of the dam which is obtained from the following relation.[8] F e =KL In the above equation, k is a coefficient which can be estimated from table (). L refers to the length of the reservoir and W represents the mean width of the reservoir. The above relation was suggested by Saville (959). In the above relations, Fe has the following constrain. F e 0 V (max) =. 03 The following figure represents the general steps for the algorithm of determining the optimal section of embankment dams in a flowchart form.[9] 0

6 Barahmand and Dini, 05 Figure.6-Flowchart of Bee Algorithm to Define Optimization of Section of Embankment Dams[3] Application of Algorithm of Bee Colony (ABC) Optimization for Two Problems of Optimizing Sections of Embankment Dam In the present paper, the parameters of two samples of clay soil as shown in table () are used to optimize the earthworks of a real dam.

7 J. Appl. Environ. Biol. Sci., 5(9)6-6, 05 Table.-Enginnering Characteristics of Two Samples of Clay in Triaxial Test (Unconsolidated Undrained; UU))[8] Row Type of Soil Internal Friction Angle Cohesion (kg.m 3 ) Specific Gravity (Degree) (kg.m 3 ) Clay Soil (Type ) Clay Soil (Type ) Characteristics of Bostan Dam (Golestan ) The characteristics of Bostan Dam are shown in the following table. Table.- Characteristic of Bostan Dam Type of Dam Embankment, Homogeneous Length of Crest 66m Width of Crest 0m Width in Bottom 65m Height from Bottom 35m Normal Height of Lake 30 m Volume of Dam Reservoir million m Type of spillway Free Capacity of spillway 550 m 3.s Area of lake 40 hectares in normal seasons 440 hectares in maximal-rainfall seasons Length of lake 6 km in normal seasons Total volume of reservoir 5 million m 3 in normal seasons Useful Volume 44 million m 3 Based on figure (7), the construction of a platform at the upstream and downstream of the dam leads to the obtained results by the application as shown in tables (3) and (4).[8] Figure.7-General View of Section of Embankment Dam without Platform in Upstream and Downstream

8 Barahmand and Dini, 05 In the following, the application s output to optimize the volume of earthwork of the dam in a case without platform and considering the characteristic of soil sample of type () is represented. The computational operation was iterated up to 5 steps and the best obtained result for geometrical characteristics of the dam body for the least volume of earthworks per meter of length is represented. Table.3-Result of Application Output for a Platform in Upstream and Downstream of Dam with Clay Soil (Type ) In the following, the application s output to optimize the volume of earthwork of the dam in a case without platform and considering the characteristic of soil sample of type () is represented. The computational operation was iterated up to 5 steps and the best obtained result for geometrical characteristics of the dam body for the least volume of earthworks per meter of length is represented. Table.4-Result of Application Output for a Platform in Upstream and Downstream of Dam with Clay Soil (Type ) As shown in the following figure, the construction of a platform in upstream and downstream of the dam leads to the results shown in table (5) and (6). Figure.8-General View of Section of Embankment Dam with One Platform in Upstream and Downstream of Dam Table.5-Results of Application Output for One Platform at Upstream and Downstream of Dam with Clay Soil (Type.) Table.6-Results of Application Output for One Platform at Upstream and Downstream of Dam with Clay Soil (Type.)

9 J. Appl. Environ. Biol. Sci., 5(9)6-6, 05 As shown in the following figure, the construction of two platforms in upstream and downstream of the dam leads to the results shown in table (7) and (8). Figure.9-General View of Section of Embankment Dam with Two Platforms in Upstream and Downstream of Dam In the following, the application s output to optimize the volume of earthwork of the dam in a case of constructing two platforms at upstream and downstream of the dam along with considering the characteristic of soil sample of type () is represented. The computational operation was iterated up to 5 steps and the best obtained result for geometrical characteristics of the dam body for the least volume of earthworks per meter of length is represented. Table.7-Result of Application Output for Two Platforms in Upstream and Downstream of Dam with Clay Soil (Type ) 8, In the following, the application s output to optimize the volume of earthwork of the dam in a case of constructing two platforms at upstream and downstream of the dam along with considering the characteristic of soil sample of type () is represented. The computational operation was iterated up to 5 steps and the best obtained result for geometrical characteristics of the dam body for the least volume of earthworks per meter of length is represented. Table.8-Result of Application Output for Two Platforms in Upstream and Downstream of Dam with Clay Soil (Type ) Following the comparison of above results, one can observe that constructing a platform at the upstream and downstream of the dam can significantly reduce the volume of materials used in the dam body. The latter issue is directly associated with total cost of constructing the dam. However, the soil type evidently plays a significant role in the obtained results. As a result, because the costs of carrying soil is influential upon selection of site, one should do an analysis of the cost of carrying the intended soil to the site of constructing dam along with the proportional reduction in the volume of earthworks when a definite type of soil is used. As a result, one can select the loading site of soil with better characteristics if it is sufficiently cost-effective. In the following table, the comparison of percentile reduction of the volume of earthworks when using the clay soils of type () and type () in the cases of no platform, one platform and two platforms in upstream and downstream of dam is done. 4

10 Barahmand and Dini, 05 Table.9-Percentile Reduction of Earthwork Volume in Bostan Dam during Optimization Operation Type of Material No Platform One Platform Two Platforms Clay Soil (Type.).6% 9.6% 5.8% Clay Soil (Type.).6% 7.9% 4.% As a result, in the optimal case for the intended dam, one can construct a platform at upstream and downstream of the dam to reduce the volume of earthwork operation. This is generally the case for different types of homogeneous embankment dam considering the main conditions of the project. As a result, the soil of type () provides better results compared with sample (). CONCLUSION In the present study, the bee optimization algorithm is used to find the optimal section for embankment dam. The obtained results were analyzed and evaluated which led to the following conclusions: -For embankment and earth-fill dams with the height of less than 80 m constituted of large-grained soils on high-strength foundations, the usage of platforms with sufficient number, width and arrangement in the section can significantly reduce the size of earthworks and reduce the executive requirements of the project. In dams whose height is more than 80 m, the reduction of the size of earthworks is directly associated with the height of the dam and this can significantly influence the direct and indirect costs of the project. -In regard to embankment and earth-fill dams, there is an optimal number of platforms for each height of the dam so that more or less number of platforms relative to the optimal number would increase the size of earthworks. 3-Using non-uniform slopes might reduce the size of earthworks and lead to a more optimal section compared with sections of uniform slope in regard to embankment and earth-filled dam. Of course, in the first scenario, the slope should increase from bottom to the top of the dam. REFERENCES [] T. Sato and M. Hagiva, 997 Bee system: finding soloution by a Concentrated search, in: Proceeding of the IEEE International Conference on systems, Man and Cybrenetics: Computational Cybrenetics and Simolation: Orlando, Fl, USA, PP ,. [] P. Lucic and D. Teodorovic, 00 Transportation inodeling : on ortificial life approach, in : Proceeding of the 4 th IEEE International Conference on Tools with Artificial Intelligence, Washington, DC, pp [3] D. T. Pham, A. Ghanbarzadeh, E. koc, S. Otri, and M. Zaidi,006 the bees Algorithm-a novel tool for complex optimization problems, in Proceeding of the th Vitual International conference on Intelligent Production Machines and systems (IPROMS 006), Elsevier, Cardiff, pp [4] D. Karaboga,005 An idea based on honey bee swarm for numerical Optimization, Technical Report TR06, Erciyes University, Engineering Faculty, Computer Engineering Department. [5] D. Teodorovic, Bee Colony Optimisation(BCO), 009 in: C. P. C. jain and Dehuri(Eds), Innovation in Swarm Intelligence, Springer-Verlag, Berlin Heidelbeg, pp , [6] Smith. C.D., 978 Hydraulic Structures, University of Saskatchewan Printing Services, 978. [7] ASTM D-653. [8] Stutzle, T., & Hoos, H. H MAX-MIN Ant system and local search for combinatorial optimization problems. In S. Martello, I. Osman, & C Roucairol (Eds), Meta-Heuristics Advances and trends in local Search Paradigms for Optimization (pp ). Dordrecht, Netherlands, Kluwer Academic Publishers. [9] Taillard E. D FANT: Fast Ant System. Technical report IDSIA-46-98, IDSIA, Lugano, Switzerland. [0] Stutzle, T., & Dorigo, M. 00. A short convergence proof for a class of ACO algorithms. IEEE Transactions on Evolutionary Computation, 6(4),

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