Procedia Engineering 150 ( 2016 ) 1804 – 1810

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of ICIE 2016doi: 10.1016/j.proeng.2016.07.174

ScienceDirectAvailable online at www.sciencedirect.com

International Conference on Industrial Engineering, ICIE 2016

Optimizing the Parameters of Water-Retaining Protective Structures under Small Stream Conditions

D.V. Kasharin* Platov South-Russian State Polytechnic University (NPI), 132, St. Prosvescheniya, Rostov region, Novocherkassk, 346428, Russian Federation

Abstract

The article tackles issues on the creation of optimized models for the water-retaining protective structures for small streams. It was based on the selection of a mathematical model for a multi-criteria optimization, and imposing mathematical models are included to define the target functions. The weighted sum model was selected as the main optimization method. Based on the developed mathematical model and the weighted sum optimization method, a computer program was created that allows to automate the designing process of water retaining structures of the engineering protection for conditions of small streams, taking into account the preferences of the decision maker. Its use allows the decision maker to avoid critical errors when designing the cable-membrane and soil-reinforced structures, including moment-free shells made of composite materials. © 2016 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the organizing committee of ICIE 2016.

Keywords: small streams; water-retaining structures; engineering protection; shells; composite materials; optimization;

1. Introduction

Existing engineering protection systems against flooding principally involve embankment dams and water retaining structures that are part of flood control reservoirs. The parameters of these structures are calculated based on short-term catastrophes involving excessive water periods and may falter under the influence of extreme loads, or after long-term operation over non-uniform weak soil foundations, typical for floodplains. They can also have a significant negative impact on the ecosystems of small streams, limiting their catchment and riverbed system [1, 2]

* Corresponding author. Tel.: +7-928-603-69-67; fax: +7-8635-22-71-17.

E-mail address: dendvk1@mail.ru

© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Peer-review under responsibility of the organizing committee of ICIE 2016

1805 D.V. Kasharin / Procedia Engineering 150 ( 2016 ) 1804 – 1810

Thus, it is necessary to create mobile, temporary and season sensitive class IV structures for small streams, for the least negative impact on the territory of their watershed and environmental infrastructure, as well as local protection of water - and power supply of economic and agricultural objects in case the permanent structural engineering protections are destroyed [1, 3]. These structures include prefabricated water retaining structures - membrane-cable dam, which collects surface water above the protected section with a possibility of evacuating part of the water through flexible water-filled dams and trays, made of composite materials [3–6]. Also, water retaining soil reinforced structures can be used as stand-alone structures over a weak soil foundation and as flood bed membrane-cable dams, increasing the height of permanent embankment dams and to restore them. When erecting soil-reinforced structures, industrial soil and waste that do not pollute the environment may be used as construction materials [1, 7, 8].

Despite the fact that these structures are not classified as highly reliable, it is necessary to take into account the complexity of calculating the components of their shell structures made of composite materials when designing them. This is due to the fact that the dependence of the described hydrodynamic loads and functions, reflecting the shape of the shell surface and its stress-strain state (SSS), is not clear and the decision-maker (DM) with insufficient experience may get non-optimal parameters and make critical mistakes when designing water retaining structures of this type.

Hence, to extend the possibility of using these structures for small streams, it is necessary to develop algorithms and software, which would determine the optimal parameters for water retaining structures of engineering protection and automate their design process based on a database of simulation results on shell structures [6, 7, 9-15].

To create a software, it is necessary to develop a mathematical model and justify the choice of the method used to optimize the parameters of water-retaining structures.

2. Mathematical model of water-retaining protective structures

The mathematical model (MM) for water retaining structures of engineering protection should allow the combination of its elements in proportion to the importance of a single system, based on which optimization is to occur.

Consider the basic elements of water retaining structures. For membrane-cable dams, these elements include: drooping; anchor support; cable-stayed systems; water retaining shells and jacket; aprons (Fig. 1, a) [1, 3, 6, 9, 15].

Soil-reinforced structures (Fig.1, b) include the following main elements: a system of reinforced-tapes and anchors; a front wall, a draining system (Fig. 2) [1, 7, 11].

Fig. 1. (a) Design scheme for the membrane cabling dam; (b) design scheme of soil-reinforced structure: 1 –drooping; 2 – bank anchor support;3 – cable system; 4 – water-retaining shell; 5 – flexible apron; 6 – front wall; 7 –reinforced tape; 8 – compacted soil; 9- anchor; 10 – draining

system

Each element of the water-retaining structures (Fig. 1, 2) is a subsystem, which, depending on the target functions, integrates the criteria of selection and the range of parameters in the optimal structure. The developed MM optimization for the protective structure is a correlation system of elements, for which the parameters are defined in accordance with the original data, requirements, allowed parameters and the achievement of common goals [16].

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Permitted parameters of the membrane-cable dam and the criteria of selection are presented in Fig. 3 and in table 1 [1, 6, 14, 16, 17].

Fig. 2. Estimate diagram of the soil-reinforced structure reinforcement element: (a), (b), (c) reinforced-element cuts; (d) dependence on the depth of coefficient K, joining the horizontal and vertical tensions in the reinforced soil: A , erA – the cross-sectional area of the reinforced-tape and

the soil element respectively, m2; ab , ay , az - steps along the horizontal and vertical lines of the reinforced-tape, respectively, m

In invariant form, the MM of the membrane cable dam, developed by the authors, is expressed in the form of equations systems of the objective functions in the following form [1, 6, 11, 12, 14, 15–17]:

; min;

min;

; min .

up os b

c c

C C

h L = f

C f N;L;B;R

N B f R f

(1)

where /uph L – is the relative depth from upstream to the shell perimeter L ; /CN B – is the ratio of the tension per unit length to overlap span B ; cC – the relative cost of membrane cable dam as compared to a concrete dam; CR – the radius of the cabling system of the membrane-cable dam; ,os b - the attachment angle and base for the open shell of the membrane-cable dam.

In accordance with the invariant form (1), we compose a calculation sequence of the optimization model for the water retaining shell of the membrane cable dam and its optimal parameters.

The following invariant MM was obtained for soil-reinforced dams [1, 7, 12, 17]:

cr

1 ; min;

; + min;

; min,

hsm lr efw up p

C lr efw

lfa hsm

H l L f h B;C

C f N l L

N N f l H

(2)

where hsmH - the height of the soil mound of the water retaining structures; lrl - length of the reinforced tape; efwL - length of front wall; efal - length of the reinforced tape sealing in the first approximation; pC – the relative

cost solid-reinforced dam.

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Fig. 3. The structure of the mathematical model of optimization of water-retaining protective structures

In accordance with the MM structure presented Fig. 3 and (table 1) it is necessary to select the method of multi-criterial optimization using dependencies (1) (2) [1].

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Table 1. Notation in the structure of the mathematical model of optimization of water-retaining structures. Name ( xplanation of symbols) Symbol

Criteria

1 Shear Stability (R – total resistance forces and the resultant shift F) /R F

2 Relative filtration gradient ( estI an averaged calculated value of the critical pressure gradient) , ,/est m cr jI I

3 Relative rainfall ( S – factual value; S – practical value); /S S

4 Relative capital investments ( rc - reinforced concrete structure) /p rc

5 Relative depth of the upstream /uph L

6 Relative overlapped span ( fB -overlapped span; rB - bed width) /f rB B

7 Relative damming the watercourse ( uvV , rivW -useful and river flow volume)

/uv rivV W

8 Relative regulation time ( st - installation time structure, rt critical time) s crt t

9 Capacity of the dam ( m - weir flow coefficient) m

10 Tensile properties ( pN - relative tension per unit length; maxN - tensile strength per unit length) max/pN N

11 Relative deformation of the shell material

12 Relative tension cable system /N B

13 Tensile properties of the material of the cables and membranes (domestic depth ddh ; the first h and second h conjugate depth)

/ddh h h

14 Relative area of reinforced soil element /erA H B

15 Ratio of the width and height of the thalweg soil-reinforced structures /rL H

16 Active soil pressure coefficient NSK

17 Ratio of reinforcement over the area aK

Parameters

18 Relative width of the structures /B H

19 Depth of the upstream, m uph

20 Shell perimeter, m L

21 Overlapped span, m B

22 Chase tension, kN/m2 pN

23 Length of the retaining cable, m l

24 Length of soil-reinforced water retaining structure, m rL

3. Multi-criterial optimization with parameters of the water-retaining protective structures

3.1. Selecting the method of multi-criterial optimization

When analyzing the existing methods of multi-criterial optimization a priori and posteriori methods were analyzed.

Posteriori methods include the participation of the DM in the multi-criterial optimization (MCO) system which is to provide his preferences in the information system after receiving a set of non-dominant solutions. The main disadvantage of posteriori methods includes the fact that uniform approximation of plurality and/or Pareto front requires large computational cost. Increasing the accuracy of approximation is achieved by increasing the number of non-dominated solutions which is more time consuming for the DM [18-25].

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A priori methods do not require, as opposed to posteriori, the entire set of solutions to be created. These methods include: the scalar convolution technique; restrictions and lexicographical ordering; target programming. The main disadvantage is that it is difficult for the DM to articulate his preferences before the water retaining protective structures are designed.

It was decided to use a priori methods, as the DM can predetermine his preferences on such structures for a known range of parameters. Also, the optimization of these methods are the least demanding in terms of computer resources. We used a scalar convolution technique as a base for modification, called the method of weighted sums. With this method, multi-criteria optimization problems are reduced to one with a single criterion by replacing the vector optimality criterion, consisting of several partial criteria, with one generic criterion, called the target function.

The minimum for the target function is set as the optimal solution considering the limitations from the DM [17, 25].

3.2. Development of a method of multi-criterial optimization parameters for the MMHEP

When solving the issue with selecting optimal parameters of water-retaining protective structures under small stream conditions, several options are considered for an alternative arrangement of elements and parameters including closed and open shells made of composite materials, the characteristics of various aggregates, they are compared with traditional elements.

The structure of the multistage optimization of water-retaining protective structures is based on a modular principle and consists of five levels: 1 - analysis and optimization of the source data, criteria and limitation selection for the elements of the water retaining protective structures; 2 - construction of MM elements; 3 - select one-criterion optimization of parameters for special-purpose functions of the elements; 4 - definition multi-criterial optimization of parameters for multi-purpose functions of the elements; 5 - the final calculations of the selected structure and its elements using the developed calculation methods.

Let us consider in more detail the optimization of water retaining protective structure parameters, for membrane-cable and soil-reinforced structures [17, 25, 26]:

, ,1 2 3

/ , / , /P( , ) S( , )CF

P Sest m cr jos b os b

mcst st st

R F I I S S;

1 2 3

,S / ; y / ; / ; / P A / , /CF

S P

NS aa a efa r efw

rst st st

K Kb H H l L L l H B l H ,

CFmc , CFr - are the generalized criteria cable-membrane and soil-reinforced dams respectively; 1 , 2 , 3 - the significance coefficient of weight, cost and reliability for the operation of water retaining structures respectively; P , S , - the current function of weight, cost and reliability of the described structure type, respectively; Pst , Sst ,

st - the reference function significance of weight, cost and reliability respectively. Based on this optimization sequence, the "Optimization of selection and calculation of structures made of

composite materials for the engineering protection at water management construction" [17, 25, 27] program was created with the participation of the author, thus allowing to optimize the process of designing water-retaining structures made of composite materials, for engineering protection.

4. Conclusion

1. As a result of the analysis of optimization techniques, the methods of scanning with variable steps and random directions were chosen as the most effective one for the creation of a mathematical model for the optimization of the parameters of water-retaining protective structures.

2. A program was developed to optimize the selection and calculation of engineering protection structures made of composite materials using the principle of multi-stage optimization of problem solving in variant design,

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significantly reducing the time needed to choose the place to implement structural and computational justifications. Also, it reduces the risk of the DM making inappropriate decisions, as a result of insufficient experience in designing water-retaining protective structures.

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