Anti―slide Pile Design and Application Based on Multi―objective Optimization Theory.doc

1、1Antislide Pile Design and Application Based on Multiobjective Optimization TheoryAbstract. In order to solve the contradiction between the project cost and rational design， this paper adopts multi-objective optimization design theory， applies stratified sequence method to the actual project， and op

2、timizes its sectional dimension and pile spacing. Taking single pile-sectional dimension， tensile reinforcement size and pile spacing as decision variables， an optimal solution is sought under the premise of meeting the geometric constraints， strength constraints， reinforcement constraints and pile

3、spacing constraints， so as to achieve the optimal solution for objective function. Through the preparation of Lingo program， selection of actual project， the optimal solution is obtained. The results proved that the optimization design is satisfactory， and can help to reduce the project cost and pro

4、vide a reference for similar projects. Keywords： landslide treatment； anti-slide pile； optimization design 1. Introduction 2At present， in anti-slide pile design， the cross section width ratio is approximated as the ratio of simply supported beam or over hanging beam， and the value is taken by exper

5、iences. The length-width ratio of anti-slide piles section is generally taken to be 1.5 to 2.1， because the crossrange of ordinary simply supported beam is free， and the side direction of anti-slide pile has soil pressure， it is conducive to piles lateral stability. Therefore， in general engineering

6、， the improper length-width ratio of anti-slip piles section may cause unnecessary waste of materials and increase the total project costs. Under certain project conditions， in order to save costs and meet various safety requirements， appropriate optimization algorithms are used to calculate the opt

7、imum configurations， including optimal length-width ratio of pile section and pile spacing. Based on multi-objective optimization theory stratification， this paper selects reinforcing bar， pile spacing， strength and sectional dimension as constraints， works out the Lingo program， selects an actual p

8、roject as an example， and obtains the optimal solution1，2. The results show that the optimization result is satisfactory， and can help to reduce the project cost and provide a reference for similar projects. 32. Hierarchical Optimization Multi-objective Theory 3. Project Example and Application 3.1

9、Project Overview 3.2 Optimization Design Model 3.2.1 Objective Function Decision variables X = x1， x2， x3， x4 T， x1， x2， x3， x4 represents the section height， section width， longitudinal tensile reinforcement sectional area and pile spacing respectively. Project cost is the objective function f （x）

10、， the problem is simplified as finding the decision variables x1， x2， x3， x4： （4） Making the formula： Zc， ZAs， ZAs concrete， longitudinal tensile reinforcement， erection bar （under pressure） costs； Cc， CAs， CAs unit price of concrete （RMB / m3） ， longitudinal reinforcement， unit price of erection ba

11、r （under pressure） （RMB / Kg） ； L Pile length， mm； Severe of reinforcing bar， KN/mm3； Ratio of erection bars （under pressure） sectional area to longitudinal tensile reinforcement sectional area； a0 Thickness of concrete topping， mm； 4e Steel hook length， mm； N Number of design projects piles （intege

12、r） ； S Width of landslide body， m； 3.2.2 Constraints a） Size Constraints Requirement for use function， x1 5000mm； requirement for section width lower limit， x1 1.5x2； requirement for section height upper limit， x2 x1. b） Strength Constraints normal section strength constraint （5） Making the formula：

13、 oblique section strength constraint （6） In the formula： M Anti-slide pile designs section bending moment， N ? mm； V Anti-slide pile designs shear force， N； fy Design value of longitudinal reinforcement tensile strength， N?mm-2； fcDesign value of concrete axial compressive strength， N?mm-2； 5fcm Des

14、ign value of concrete flexural compressive strength， N?mm-2； fyg Design value of stirrup tensile strength， N?mm-2； n - number of stirrup. c） Reinforcement Constraints vertical restraints （7） stirrups （8） In the formula： n Number of stirrups， double limb n = 2， four limbs n = 4； Sy Stirrup spacing， m

15、m. d） Pile Spacing The critical pile spacing is determined by forming a soil arch between piles according to the reference 3 ： 3.3 Analysis of the Results According to above optimization algorithms and models， Lingo is adopted for the preparation of corresponding programs4， Table 1 shows the results

16、 of the institutes design calculations and the comparison of optimization design methods. 6It can be seen from above table that： compared with traditional design methods， the optimization design method can save 7.57% costs in the same anti-slide pile. 33 anti-slide piles were used for the landslide

17、treatment. According to above pile spacing， 31 piles is enough， thus saving 13.29% costs. It has significant economic effects. 4. Conclusion 1） The value of pile spacing has the greatest impact on the project cost， a smaller value should be taken in compliance with the norms； constraints are set in

18、accordance with the norms， the amount of reinforcement is required to be reasonable and meet the safety requirements. 2） Hierarchical multi-objective optimization theory is feasible and practical to the anti-slide pile design optimization， and the results is satisfactory. Fine size control should be

19、 further improved， thus providing a reference for similar projects. 3） The anti-slide pile design theory is not perfect， and it has some simplification and assumption. Its optimization design still needs to be further improved， for instance， there is urgent need to further study the anchorage depth，

20、 the soil pressure distribution on the pile. 5. Acknowledgements 7This project is supported by Fund Project of Innovation in Postgraduate Education of Chongqing Jiaotong University （serial number is 20130110） ， Scientific and Technological Research Program of Chongqing Municipal Education Commission

21、（Grant No. KJ131107） ， and National and Local Joint Engineering Laboratory of Transportation and Civil Engineering Materials of Chongqing Jiaotong University （serial number is LHSYS-2012-001）. References 1 D.P. Zhou， Sh. G. Xiao， X. Xiong. Discussion on rational spacing between adjacent antislide pi

22、les in some cutting slope projects， Chinese Journal of Geotechnical Engneering， Vol. 26， No. 1（2004） ， p.132-139. 2 H.Q. Zhou. Object oriented Genetic Algorithm and Its Application in the Optimization of the Anti slide Pile， Geotechnical Engineering Technique， No. 6（2003） ， p.311-314+367. 3 G. D. Co

23、u，Sh. Sh.Chen. A design method of stabilizing piles and its optimized numerical model， Chinese Journal of Geotechnical Engneering， Vol. 25， No. 1（2003） ， p.11-17. 4 B.J. Zeng， W.X. Li.Optimization design of reinforced concrete beam based on matrix labboratory. Journal of Wuhan 8Institute of Technology， Vol. 34， No. 8（2012） ， p.50-53.