A New Multi-objective Comprehensive Optimization Model for Design of Anti-slide Piles


 Landslides have posed a huge threat to the ecological environment and human society all over the world. As the most conventional reinforcement method, anti-slide piles are widely used in the reinforcement of slopes. Currently, more and more attentions have been paid to the low-cost and high-efficiency optimal design of anti-slide piles. However, limitations in the method of the optimization design for slope reinforced with piles still exist. In this paper, a new multi-objective comprehensive optimization method was proposed for the optimization of the slope reinforced with anti-slide piles. The factor of safety, internal force and deflection of piles were selected as the optimization indexes and the optimization index weight was determined by integrating the subjective and objective weight. The influence of the pile location, pile length and pile spacing on the reinforcement effect was analyzed by the numerical simulation. Through the simulation case analysis, the proposed model had achieved good effects on the optimization design of anti-slide piles, which could effectively reduce the engineering costs. The optimization results showed that the best reinforcement effect for the homogeneous slope could be obtained when the anti-slide piles with the critical pile length and small pile spacing was located in the middle of the slope. This provides a new solution for the optimization design of other types of complex slopes, and has broad application prospects.


Introduction
With the rapid development of global engineering construction, slope stability has 77 become a worldwide significant problem in engineering practice (Hassiotis et al. 1997; 78 Li et al. 2020). The anti-slide pile as the most conventional reinforcement method is 79 widely used due to the advantages of strong anti-sliding ability and convenient  In conclusion, it is unreasonable to ignore the safety state of anti-slide piles to 132 evaluate the stability of the slope reinforced. Therefore, in this paper the multi-objective 133 comprehensive optimization model based on improved fuzzy comprehensive evaluation was developed to optimize the design of anti-slide pile, and the optimization 135 indexes system and the comprehensive index weight was established, the factor of 136 safety, bending moment, shear force and deflection were selected as the optimization 137 indexes. FLAC 3D software was used to establish a three-dimensional numerical model    In the design of slope reinforced with anti-slide piles, factors such as pile location, 163 pile length, and pile spacing are usually considered in order to achieve a good 164 reinforcement effect. However, the overly conservative design has led to high 165 engineering costs in most cases (Hu et al. 2020;Zhao et al. 2006). Therefore, the 166 optimum design of anti-slide piles aims to reduce as many engineering costs as possible 167 while satisfying the safety of supporting structure without affecting the stability of 168 reinforced slope.

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The standardized formula for the positive optimization indexes that are positively 187 correlated with the results, such as the factor of safety, can be taken as follows:   The value of k(j) determines the optimal membership degree of different schemes.

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Generally, the larger the value k(j) is, the more reasonable the scheme is.  behavior of slope soil. The initial stress field only considers the self-weight stress field.

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The entirely run-through of plastic zone is regarded as the criterion of slope instability.

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Details about the parameters of soil are shown in Table 1. The factor of safety is   Details about the parameters of anti-slide piles are shown in Table 2.   The effect of various pile locations on anti-slide pile behaviors is shown in Fig. 8. 315 The bending moment, the shear force and the deflection of the pile increase at first and    The effect of various pile lengths on the pile behaviors is shown in Fig. 10. It can be 359 seen that, when the pile length is less than the critical pile length (18m), the bending 360 moment (Fig. 10a) increases with the increase of the pile length, and the position of the maximum bending moment is continuously away from the top of piles, which 362 corresponds well to the position of the critical slip surface (Fig. 7b); the positive shear 363 force of piles (Fig. 10b) increases as the pile length increases; the pile deflection 364 increases with the increase of the pile length, but it should be noted that the distribution 365 of deflection is almost linearly (Fig. 10c) when the pile length is short, which indicates 366 that the pile is prone to overturning failure under too short pile length. When the pile 367 length exceeds the critical pile length, the bending moment, shear force and deflection 368 all tend to be a stable distribution, which is consistent with the change law of the factor 369 of safety.   is large enough (Fig. 12a4), a complete and run-through critical slip surface is formed gradually, which is nearly close to the critical slip surface of slope unreinforced (Fig.   392   6a). This may be related to the evolution of soil arch under various pile spacings.     Table 3 The standardized values of optimization indexes (Pile location L x /L p =0.1) 437 438 Table 4 The standardized values of optimization indexes (Pile location L x /L p =0.3) 439 440 Table 5 The standardized values of optimization indexes (Pile location L x /L p =0.5) 441 442 Table 6 The standardized values of optimization indexes (Pile location L x /L p =0.7) 443 444 Table 7 The standardized values of optimization indexes (Pile location L x /L p =0.9) 445 446 Decision-making AHP method was adopted to determine the subjective weight of  Table 9. 459 The comprehensive weight of each evaluating index was calculated via Eq. (4) as 460 shown in Table 9. Among them, the weight of factor of safety is the largest and that of 461 shear force of pile is the smallest.  The fuzzy comprehensive optimization value k (j) was calculated according to Eq.

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(2) The increase of pile length can significantly improve the reinforcement effect of 483 the slope, but it does not mean that the longer the pile length, the better the 484 reinforcement effect. For example, when the pile is located in the lower-middle part 485 (Lx/Lp=0.3) with the pile spacing of 5m, the value of k (j) increases slightly or even 486 decreases when the pile length exceeds 18m (Fig. 14), this is mainly because excessive   The final optimization results under various index weight types are shown in Fig. 16. 515 It can be seen that, the result (Red line in Fig. 16) by using the subjective weight only 516 indicates that scheme 35 is the optimal reinforcement option, which is basically 517 consistent with the conclusion drawn via the proposed method in this article, but the  In the current study, the numerical simulation method was used to obtain the values 537 of evaluating indexes in the multi-objective comprehensive optimization model.

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Although more reasonable optimization results had been achieved, more engineering 539 cases and field monitoring data are still needed to further study to verify the accuracy 540 and applicability of this proposed model. Besides, the comprehensive weight used in this article considers the advantages of both subjective and objective weight, and 542 minimizes the adverse effects of shortcomings of two on optimization results, but it is 543 still unavoidable that the weight obtained goes against the actual situation, which leads 544 to make an absurd decision-making. Therefore, it is necessary to further optimize the 545 index weight based on methods of big data, machine learning and deep learning.

Table captions
696 Table 1 Physical and mechanical parameters of the slope 697 Table 2 Physical and mechanical parameters of anti-slide piles 698 Table 3 The standardized values of optimization indexes (Pile location L x /L p =0.1) 699 Table 4 The standardized values of optimization indexes (Pile location L x /L p =0.3) 700 Table 5 The standardized values of optimization indexes (Pile location L x /L p =0.5) 701 Table 6 The standardized values of optimization indexes (Pile location L x /L p =0.7) 702 Table 7 The standardized values of optimization indexes (Pile location L x /L p =0.9) 703 Table 8 Subjective weight determination for optimization indexes 704 Table 9 Comprehensive weight determination for optimization indexes 705  Moi-y (m 4 ) 4.5 Density (kg/m 3 ) 2500 Coupling-gap-normal on Moi-polar (m 4 ) 6.5 Cross-sectional-area (m 2 ) 6.0 Perimeter (m) 10