Skip to main content
SpringerLink
Log in

Robust optimization of the constructional time delay in the design of double-row stabilizing piles

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

Double-row stabilizing piles are widely used to stabilize large-scale landslides. The construction process of double-row stabilizing piles is often accompanied by constructional time delay (CTD), which is defined as the time interval between the installation of front-row and rear-row stabilizing piles. The CTD is often selected based on the designer’s experience and the construction arrangement due to the lack of design guidelines for double-row stabilizing piles. In this paper, the CTD is considered as a design parameter and optimized based on the robust design concept. The signal-to-noise ratio, which is a function of the mean and standard deviation of factors of safety (FOS) of the stabilizing piles, is used as a measure of the design robustness. The FOS of the double-row stabilizing piles are computed using an analytical model that considers the CTD. A framework based on the concept of robust design is proposed for determining the most preferred CTD considering multiple objectives, including safety, cost, and design robustness. This framework is illustrated with a case study, the Hongyan landslide project, Taizhou, Zhejiang, China. Based on the outcome of this study, the most preferred CTD is obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

b :

Width of the pile cross section

b p :

Calculated width of the pile cross section

E :

Elastic modulus of the pile

F f :

FOS of the front-row stabilizing piles

F r :

FOS of the rear-row stabilizing piles

\( \overline{F_{\mathrm{f}}} \) :

Mean of the FOS of the front-row stabilizing piles

\( \overline{F_{\mathrm{r}}} \) :

Mean of the FOS of the rear-row stabilizing piles

F s :

Target factor of safety of the piles

I 1 :

Moment of inertia of the front pile

I 2 :

Moment of inertia of the rear pile

k 0 :

Coefficient of subgrade reaction

L :

Pile length

l 1 :

Length of front pile section in the sliding layer

l 2 :

Length of front pile section in the stable layer

l 3 :

Length of rear pile section in the sliding layer

l 4 :

Length of rear pile section in the stable layer

\( {l}_{\mathrm{e}}^{\mathrm{m}} \) :

Euler distance between the mth feasible design and the utopia point

M :

Number of designs in the design space

M maxf :

Maximum bending moment of the front-row stabilizing piles

M maxr :

Maximum bending moment of the rear-row stabilizing piles

M uf :

Ultimate bending moment of the front-row stabilizing piles

M ur :

Ultimate bending moment of the rear-row stabilizing piles

N :

Number of random samples of k0

\( {S}_{F_{\mathrm{f}}} \) :

Standard deviation of the FOS of the front-row stabilizing piles

\( {S}_{F_{\mathrm{r}}} \) :

Standard deviation of the FOS of the rear-row stabilizing piles

SNR 1 :

Design robustness of the front-row stabilizing piles

SNR 2 :

Design robustness of the rear-row stabilizing piles

t :

Time

t D :

Time when the rear-row stabilizing piles were installed

X i :

ith objective function in the design space

[X i]max :

Maximum value of the ith objective function Xi

[X i]min :

Minimum value of the ith objective function Xi

X n :

Normalized value of the ith objective function Xi

\( {x}_1^{\mathrm{m}} \) :

Cost of the mth feasible design

\( {x}_2^{\mathrm{m}} \) :

Value of SNR1 of the mth feasible design

\( {x}_3^{\mathrm{m}} \) :

Value of SNR2 of the mth feasible design

\( {x}_{\mathrm{i}}^{\mathrm{m}} \) :

Value of the ith objective for the mth feasible design

y top(t):

Head displacement history of the front-row stabilizing pile

y top(t D):

Head displacement of the front-row stabilizing pile at the time when the rear-row stabilizing piles were installed

z 1 :

Independent variable in the expression of the bending moment, which ranges from 0 to l1

z 2 :

Independent variable in the expression of the bending moment, which ranges from 0 to l2

z 3 :

Independent variable in the expression of the bending moment, which ranges from 0 to l3

z 4 :

Independent variable in the expression of the bending moment, which ranges from 0 to l4

α :

Intermediate parameter that is used to reduce the complexity of the bending moment expressions in Eq. (7)

β 1 :

Characteristic value of a beam on elastic foundation of the front pile

β 2 :

Characteristic value of a beam on elastic foundation of the rear pile

\( {\delta}_{y_{\mathrm{top}}} \) :

Intermediate parameter that is used to reduce the complexity of the bending moment expressions in Eq. (2)

\( {\delta}_{y_{\mathrm{top}}}^{\prime } \) :

Intermediate parameter that is used to reduce the complexity of the bending moment expressions in Eq. (7)

λ 1, λ 2, λ 3, λ 4 :

Intermediate parameters of the earth pressure calculation coefficient of the front pile

λ 1′, λ 2′, λ 3′, λ 4′:

Intermediate parameters of the earth pressure calculation coefficient of the rear pile

η 1, η 2, η 3, η 4 :

Calculation coefficients of the internal force of the front pile

η 1′, η 2′, η 3′, η 4′:

Calculation coefficients of the internal force of the rear pile

References

  • Ang AHS, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental engineering, 2nd edn. Wiley, New York

    Google Scholar 

  • Ashour M, Ardalan H (2012) Analysis of pile stabilized slopes based on soil–pile interaction. Comput Geotech 39:85–97

    Article  Google Scholar 

  • Chen KT, Wu JH (2018) Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis. Eng Geol 239:269–281

    Article  Google Scholar 

  • Deb K, Gupta S (2011) Understanding knee points in bicriteria problems and their implications as preferred solution principles. Eng Optim 43(11):1175–1204

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan TAMT (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Denis A, Elachachi SM, Niandou H (2011) Effects of longitudinal variability of soil on a continuous spread footing. Eng Geol 122:179–190

    Article  Google Scholar 

  • Gong WP, Khoshnevisan S, Juang CH (2014a) Gradient-based design robustness measure for robust geotechnical design. Can Geotech J 51(11):1331–1342

    Article  Google Scholar 

  • Gong WP, Wang L, Khoshnevisan S, Juang CH, Huang H, Zhang J (2014b) Robust geotechnical design of earth slopes using fuzzy sets. J Geotech Geoenviron Eng 141(1):04014084

    Article  Google Scholar 

  • Gong WP, Juang CH, Khoshnevisan S, Phoon KK (2016a) R-LRFD: load and resistance factor design considering robustness. Comput Geotech 74:74–87

    Article  Google Scholar 

  • Gong WP, Tien YM, Juang CH, Martin JR, Zhang J (2016b) Calibration of empirical models considering model fidelity and model robustness—focusing on predictions of liquefaction-induced settlements. Eng Geol 203:168–177

    Article  Google Scholar 

  • Gong WP, Huang H, Juang CH, Wang L (2017) Simplified-robust geotechnical design of soldier pile–anchor tieback shoring system for deep excavation. Mar Georesour Geotechnol 35(2):157–169

    Article  Google Scholar 

  • He GF, Li ZG, Yuan Y, Li XH, Hu LH, Zhang Y (2018) Optimization analysis of the factors affecting the soil arching effect between landslide stabilizing piles. Nat Resour Model 31(2):e12148

    Article  Google Scholar 

  • Juang CH, Wang L (2013) Reliability-based robust geotechnical design of spread foundations using multi-objective genetic algorithm. Comput Geotech 48:96–106

    Article  Google Scholar 

  • Juang CH, Zhang J, Shen MF, Hu JZ (2019) Probabilistic methods for unified treatment of geotechnical and geological uncertainties in a geotechnical analysis. Eng Geol 249:148–161

    Article  Google Scholar 

  • Kang GC, Song YS, Kim TH (2009) Behavior and stability of a large-scale cut slope considering reinforcement stages. Landslides 6(3):263–272

    Article  Google Scholar 

  • Khoshnevisan S, Gong WP, Wang L, Juang CH (2014) Robust design in geotechnical engineering—an update. Georisk Assess Manag Risk Eng Syst Geohazards 8(4):217–234

    Article  Google Scholar 

  • Li CD, Liu XW, Liu QT, Liu T (2016) Influence of isosceles trapezoid cross-section on the reinforcement effect of stabilizing piles. KSCE J Civ Eng 20(7):2670–2676

    Article  Google Scholar 

  • Li CD, Wang XY, Tang HM, Lei GP, Yan JF, Zhang YQ (2017) A preliminary study on the location of the stabilizing piles for colluvial landslides with interbedding hard and soft bedrocks. Eng Geol 224:15–28

    Article  Google Scholar 

  • Lü Q, Low BK (2011) Probabilistic analysis of underground rock excavations using response surface method and SORM. Comput Geotech 38(8):1008–1021

    Article  Google Scholar 

  • Lü Q, Sun HY, Low BK (2011) Reliability analysis of ground–support interaction in circular tunnels using the response surface method. Int J Rock Mech Min Sci 48(8):1329–1343

    Article  Google Scholar 

  • Lü Q, Chan CL, Low BK (2012) Probabilistic evaluation of ground-support interaction for deep rock excavation using artificial neural network and uniform design. Tunn Undergr Space Technol 32:1–18

    Article  Google Scholar 

  • Miao FS, Wu YP, Xie YH, Li YN (2018) Prediction of landslide displacement with step-like behavior based on multialgorithm optimization and a support vector regression model. Landslides 15(3):475-488

    Article  Google Scholar 

  • Ministry of Housing and Urban-Rural Construction of the People’s Republic of China (2015) Code for design of concrete structures, GB 50010-2010

  • Ministry of Land and Resources of the People’s Republic of China (2006) Specification of design and construction for landslide stabilization, DZ/T 0219-2006

  • Qian TH, Tang HM (2008) Double-row anti-sliding piles: analysis based on a spatial framework structure. In: Proceedings of the 10th International Symposium on Landslides and Engineered Slopes, Xi’an, China, June/July 2008, vols 1 and 2, pp 881–886

    Chapter  Google Scholar 

  • Shen YJ, Wu ZJ, Xiang ZL, Yang M (2017a) Physical test study on double-row long-short composite anti-sliding piles. Geomech Eng 13(4):621–640

    Google Scholar 

  • Shen YJ, Yu Y, Ma F, Mi FL, Xiang ZL (2017b) Earth pressure evolution of the double-row long-short stabilizing pile system. Environ Earth Sci 76(16):586

    Article  Google Scholar 

  • Sun HY, Zhao Y, Shang YQ, Zhong J (2013) Field measurement and failure forecast during the remediation of a failed cut slope. Environ Earth Sci 69(7):2179–2187

    Article  Google Scholar 

  • Wu JJ, Li CD, Liu QT, Fan FS (2017a) Optimal isosceles trapezoid cross section of laterally loaded piles based on friction soil arching. KSCE J Civ Eng 21(7):2655–2664

    Article  Google Scholar 

  • Wu JH, Lin WK, Hu HT (2017b) Assessing the impacts of a large slope failure using 3DEC: the Chiu-fen-erh-Shan residual slope. Comput Geotech 88:32–45

    Article  Google Scholar 

  • Wu JH, Lin WK, Hu HT (2018) Post-failure simulations of a large slope failure using 3DEC: the Hsien-du-Shan slope. Eng Geol 242:92–107

    Article  Google Scholar 

  • Xiao SG, Yang J (2011) Internal forces of double-row pile slope stabilization systems influenced by of pile row separation. In: Proceedings of the International Conference on Structures and Building Materials (ICSBM 2011), Guangzhou, China, January 2011, vols 168–170, pp 127–132

  • Xiao SG, He H, Zeng JX (2016) Kinematical limit analysis for a slope reinforced with one row of stabilizing piles. Math Probl Eng, article ID 5463929, 15 pp

  • Xiao SG, Zeng JX, Yan YP (2017) A rational layout of double-row stabilizing piles for large-scale landslide control. Bull Eng Geol Environ 76(1):309–321

    Article  Google Scholar 

  • Yu Y, Shang YQ, Sun HY (2012) Bending behavior of double-row stabilizing piles with constructional time delay. J Zhejiang Univ Sci A (Appl Phys Eng) 13(8):596–609

    Article  Google Scholar 

  • Yu Y, Shang YQ, Sun HY (2014) A theoretical method to predict crack initiation in stabilizing piles. KSCE J Civ Eng 18(5):1332–1341

    Article  Google Scholar 

  • Yu Y, Shang YQ, Sun HY, Wang EZ (2015) Displacement evolution of a creeping landslide stabilized with piles. Nat Hazards 75(2):1959–1976

    Article  Google Scholar 

  • Yu Y, Shen MF, Sun HY, Shang YQ (2019) Robust design of siphon drainage method for stabilizing rainfall-induced landslides. Eng Geol 249:186–197

    Article  Google Scholar 

  • Zhang J, Huang HW (2016) Risk assessment of slope failure considering multiple slip surfaces. Comput Geotech 74:188–195

    Article  Google Scholar 

  • Zhang J, Juang CH, Martin JR, Huang HW (2016) Inter-region variability of Robertson and Wride method for liquefaction hazard analysis. Eng Geol 203:191–203

    Article  Google Scholar 

  • Zhang J, Wang H, Huang HW, Chen LH (2017) System reliability analysis of soil slopes stabilized with piles. Eng Geol 229:45–52

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to acknowledge the financial support of the National Natural Science Foundation of China (41807224, 41772276, 41772287), the Natural Science Foundation of Zhejiang Province (LQ17D020001), the Key R&D project of Zhejiang Province (2017C03006), and the Zhoushan City-Ocean College of Zhejiang University Joint Fund (2017C82220) for this study. The corresponding author wishes to thank Dr. Charng Hsein Juang for his help on the research of robust geotechnical design.

Author information

Authors and Affiliations

  1. Ocean College, Zhejiang University, Zhoushan, 316021, China

    Zhu Wang, Yang Yu & Hongyue Sun

  2. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, China

    Qing Lü & Yuequan Shang

Authors
  1. Zhu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyue Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qing Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuequan Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Yu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Yu, Y., Sun, H. et al. Robust optimization of the constructional time delay in the design of double-row stabilizing piles. Bull Eng Geol Environ 79, 53–67 (2020). https://doi.org/10.1007/s10064-019-01554-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-019-01554-7

Keywords

Search

Navigation