Simplified Design Method of Laterally Loaded Rigid Monopiles in Cohesionless Soil
Abstract
:1. Introduction
2. Proposed Design
2.1. Depth of Rotation Point of Rigid Monopile
2.2. Mobilization Coefficient of Soil Lateral Reaction
- (1)
- As the depth increases, the magnitude of the lateral soil reaction around a monopile generally increases to a maximum value and then decreases to zero at the depth of the rotation point, and following that, at the rear side of the monopile, it gradually increases from this rotation point to a maximum value at the pile tip (e.g., Prasad and Chari, [30]; Zhang et al. [17]; Li et al. [18]; Wang et al. [15]). The maximum soil lateral reaction in the front side is located at a depth of Zm.
- (2)
- The maximum soil lateral pressure in the front side of the monopile is pm, which may be calculated using Rankine’s passive earth pressure theory (Kpγ′Zm) and the mobilization coefficient of ultimate soil resistance η, where γ′ is the effective unit weight of soil, and Kp is the coefficient of Rankine’s passive earth pressure. The mobilization coefficient η is introduced to quantify the amount of soil pressure/reaction mobilized under a certain loading magnitude. At a given depth of the monopile, to account for the non-uniformity distribution of soil lateral pressure across the diameter of a circular monopile, a reduction factor of 0.8 is usually introduced (e.g., Zhang et al. [17]; Prasad and Chari [30]).
- (3)
- According to the equilibrium of lateral force and moment on the monopile, the depth of the maximum soil pressure Zm in front of the monopile can be determined using Equation (1), while the correlation between the applied lateral load and the mobilization coefficient η is given by Equation (2). The derivation process of Equations (1) and (2) can be referred to Appendix A. Equation (1) demonstrates that the depth of the maximum soil pressure Zm is only related to the pile embedded depth Lem and load eccentricity Lup, and it is independent of the magnitude of the applied lateral load F, which is in line with the findings by other researchers (e.g., Georgiadis et al. [21]; Zhu et al. [27]; Prasad and Chari [30]).
2.3. Correlation between Pile Head Rotation and Mobilization Coefficient
- (1)
- As expected, the value of mobilization coefficient η increases with pile head rotation θ in a nonlinear pattern.
- (2)
- The relationship between η and θ depends on the critical friction angle of soil ϕc and the relative density Dr, i.e., piles in similar ground conditions generate nearly identical η–θ correlations.
- (3)
- A power function, as shown in Equation (4), is capable of modeling the relationship between η and θ, where m and n are the model parameters.
2.4. General Design Procedures
- Set a specific value of pile head rotation θi;
- According to the ground conditions, including the sand critical friction angle ϕc and relative density Dr, the value of mobilization coefficient ηi can be calculated using Equation (4), where m = (0.26 ϕc − 4.8)Dr; n = 0.45.
- Calculate the corresponding pile head load Fi using Equation (5), as well as the pile head displacement using Equation (6).
- Repeating steps 1 to 3, the general pile head response of a monopile can be estimated.
3. Validation
3.1. Database
3.2. Pile Head Response
- (4)
- Erith sand consists of pure quartz grains with subrounded shape with critical friction angle ϕc of 35° [40].
- (5)
- The peak friction angle ϕp of Erith sand can be determined according to Equation (7).
3.3. Soil Lateral Reaction Profile
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Notation
D | outer diameter of pile |
Dr | relative density of sand |
Ep | elastic modulus of pile |
F | lateral force acted on pile head |
Fu | pile ultimate load capacity |
h | height of displacement measured |
Kp | coefficient of Rankine’s passive earth pressure |
Lem | embedded length of pile |
Lup | loading eccentricity of pile |
M0 | moment acted on pile head |
m, n | parameters of correlation between η and θ |
m′ | normalized model parameter |
nh | constant of horizontal subgrade reaction |
P | lateral soil reaction |
pm | maximum soil pressure in the front side of monopile |
y | lateral displacement of rigid pile |
Zm | depth of maximum lateral soil reaction |
Zr | depth of rotation point |
ϕc | critical friction angle of sand |
ϕp | peak friction angle of sand |
γ′ | effective density of sand |
θ | rotation of pile |
η | mobilization coefficient of ultimate soil resistance |
Qb | normalized load magnitude |
Appendix A. Derivation of Mobilization Coefficient η
References
- Poulos, H.G.; Hull, T.S. The role of analytical geomechanics in foundation engineering. In Foundation Engineering: Current Principles and Practices; ASCE: Reston, VA, USA, 1989; pp. 1578–1606. [Google Scholar]
- Tomlinson, M.; Woodward, J. Pile Design and Construction Practice; Taylor & Francis: London, UK; New York, NY, USA, 2015. [Google Scholar]
- Li, W.; Zhu, B.; Yang, M. Static Response of Monopile to Lateral Load in Overconsolidated Dense Sand. J. Geotech. Geoenviron. Eng. 2017, 143, 04017026. [Google Scholar] [CrossRef]
- Yang, M.; Luo, R.; Li, W. Numerical study on accumulated deformation of laterally loaded monopiles used by offshore wind turbine. Bull. Eng. Geol. Environ. 2018, 77, 911–921. [Google Scholar] [CrossRef]
- Luo, R.; Hu, M.; Yang, M.; Li, W.; Wang, A. Static Design for Laterally Loaded Rigid Monopiles in Cohesive Soil. J. Mar. Sci. Eng. 2023, 11, 817. [Google Scholar] [CrossRef]
- Zhang, L. Nonlinear analysis of laterally loaded rigid piles in cohesionless soil. Comput. Geotech. 2009, 36, 718–724. [Google Scholar] [CrossRef]
- Motta, E. Lateral deflection of horizontally loaded rigid piles in elastoplastic medium. J. Geotech. Geoenviron. Eng. 2013, 139, 501–506. [Google Scholar] [CrossRef]
- Reese, L.C.; Cox, W.R.; Koop, F.D. Analysis of Laterally Loaded Piles in Sand. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 6–8 May 1974; pp. 95–105. [Google Scholar]
- Kozubal, J.; Puła, W.; Wyjadłowski, M.; Bauer, J. Influence of varying soil properties on evaluation of pile reliability under lateral loads. J. Civ. Eng. Manag. 2013, 19, 272–284. [Google Scholar] [CrossRef]
- Ashour, M.; Norris, G.; Pilling, P. Lateral loading of a pile in layered soil using the strain wedge model. J. Geotech. Geoenviron. Eng. 1998, 124, 303–315. [Google Scholar] [CrossRef]
- Higgins, W.; Vasquez, C.; Basu, D.; Griffiths, D.V. Elastic solutions for laterally loaded piles. J. Geotech. Geoenviron. Eng. 2012, 139, 1096–1103. [Google Scholar] [CrossRef]
- Suryasentana, S.; Lehane, B. Numerical derivation of CPT-based p–y curves for piles in sand. Géotechnique 2014, 64, 186–194. [Google Scholar] [CrossRef]
- Abdel-Rahman, K.; Achmus, M. Finite element modelling of horizontally loaded monopile foundations for offshore wind energy converters in Germany. In International Symposium on Frontiers in Offshore Geotechnics; Cassidy, M., Gourvenec, S., Eds.; Taylor & Francis: Perth, Australia, 2015; pp. 391–396. [Google Scholar]
- Hu, Q.; Han, F.; Prezzi, M.; Salgado, R.; Zhao, M. Lateral load response of large-diameter monopiles in sand. Géotechnique 2022, 72, 1035–1050. [Google Scholar] [CrossRef]
- Wang, H.; Lehane, B.M.; Bransby, M.F.; Wang, L.Z.; Hong, Y.; Askarinejad, A. Lateral behavior of monopiles in sand under monotonic loading: Insights and a new simple design model. Ocean. Eng. 2023, 277, 114334. [Google Scholar] [CrossRef]
- Brinch-Hansen, J. The Ultimate Resistance of Rigid Piles against Transversal Forces; Bulletin 12; Danish Geotechnical Institute: Copenhagen, Denmark, 1961; pp. 1–9. [Google Scholar]
- Zhang, L.; Silva, F.; Grismala, R. Ultimate lateral resistance to piles in cohesionless soils. J. Geotech. Geoenviron. Eng. 2005, 131, 78–83. [Google Scholar] [CrossRef]
- Li, W.; Gavin, K.; Doherty, P. Experimental investigation on the lateral load capacity of monopiles in dense sand. In Proceedings of the 38th Annual Conference on Deep Foundations, Phoenix, AZ, USA, 25–28 September 2013; pp. 67–75. [Google Scholar]
- Zhang, L.; Ahmari, S. Nonlinear analysis of laterally loaded rigid piles in cohesive soil. Int. J. Numer. Anal. Methods Geomech. 2013, 37, 201–220. [Google Scholar] [CrossRef]
- Murphy, G.; Doherty, P.; Cadogan, D.; Gavin, K. Field experiments on instrumented winged monopiles. Proc. Inst. Civ. Eng.-Geotech. Eng. 2016, 169, 227–239. [Google Scholar] [CrossRef]
- Georgiadis, M.; Anagnostopoulos, C.; Saflekou, S. Centrifugal testing of laterally loaded piles in sand. Can. Geotech. J. 1992, 29, 208–216. [Google Scholar] [CrossRef]
- Klinkvort, R.T.; Hededal, O. Effect of load eccentricity and stress level on monopile support for offshore wind turbines. Can. Geotech. J. 2014, 51, 966–974. [Google Scholar] [CrossRef]
- El Naggar, M.H.; Wei, J.Q. Response of tapered piles subjected to lateral loading. Can. Geotech. J. 1999, 36, 52–71. [Google Scholar] [CrossRef]
- Qin, H.; Guo, W.D. Response of static and cyclic laterally loaded rigid piles in sand. Mar. Georesour. Geotechnol. 2016, 34, 138–153. [Google Scholar] [CrossRef]
- Choo, Y.W.; Kim, D. Experimental Development of the p–y Relationship for Large-Diameter Offshore Monopiles in Sands: Centrifuge Tests. J. Geotech. Geoenviron. Eng. 2016, 142, 04015058. [Google Scholar] [CrossRef]
- Mu, L.; Kang, X.; Feng, K.; Huang, M.; Cao, J. Influence of vertical loads on lateral behaviour of monopiles in sand. Eur. J. Environ. Civ. Eng. 2018, 22 (Suppl. S1), 286–301. [Google Scholar] [CrossRef]
- Zhu, B.; Sun, Y.X.; Chen, R.P.; Guo, W.D.; Yang, Y.Y. Experimental and Analytical Models of Laterally Loaded Rigid Monopiles with Hardening p–y Curves. J. Waterw. Port Coast. Ocean. Eng. 2015, 141, 04015007. [Google Scholar] [CrossRef]
- Ahmed, S.S.; Hawlader, B. Numerical Analysis of Large-Diameter Monopiles in Dense Sand Supporting Offshore Wind Turbines. Int. J. Geomech. 2016, 16, 04016018. [Google Scholar] [CrossRef]
- Wang, H.; Lehane, B.; Bransby, M.; Askarinejad, A.; Wang, L.; Hong, Y. A simple rotational spring model for laterally loaded rigid piles in sand. Mar. Struct. 2022, 84, 103225. [Google Scholar] [CrossRef]
- Prasad, Y.V.; Chari, T. Lateral capacity of model rigid piles in cohesionless soils. Soils Found. 1999, 39, 21–29. [Google Scholar] [CrossRef] [PubMed]
- Chari, T.R.; Meyerhof, G.G. Ultimate capacity of rigid single piles under inclined loads in sand. Can. Geotech. J. 1983, 20, 849–854. [Google Scholar] [CrossRef]
- Li, W.; Igoe, D.; Gavin, K. Evaluation of CPT-based P–y models for laterally loaded piles in siliceous sand. Geotech. Lett. 2014, 4, 110–117. [Google Scholar] [CrossRef]
- Bolton, M.D. The strength and dilatancy of sands. Géotechnique 1986, 36, 65–78. [Google Scholar] [CrossRef]
- Joo, J.S. Behaviour of Large Scale Rigid Model Piles under Inclined Loads in Sand. Master’s Thesis, Memorial University of Newfoundland, St. John’s, NL, Canada, 1986. [Google Scholar]
- Agaiby, S.W.; Kulhawy, F.H.; Trautmann, C.H. Experimental Study of Drained Lateral and Moment Behavior of Drilled Shafts during Static and Cyclic Loading; Final Report; Electric Power Research Inst.: Palo Alto, CA, USA; Cornell Univ.: Ithaca, NY, USA; Geotechnical Engineering Group: Grand Junction, CO, USA, 1992. [Google Scholar]
- Nazir, R.B. The Moment Carrying Capcity of Short Piles in Sand. Ph.D. Thesis, University of Liverpool, Liverpool, UK, 1994. [Google Scholar]
- Leth, C.T. Improved Design Basis for Laterally Loaded Large Diameter Pile. Ph.D. Thesis, Department of Civil Engineering, Aalborg University, Aalborg, Denmark, 2013. [Google Scholar]
- Dickin, E.; King, G. Numerical modelling of the load-displacement behaviour of anchor walls. Comput. Struct. 1997, 63, 849–858. [Google Scholar] [CrossRef]
- Laman, M.; King, G.; Dickin, E. Three-dimensional finite element studies of the moment-carrying capacity of short pier foundations in cohesionless soil. Comput. Geotech. 1999, 25, 141–155. [Google Scholar] [CrossRef]
- Dickin, E.; Laman, M. Uplift response of strip anchors in cohesionless soil. Adv. Eng. Softw. 2007, 38, 618–625. [Google Scholar] [CrossRef]
Pile No. | Field/ Lab | Soil Condition | Prototype Pile Dimensions | Pile Type | Reference | ||
---|---|---|---|---|---|---|---|
D (m) | Lem/D | Lup/D | |||||
PR1 | Field | Dense sand | 0.34 | 6.5 | 1.18 | Steel Pipe Pile | Li et al. [3] |
PR2 | Field | Medium-dense | 0.245 | 6.1 | 1.63 | Steel Pipe Pile | Murphy et al. [20] |
PR3 | Field | Medium-dense | 0.245 | 6.1 | 1.63 | Steel Winged Pipe Pile | Murphy et al. [20] |
PR4 | Lab | Medium-dense to dense | 1.092 | 8.3 | 1.14 | Steel Pipe Pile | Georgiadis et al. [21] |
PR5 | Lab | Dense sand | 3 | 6.0 | 15 | Steel Pipe Pile | Klinkvort & Hededal [22] |
PR6 | Lab | Loose sand | 0.168 | 7.1 | 1.16 | Steel Pipe Pile | Naggar & Wei [23] |
PR7 | Lab | Dense sand | 0.032 | 15.6 | 3.59 | Steel Pipe Pile | Qin & Guo [24] |
PR8 | Lab | Dense sand | 0.032 | 12.5 | 3.59 | Steel Pipe Pile | Qin & Guo [24] |
PR9 | Lab | Dense sand | 6 | 5.2 | 5.5 | Steel Pipe Pile | Choo & Kim [25] |
PR10~ PR12 | Lab | Dense sand | 0.048 | 8.3 | 1.04 | Steel Pipe Pile | Mu et al. [26] |
PR13~ PR18 | Lab | Dense sand | 0.165 | 5.5 | 6 | Steel Pipe Pile | Zhu et al. [27] |
Pile No | Pile Dimensions in Prototype | Soil Properties | Test Description | Height of Displacement Measured (m) | Reference | |||||
---|---|---|---|---|---|---|---|---|---|---|
D(m) | Lem/D | Lup/D | γ′ (kN/m3) | ϕp (°) | ϕc (°) | Dr (%) | ||||
P1 | 0.075 | 13.3 | 1 | 15.25 | 46 | 32 a | 82 | Angular dry sand 1 g model test | 0 | Chari and Meyerhof [31] |
P2 | 1 | 6 | 15 | 16.7 | 43.2 | 30 | 93 | Dry/Saturated Fontainebleau sand, centrifuge test | 1.375 | Klinkvort and Hededal. [22] |
P3 | 3 | 8.25 | 10.3 | 42.5 | 88 | 4.125 | ||||
P4 | 3 | 10.5 | 10.4 | 43.4 | 93 | 4.125 | ||||
P5 | 3 | 12.75 | 10.2 | 42.3 | 87 | 4.125 | ||||
P6 | 0.102 | 6 | 1.5 | 18.3 | 43 | 33.3 b | 75 | Well-graded angular dry sand 1 g model test | 0 | Prasad and Chari [30] |
P7 | 0.165 | 5.55 | 6 | 9.1 | 41.5 | 35.5 | 88 | Saturated Hangzhou silt sand, 1 g model test | 0.99 | Zhu et al. [27] |
P8 | 0.495 | |||||||||
P9 | 0.165 | |||||||||
P10 | 8.8 | 37.4 | 70 | 0.99 | ||||||
P11 | 0.495 | |||||||||
P12 | 0.165 | |||||||||
P13 | 0.34 | 6.5 | 1.18 | 20 | 54 | 37 | 100 | Heavily over-consolidated Blessington sand | 0 | Li et al. [32] |
Pile No. | Prototype Pile Dimensions | Soil Properties | Test Description | Measured Curves b | η~θ | Reference | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
D(m) | Lem/D | Lup/D | γ′ (kN/m3) | ϕp (°) | ϕc (°) | Dr (%) | |||||
1 | 0.073 | 10 | 2.33 | 15.1 | 41.2 | 32 a | 77 | 1 g model tests | F-y | η = 2.7θ0.45 | Joo [34] |
2 | 0.09 | 8.9 | 2.78 | ||||||||
3 | 0.102 | 8.8 | 2.75 | ||||||||
4 | 1.224 | 7.4 | 1 | 16.3 | 36 | 30 | 60 | centrifuge tests | F-y | η = 1.8θ0.45 | Georgiadis et al. [21] |
5 | 0.076 | 9 | 0.92 | 16.42 | 41.4 | 32.9 | medium dense | 1 g model tests | F-y | η = 1.8θ0.45 | Agaiby et al. [35] |
6 | 8.6 | 41.4 | |||||||||
7 | 6 | 41.7 | |||||||||
8 | 3 | 42.3 | |||||||||
9 | 0.152 | 3 | 0.53 | 41.7 | |||||||
10 | 6 | 41.2 | |||||||||
11 | 9 | 40.9 | |||||||||
12 | 0.076 | 3 | 3 | 42.3 | |||||||
13 | 9 | ||||||||||
14 | 15 | ||||||||||
15 * | 1 | 2 | 6 | 16.4 | 51 | 35 | 85 | centrifuge tests | M-θ | η = 3.7θ0.45 | Nazir [36] |
16 | 1 | 6 | 2.5 | 16.2 | 43 | 30 | 80 | centrifuge tests | F-y | η = 2.4θ0.45 | Leth [37] |
17 | 8 | 42.5 | |||||||||
18 | 10 | 42 | |||||||||
19 | 2 | 6 | 1.43 | 41.6 | |||||||
20 | 8 | 40.9 | |||||||||
21 | 10 | 40.4 | |||||||||
22 | 3 | 6 | 1 | 40.5 | |||||||
23 | 3 | 8 | 39.9 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Luo, R.; Wang, A.; Li, J.; Ding, W.; Zhu, B. Simplified Design Method of Laterally Loaded Rigid Monopiles in Cohesionless Soil. J. Mar. Sci. Eng. 2024, 12, 208. https://doi.org/10.3390/jmse12020208
Luo R, Wang A, Li J, Ding W, Zhu B. Simplified Design Method of Laterally Loaded Rigid Monopiles in Cohesionless Soil. Journal of Marine Science and Engineering. 2024; 12(2):208. https://doi.org/10.3390/jmse12020208
Chicago/Turabian StyleLuo, Ruping, Anhui Wang, Jie Li, Wenyun Ding, and Bitang Zhu. 2024. "Simplified Design Method of Laterally Loaded Rigid Monopiles in Cohesionless Soil" Journal of Marine Science and Engineering 12, no. 2: 208. https://doi.org/10.3390/jmse12020208