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Fully assessing foundation failure envelopes under combined loads in spatially variable clay

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Abstract

Soil spatial variability is a common situation in marine geotechnical engineering, while most studies have primarily focused on evaluating the uniaxial vertical (V), horizontal (H), or moment (M) bearing capacity of foundations in spatially variable clay. Whereas the process of combined bearing capacity analysis by probe method is complex, resulting in low efficiency. As a result, the simplified modified swipe (SMS) method is proposed in this paper, which can represent the capacity in any direction of the load space accurately and takes just 6.5 times the duration of a single probe loading for a half-failure envelope. Based on the established three-dimensional random finite element models, the effectiveness of this method is demonstrated by analyzing the combined bearing capacity of five kinds of foundations in spatially variable clay. Furthermore, Monte Carlo simulations revealed that the spatial variability of the soil cause various failure envelopes, and the response of the combined bearing capacity is not identical in all directions. The VHM failure envelopes with different probabilities are given and could be found that the safety factors recommended by the guidelines are insufficiently conservative for structures susceptible to soil spatial variability. Finally, a strategy for applying different safety factors to both load directions is proposed, which could be helpful for the design of foundations in spatially variable clay.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

Not applicable.

Abbreviations

A :

Cross-sectional plan area of foundations

COV:

Coefficient of variation

D :

Foundation diameter

E :

Young’s modulus

Fs:

Factor of safety

Fs_x :

Factor of safety in x direction

Fs_y :

Factor of safety in y direction

H :

Horizontal loading

H ult :

The horizontal ultimate bearing capacity

L :

Skirt length of caissons and tripod bucket foundations

M :

Moment loading

MCS:

Monte Carlo simulation

M ult :

The moment ultimate bearing capacity

N :

Number of Monte Carlo simulations

N c H :

The horizontal bearing capacity factor

N c H_ Det :

The horizontal bearing capacity factor in deterministic soil

N c M :

The moment bearing capacity factor

N c M_ Det :

The moment bearing capacity factor in deterministic soil

Nc Nor_space :

The bearing capacity factor in normalized loading space

N c V :

The vertical bearing capacity factor

N c V_ Det :

The vertical bearing capacity factor in deterministic soil

V :

Vertical loading

V ult :

The vertical ultimate bearing capacity

X amp1 :

The displacement amplitude of the first step in the first loading direction of the SMS method

X amp2 :

The displacement amplitude of the second step in the first loading direction of the SMS method

Y amp2 :

The displacement amplitude of the second step in the second loading direction of the SMS method

k :

The gradient of the undrained strength

lt:

Lid thickness of caisson; foundation thickness of surface footing and embedded foundation

s u :

The undrained shear strength

s u0 :

The undrained shear strength at the foundation tip level

s um :

The undrained shear strength at mudline

t :

Skirt thickness

v :

Poisson’s ratio

θ :

Rotational displacement

δ h :

The horizontal scale of fluctuation

δ v :

The vertical scale of fluctuation

References

  1. API R (2011) 2GEO (2011). Recommended practice for geotechnical foundation design consideration

  2. Bransby F, Randolph M (1998) Combined loading of skirted foundations. Géotechnique 48:637–655

    Article  Google Scholar 

  3. Butterfield R, Houlsby GT, Gottardi G (1997) Standardized sign conventions and notation for generally loaded foundations. Géotechnique 47(5):1051–1054

    Article  Google Scholar 

  4. Cai Y, Bransby MF, Gaudin C, Tian Y (2022) Accounting for soil spatial variability in plate anchor design. J Geotech Geoenviron Eng 148(2):04021178

    Article  Google Scholar 

  5. Cassidy MJ, Uzielli M, Tian Y (2013) Probabilistic combined loading failure envelopes of a strip footing on spatially variable soil. Comput Geotech 49:191–205

    Article  Google Scholar 

  6. Charlton TS, Rouainia M (2016) Probabilistic capacity analysis of suction caissons in spatially variable clay. Comput Geotech 80:226–236

    Article  Google Scholar 

  7. Chen X-J, Fu Y, Liu Y (2022) Random finite element analysis on uplift bearing capacity and failure mechanisms of square plate anchors in spatially variable clay. Eng Geol 304:106677

    Article  Google Scholar 

  8. Chen X, Li D, Tang X, Liu Y (2021) A three-dimensional large-deformation random finite-element study of landslide runout considering spatially varying soil. Landslides 18(9):3149–3162

    Article  Google Scholar 

  9. Cheng P, Liu Y, Li YP, Yi JT (2022) A large deformation finite element analysis of uplift behaviour for helical anchor in spatially variable clay. Comput Geotech 141:104542

    Article  Google Scholar 

  10. El Haj A-K, Soubra A-H (2020) Efficient estimation of the failure probability of a monopile foundation using a Kriging-based approach with multi-point enrichment. Comput Geotech 121:103451

    Article  Google Scholar 

  11. Fan S, Zhang Y, Li S, Han M, Liu J (2023) Correction and simplification of swipe category methods for determining the failure envelope on cohesive soil. Comput Geotech 164:105853

    Article  Google Scholar 

  12. Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical. Engineering. https://doi.org/10.1002/9780470284704

    Article  Google Scholar 

  13. Fu D, Gaudin C, Tian Y, Cassidy MJ, Bienen B (2017) Uniaxial capacities of skirted circular foundations in clay. J Geotech Geoenviron Eng. https://doi.org/10.1061/(asce)gt.1943-5606.0001685

    Article  Google Scholar 

  14. Fu D, Zhang Y, Yan Y (2020) Bearing capacity of a side-rounded suction caisson foundation under general loading in clay. Comput Geotech 123:103543

    Article  Google Scholar 

  15. Gourvenec S (2008) Effect of embedment on the undrained capacity of shallow foundations under general loading. Géotechnique 58(3):177–185

    Article  Google Scholar 

  16. Gourvenec S, Barnett S (2011) Undrained failure envelope for skirted foundations under general loading. Géotechnique 61(3):263–270

    Article  Google Scholar 

  17. Gourvenec SM, Feng X, Randolph MF, White DJ (2017) A toolbox for optimizing geotechnical design of subsea foundations. In: Offshore Technology Conference

  18. Gourvenec S, Randolph M (2003) Bearing capacity of a skirted foundation under VMH loading. Proc Int Conf Offshore Mech Arctic Eng OMAE 3:413–416

    Google Scholar 

  19. He X, Wang F, Li W, Sheng D (2022) Deep learning for efficient stochastic analysis with spatial variability. Acta Geotech 17(4):1031–1051

    Article  Google Scholar 

  20. Hung LC, Kim SR (2014) Evaluation of undrained bearing capacities of bucket foundations under combined loads. Mar Georesour Geotechnol 32(1):76–92

    Article  CAS  Google Scholar 

  21. ISO 19901-4 (2003) Geotechnical and foundation design considerations

  22. Lacasse S, Nadim F (1997) Uncertainties in characterising soil properties. Publikasjon - Norges Geotekniske Institutt

  23. Li L, Li J, Huang J, Gao F-P (2017) Bearing capacity of spudcan foundations in a spatially varying clayey seabed. Ocean Eng 143:97–105

    Article  Google Scholar 

  24. Li L, Li J, Huang J, Liu H, Cassidy MJ (2017) The bearing capacity of spudcan foundations under combined loading in spatially variable soils. Eng Geol 227:139–148

    Article  Google Scholar 

  25. Li J, Luo W, Tian Y, Wang Y, Cassidy MJ (2021) Modeling of large deformation problem considering spatially variable soils in offshore engineering. Mar Georesour Geotechnol 39(8):906–918

    Article  Google Scholar 

  26. Li JH, Zhou Y, Zhang LL, Tian Y, Cassidy MJ, Zhang LM (2016) Random finite element method for spudcan foundations in spatially variable soils. Eng Geol 205:146–155

    Article  Google Scholar 

  27. Liu Y, Lee F-H, Quek S-T, Beer M (2014) Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties. Probab Eng Mech 38:42–53

    Article  Google Scholar 

  28. Luo W, Li J (2022) Effects of installation on combined bearing capacity of a spudcan foundation in spatially variable clay. Appl Ocean Res 120:103055

    Article  Google Scholar 

  29. Luo W, Li J, Zhang Y (2020) Quantifying installation risk during spudcan penetration. Ocean Eng 216:108050

    Article  Google Scholar 

  30. Martin CM, Houlsby GT (2001) Combined loading of spudcan foundations on clay: numerical modelling. Géotechnique 51(8):687–699

    Article  Google Scholar 

  31. Phoon K-K, Kulhawy FH (1999) Characterization of geotechnical variability

  32. Phoon K, Nadim F, Uzielli M, Lacasse S (2006) Soil variability analysis for geotechnical practice. Charact Eng Prop Nat Soils. https://doi.org/10.1201/NOE0415426916.ch3

    Article  Google Scholar 

  33. Qiu C, Wang W, Yan Y, Fu D, Yan S (2022) The optimisation of anti-overturning capacities for tripod suction bucket foundations in clay. Ocean Eng 264:112496

    Article  Google Scholar 

  34. Shen Z, Jin D, Pan Q, Yang H, Chian SC (2020) Probabilistic analysis of strip footings on spatially variable soils with linearly increasing shear strength. Comput Geotech 126:103653

    Article  Google Scholar 

  35. Shen Z, Jin D, Pan Q, Yang H, Chian SC (2021) Effect of soil spatial variability on failure mechanisms and undrained capacities of strip foundations under uniaxial loading. Comput Geotech 139:104387

    Article  Google Scholar 

  36. Shen Z, Pan Q, Chian SC, Gourvenec S, Tian Y (2022) Probabilistic failure envelopes of strip foundations on soils with non-stationary characteristics of undrained shear strength. Géotechnique 73:716

    Article  Google Scholar 

  37. Shu S, Gao Y, Wu Y, Ye Z (2021) Undrained bearing capacity of two strip footings on a spatially variable soil with linearly increasing mean strength. Int J Geomech 21(2):06020037

    Article  Google Scholar 

  38. Shu S, Gao Y, Wu Y, Ye Z, Song S (2020) Bearing capacity and reliability analysis of spudcan foundations embedded at various depths based on the non-stationary random finite element method. Appl Ocean Res 100:102182

    Article  Google Scholar 

  39. Simulia DS (2010) Abaqus analysis user’s manual. Dassault Systemes, Pawtucket, USA

  40. Suryasentana SK, Dunne HP, Martin CM, Burd HJ, Byrne BW, Shonberg A (2020) Assessment of numerical procedures for determining shallow foundation failure envelopes. Géotechnique 70(1):60–70

    Article  Google Scholar 

  41. Tabarroki M, Ching J (2019) Discretization error in the random finite element method for spatially variable undrained shear strength. Comput Geotech 105:183–194

    Article  Google Scholar 

  42. Taiebat HA, Carter JP (2010) A failure surface for circular footings on cohesive soils. Géotechnique 60(4):265–273

    Article  Google Scholar 

  43. Vulpe C (2015) Design method for the undrained capacity of skirted circular foundations under combined loading: effect of deformable soil plug. Géotechnique 65(8):669–683

    Article  Google Scholar 

  44. Vulpe C, Gourvenec S, Power M (2014) A generalised failure envelope for undrained capacity of circular shallow foundations under general loading. Géotech Lett 4(3):187–196

    Article  Google Scholar 

  45. Wang Y, Cassidy MJ, Bienen B (2020) Numerical investigation of bearing capacity of spudcan foundations in clay overlying sand under combined loading. J Geotech Geoenviron Eng 146(11):04020117

    Article  CAS  Google Scholar 

  46. Wang Z-Z, Goh SH (2021) Novel approach to efficient slope reliability analysis in spatially variable soils. Eng Geol 281:105989

    Article  Google Scholar 

  47. Wang ZZ, Xiao C, Goh SH, Deng M-X (2021) Metamodel-based reliability analysis in spatially variable soils using convolutional neural networks. J Geotech Geoenviron Eng 147(3):04021003

    Article  Google Scholar 

  48. Ye Z, Gao Y, Shu S, Wu Y (2021) Probabilistic undrained bearing capacity of skirted foundations under HM combined loading in spatially variable soils. Ocean Eng 219:108297

    Article  Google Scholar 

  49. Zhang Y (2013) A force resultant model for spudcan foundations in soft clay. PhD Thesis, University of Western Australia

  50. Zhang Y, Bienen B, Cassidy MJ, Gourvenec S (2011) The undrained bearing capacity of a spudcan foundation under combined loading in soft clay. Mar Struct 24(4):459–477

    Article  Google Scholar 

  51. Zhou M, Yang N, Tian Y, Zhang X (2023) Inclined pullout capacity of suction anchors in clay over silty sand. J Geotech Geoenviron Eng 149(6):04023030

    Article  CAS  Google Scholar 

  52. Zou X, Wang Y, Zhou M, Zhang X (2023) Failure mechanism and combined bearing capacity of monopile–friction wheel hybrid foundation in sand-over-clay deposit. Acta Geotech. https://doi.org/10.1007/s11440-023-01972-8

    Article  Google Scholar 

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Acknowledgements

The work forms part of the activities of the State Key Laboratory of Hydraulic Engineering Simulation and Safety at Tianjin University. The corresponding author is supported by the National Natural Science Foundation of China (No. 51890911). The support is gratefully acknowledged.

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  1. State Key Laboratory of Hydraulic Engineering Simulation and Safety, School of Civil Engineering, Tianjin University, Jinnan District, 135 Yaguan Road, Tianjin, 300350, China

    Shuntao Fan, Yurong Zhang & Sa Li

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  1. Shuntao Fan
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Fan, S., Zhang, Y. & Li, S. Fully assessing foundation failure envelopes under combined loads in spatially variable clay. Acta Geotech. (2024). https://doi.org/10.1007/s11440-023-02214-7

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