Investigation of the torsional behaviour of circular piles in double-layered nonhomogeneous soil
Introduction
For offshore engineering, circular piles have been widely used as one of the main types of foundations for structures, such as offshore wind turbines [1]. It is noted that the analysis of the response of piles under vertical, horizontal and moment load is a common practice in the pile analysis [2]. However, there are some types of structures, such as the offshore monopiles, which are subjected to significant torsional loads (e.g. induced by eccentric wind or wave forces, or even ship collision) [3,4]. During the last two decades, numerous pile foundations failed due to insufficient torsional bearing capacity [4]. The elastoplastic behaviour of soil and nonlinear variation of soil profile have been widely faced for engineers, which have a significant influence on the behaviour of structures around soils [1,[4], [5], [6], [7], [8], [9], [10], [11]].
An extensive literature survey has been conducted on the analysis of the torsional responses of piles. Poulos [12] developed a closed-form elastic solution for the relationship between the torque and torsion angle at the top of a single pile in a subsoil, where the shear modulus was either constant or increased linearly with depth. A number of earlier studies through analytical solutions have been conducted to investigate the pile torsional bearing capacity in a single soil layer [3,6,13,14]. For layered soil profiles, quite a few earlier studies through analytical solutions have been carried out to investigate the torsional loaded pile in two-layered homogeneous and non-homogeneous soil profiles [15,16]. In these studies, the soil was assumed to behave linearly elastically at small strain stage and to yield when the shear stresses at the pile-soil interface reach the corresponding maximum shear resistance, where the shear modulus varies linearly with depth. However, very complicated variation principle and integral iteration are needed for these methods. Furthermore, for the method in Ref. 15, the sliding failure of the interface of pile and soils has not been considered; and for the method in Ref. 16, it can only be employed for double layered Gibson foundation. Further, numerical analysis methods, such as the discrete element method (DEM), the finite element method (FEM) and the boundary element method (BEM), have been employed to analyse the torsional bearing capacity of piles [17], [18], [19]. In addition to the above studies, a few studies were reported to investigate the responses of piles subjected to torsional load through model tests [12,20,21].
All the studies discussed so far are mainly focusing on the investigation of the nonlinear torsional responses of piles in uniform, single-layered non-homogenous or homogenous soil deposits, double layered Gibson foundation, and multi-layered soil. And for the case of multi-layered soil profile, an elastic and homogeneous profile was presumed for each layer soil. The behaviour of the torsional bearing capacity of a pile in a double-layered non-homogenous soil considering yielding and nonlinear variation of soil profile is yet to be explored. However, it is very important for understanding the behaviour of offshore piles.
In this study, a new analytical design method has been developed, which considers the nonlinear variation of a soil profile (i.e. variation of the shear modulus of each stratum and the limiting friction resistance, τf), and the relative slip along the pile-soil interface. Then, the new method was developed to predict the limiting torsional bearing capacity of a pile in a double-layered non-homogenous subsoil. Finally, the new method has been applied to the piles in sand over clay soil deposit to show the applicability of the method, and to investigate the torsional bearing capacity of a pile in a double-layered sand over clay soil deposits.
Section snippets
Computational model and basic assumptions
In this study, as shown in Fig. 1, a circular pile of radius r0 and length L pre-embedded in a double-layered nonhomogeneous soil deposit has been considered. The shear moduli of the top and bottom soil layers, G(z), increase nonlinearly, as shown in Eq. (1) [19].where L1 is the thickness of the upper soil layer (m); μ1 and μ2 are the shear moduli at the surfaces of the top and bottom soil layers (kPa), respectively; m1, m2, α1 and α2 are
Analysis of a torsional loaded pile in two-layered nonhomogeneous soil
Considering the displacement coordination of a pile-soil interface, in the elastic range, the torsion angle of a pile body equals the torsion angle of the soil. For a pile body, it becomeswhere (GJ)p is the torsional rigidity of pile (kN.m2); and Φ(z) is the angle of twist (rad).
Verification of the new method
The results from the new analytical method developed have been verified by comparing with experimental and previously published data for the following cases: (1) a pile in a single-layered nonhomogeneous subsoil in elastic range; (2) a pile in a double-layered homogeneous subsoil in elastic stage; (3) a pile in sand; and (4) a pile in clay.
Illustrative example
To illustrate how the new method can be applied to a practical situation, the method has been used to analyse a typical case of a pile pre-embedded in sand over clay soil deposit. For loose and dense sand, the soil properties have been taken from Karthigeyan et al. [24], whereas the properties for clay have been taken from Basack [22].
For a pile in sand, τf, can be estimated from the following equation:where K is the lateral earth pressure coefficient; γ’ is the effective unit weight
Conclusions
In this study, a new analytical method has been developed, which can predict the nonlinear response of torsional loaded pile in a double-layered soil profile, with considering the soil yielding . The variations of the shear moduli of the double-layered soil with depth and the limiting shaft friction with depth can be expressed by power laws with increasing torque and partial slip occurs between the pile and the soil. The slip appears when the shear stress of the soil reaches the limiting shaft
Declaration of Competing Interest
The author declare that they have no competing financial interests or personal relationship that could have appeared to influence the work reported in this paper
Acknowledgements
The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (grant no. 51578231 & No. 51378197). This work is also supported by the Research on Stability of Residual Soil Slope under Seepage and New Ecological Protection Technology (2018-ZJKJ-PTJS01), and the State Key Laboratory of Subtropical Building Science, South China University of Technology (2017KA04), Science and technology program of Guangzhou (201707020047) and the Sino-German
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