An analytical approach to pile-to-pile interaction for end-bearing piles

Due to a growing number of offshore wind farm projects in seismic areas, existing design procedures for slender piles under seismic loading need to be revised to allow for the design of larger and stockier monopiles. This study illustrates how advanced finite element analyses can be used to investigate the combination of seismic loads and may thus inform standard design procedures commonly adopted in practice. In standard design methods, a soil-pile foundation system is represented by a simplified beam-on-nonlinear-springs model [1]. Earthquake loads acting on this system can be decomposed into inertial forces, which originate from the acceleration of a superstructure mass, and kinematic loads due to ground displacements caused by the propagation of seismic waves. Inertial loads are typically derived from modified acceleration spectra which account for the difference between the pile head movement and the soil displacement in the free-field [2, 3, 4]. Maximum displacement profiles can be obtained from site response analyses of the free-field soil column. The distribution of pile bending moments and internal forces can thus be found by superposition of the two loads. However, unless numerical time-domain analyses are carried out, it is not evident whether these components are acting simultaneously on the pile. In the design of long and slender piles, a common assumption is that inertial and kinematic loads may be considered separately, as the former tend to affect only the near-surface zones while the latter dominate at larger depths [2]. However, their combined effect on a far less flexible monopile exhibiting rotational mechanisms is not yet understood, neither is the influence of soil liquefaction triggered by the seismic ground shaking. Experiments on pile groups presented in the literature suggest a dependence of the phase angle on the ratio between the fundamental frequency of the soil deposit and the superstructure [5]. The analogous scenarios are illustrated for a monopile-supported wind turbine in Figure 1.
 The turbine is considered as a single-degree-of-freedom system with the mass off the rotor nacelle assembly lumped together and located at hub height. The time history of the inertial force acting at hub height (), as well as the horizontal ground displacement at surface level (), are schematically shown in Figure 1(b) for a very stiff soil. In this case, the fundamental period of the soil deposit () is significantly lower than that of the superstructure (), which causes the response of the turbine system to act out of phase with the ground movement by 180°. For a soft soil deposit with much higher fundamental period than the turbine (Figure 1(c)), the kinematic and inertial loads are expected to act in phase.
 To investigate the combination of seismic loads acting on a monopile foundation in the time-domain, advanced numerical analyses are carried out on three-dimensional Finite Element models. Soil layers with widely different material properties are considered, including stiff marine clays and liquefiable sands with varying relative densities. The uni-directional motion records adopted as base excitations are sufficiently strong to induce large lateral ground movements and impose significant kinematic loads on the foundation. Through the of use of appropriate constitutive models in a hydro-mechanically coupled formulation, the response of the turbine sub-structure system is simulated while accounting for the degradation of stiffness in the surrounding soil and significant rises in excess pore pressures in the sand layers. An intensely nonlinear material behaviour typically leads to a shift of the fundamental frequency of the deposit [6], which can be deduced from the amplification of accelerations at various depths, with high frequencies dominating in the stiff soil layers and low frequencies in the soft liquefied sand. For a stiff soil deposit prior to liquefaction, local extrema in pile displacements at mudline level are therefore expected to act out of phase with the inertial force resulting from the acceleration of the rotor nacelle assembly at the turbine tower top (Case ). As the stiffness diminishes in a soft or fully liquefied ground, pile and free-field ground displacements are expected to move in-phase with the inertial load, as is characteristic for cases where the period of the soil deposit exceeds that of the superstructure (Case ). This change in behaviour highlights the influence of soil stiffness degradation and extensive ground liquefaction on the combination of seismic soil-structure interaction effects in the time-domain, which can be captured by advanced numerical methods.

The thermal–mechanical behavior of the energy pile under three kinds of climatic conditions was investigated in this study. A small-scale floating energy pile and a small-scale end-bearing energy pile, which were embedded in normally consolidated clay, were employed. The energy piles were subjected to cyclic heating/cooling, heating/recovery and cooling/recovery to simulate the energy pile work in the regions of warm/cold balanced climate, warm-dominated climate and cold-dominated climate, respectively. The thermal response and the mechanical response of the energy pile under different climatic conditions, as well as the different response between the floating energy pile and the end-bearing energy pile, were analyzed and discussed comprehensively. The results show that the thermo-mechanical performance of energy pile depends on the types of climatic conditions, and the behavior of the floating energy pile is different from the end-bearing pile. Larger irreversible displacement could be induced by thermal cycles for the floating energy pile compared to the end-bearing energy pile, while irreversible tip resistance could be induced for end-bearing energy pile. Under warm/cold balanced climate, the largest irreversible tip resistance and pile displacement could be induced for end-bearing energy pile and floating energy pile, respectively, and the smallest thermally induced irreversible displacement was observed when the energy pile was under cold-dominated climate.

Pseudostatic analysis for seismic responses of extended piles considering inertial and kinematic effects

Pile foundations in sloping or gently sloped liquefiable soils are often subjected to a combination of inertial and lateral spreading loads. Current design codes vary significantly in terms of the methods used to analyze and design piles that are subjected to combined loading. The results from a full-scale shake table test on a 0.25-m-diameter reinforced concrete pile in gently sloping ground are used in this study to back-calculate the inertial loads, the kinematic loads, and the interaction between inertial and kinematic loads during seismic loading. It was found that large pile strains developed after liquefaction was triggered. The maximum pile strains (and curvatures) at shallow depths within the nonliquefiable crust were correlated with maximum inertial loads in the upslope direction that were resisted by a crust load applied in the downslope direction, indicating an out-of-phase interaction. The maximum pile strains (and curvatures) at deeper locations below the loose liquefiable sand were correlated with the maximum inertial loads in the downslope direction but without any resistance or driving load from the crust (i.e., no lateral spreading load during peak downslope inertial cycles). The lack of crust load during the downslope inertial cycles was attributed to the pile head outrunning the crust displacement, causing the pile to be pushed into a gap that had formed on the downslope front of the pile. The findings of this study contribute a data point to a wide range of inertial and kinematic interaction factors proposed by other studies and highlight the site- and project-dependency of interactions between inertial and kinematic loads.

The seismic behavior of a RC pile with a diameter of 0.25 m subjected to liquefaction-induced lateral spreading was investigated using a shake table experiment that was conducted at the University of California, San Diego by Professor Ahmed Elgamal and Dr. Ahmed Ebeido (Ebeido and Elgamal 2019). A sinusoidal motion was applied at the base of a model that was inclined by 4 degrees. The loose and dense sand layers liquefied during the test, resulting in a permanent lateral spreading displacement of approximately 0.4 m (Figure E1). The pile was subjected to the combined effects of inertial loads from the acceleration of the superstructure mass and kinematic loads from the overlying nonliquefiable, dry crust. The dynamic responses of the soil and pile were analyzed to evaluate the relative contributions of inertial and kinematic loads during critical cycles (i.e., at the time of maximum inertia and the time of maximum pile strains). It was found that large pile strains developed after liquefaction was triggered. Large pile strains (and curvature) were recorded at a shallow depth within the crust (0.49 m) and a deeper location below the loose liquefiable sand (1.89 m). Large pile strains at shallow depth were found to be correlated with the inertial loads applied in the upslope direction. These upslope inertial loads were resisted by downslope crust loads, indicating an out-of-phase interaction. In contrast, large pile strains that occurred at deeper locations were correlated with downslope inertial loads and were accompanied by zero crust load, indicating that there was no lateral spreading force during the downslope inertial cycles. A gap at the downslope area in front of the pile formed because the soil displacements exceeded the pile displacements during the cyclic phase after liquefaction was triggered. The lack of crust load during the downslope inertial cycles is attributed to the pile head outrunning the crust displacement and causing the pile to be pushed into the gap at the downslope area in front of the pile. The interaction of inertia and kinematics appears to be a site- and project-specific phenomena. Therefore,the findings of this study—and, specifically, the lack of lateral spreading crust load during downslope inertial cycles—should be considered in design as one possible scenario in addition to the scenarios from several other studies that suggest combining the inertial loads with a lateral spreading force (e.g., Boulanger et al. 2007, Turner et al. 2016, Souri et al. 2022, Tokimatsu et al. 2005, Cubrinovski et al 2017).

Composite foundations have been widely used and promoted in practical engineering applications. However, research on the joint-bearing mechanism of piles and soil within composite foundations is still not comprehensive enough. This paper proposes a method for calculating the additional internal forces of piles and soil within composite foundations. Based on a three-dimensional finite element analysis, this study investigates the variation patterns of the stress, displacement, and additional internal forces of piles and soil in the depth direction under the action of upper loads when using friction piles and end-bearing piles. This research aims to reveal the bearing performance of piles and soil. The results showed that, under the same conditions and due to the presence of end-bearing effects, the internal forces experienced by the entire pile body of the end-bearing piles were more uniform, exhibiting significant advantages in resisting deformation and being able to withstand larger loads. Additionally, the diffusion mechanism of the vertical forces, stresses, and displacements of piles and soil is discussed. Due to the negative frictional resistance of soil and the influence of pile end-bearing effects, the distribution of internal forces and the displacements of piles and soil exhibited different characteristics. This study provides a scientific reference for the theoretical analysis and design of composite foundations.

While both American Society of Civil Engineers (ASCE) 7 and ASCE 61 require that kinematic (soil movement) loads be considered, they do not provide detailed guidance on the method(s) by which these loads on the structural system can be evaluated. This study discusses the modes of failure observed in real world kinematic movements, the analytical techniques used to evaluate pile-supported structures based on input soil movements, and appropriate performance limits for operational, life safety, spill prevention, and collapse prevention. The combination of kinematic and inertial loads, including simultaneous loading as well as post-kinematic inertial response is addressed. Acceptability of in-ground soil hinging and shearing is discussed in regards to acceptable performance levels. Significant parameters in the evaluation of kinematic loads are also addressed and recommendations are made on appropriate techniques for evaluation of kinematic loading.

Effects of long duration earthquakes on the interaction of inertial and liquefaction-induced kinematic demands on pile-supported wharves

This paper develops a novel reference analytical solution for axially loaded piles in inhomogeneous soils, extending the pioneering elastodynamic model of Nogami and Novak (1976) to piles embedded in vertically inhomogeneous soils. Following the classical earlier model, the pile is modelled as a rod, using the strength‐of‐materials solution, and the soil layer as an approximate continuum, which rest on rigid rock. The approximation lies in reducing the number of dependent variables by eliminating certain stresses and displacements in the governing elastodynamic equations: the vertical normal and vertical shear stresses in the soil are controlled exclusively by the vertical component of the soil displacement. Soil inhomogeneity is introduced via a power law variation of shear modulus with depth, and perfect bonding is assumed at the soil–pile interface. The proposed generalized formulation treats two types of inhomogeneity by employing pertinent eigen expansions of the dependent variables over the vertical coordinate. The response is expressed in terms of generalized Fourier series and includes: (i) displacements and stresses along the pile and the pile–soil interface; and (ii) displacement and stress in the soil. Contrary to available models for homogeneous soils, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered.

A new computer program “PILESET” is developed for use in predicting the bearing capacity and load-settlement behaviour of axially loaded single piles. The program can analyse almost any soil profile and accommodates (a) displacement piles (b) replacement (c) friction piles, (d) end-bearing piles, (e) under-reamed piles and (f) partially sleeved piles. A variety of soil input data can be used, including: (i) standard penetration tests, (ii) cone/piezo-cone tests, (iii) pressure-meter tests and (iv) laboratory tests. The above data types can be combined, if desired, for pile analysis by PILESET. The program calculates the shaft and base capacities of a pile based on 23 methods published in design guides in over 10 European countries. PILESET also predicts the pile load-settlement curve using five published methods, which include two modified load transfer (t-z) approaches formulated by the author. To demonstrate the capabilities of the program, analysis is carried out for case study involving seven full-scale screw piles formed in sand and tested to failure. In each case, the load-settlement curve computed using the author’s modified method in PILESET is found to be in excellent agreement with the actual pile test results.

Earthquakes usually cause both inertial and kinematic loading of pile foundations. Inertial loading and lateral pile response can be predicted to a certain extent by lateral pile load tests for important engineering projects. However, there is no accepted in situ assessment method for pile behavior due to kinematic loading. Therefore, it is important for geotechnical engineering practice to validate the practice oriented models and examine the influence of soil strength parameters on the performance of kinematically loaded piles due to lateral spreading. For this purpose, a well-documented case of full-scale lateral spreading test conducted at Port of Tokachi in Japan by Ashford et al. (2006) is selected as a primary reference in terms of test data and site conditions. Four p-y analyses are performed using a special purpose software based on finite difference technique. The first two investigate the employment of different p-y curves suggested in the literature. The third one investigates the influence of variations in internal friction angle and undrained shear strength. In the fourth analysis, liquefied shear strength and residual shear strength approaches are utilized for the liquefiable layers and their effects are investigated. In all analyses, mobilized lateral pressures in non-liquefied layers are also scrutinized. The results of the analyses are discussed and compared with the measured values in the field. Finally, conclusions are given based on the analyses and discussions.

Analytical solution for horizontal vibration of end-bearing single pile in radially heterogeneous saturated soil

Evaluation of thermo-mechanical behaviour of composite energy piles during heating/cooling operations

ABSTRACTDrilled displacement (DD) piles with a screw-shaped shaft (referred to as DD piles) are installed using a continuous full thread hollow rod (without a displacement body) inserted and advanced in the soil by both a vertical force and a torque. As a type of newly developed pile, current understanding of the bearing mechanism of DD piles is unsatisfactory, which restricts their further applications in engineering. The primary aim of this paper is to study the bearing mechanism of this type of pile using a numerical method. First, a numerical model for calculating the bearing capacity of the DD piles was created and validated by a laboratory test. Then, the effects of the parameters of pile–soil interface, soil strength, and pile geometrical parameters on the bearing mechanism of the DD piles were investigated in parametric studies. The results of parametric studies show that the limit shear stress on the pile–soil interface, the friction angle of surrounding sand, screw pitch, and thread width significantly influence the bearing capacity of the DD piles, whereas the friction coefficient at the pile–soil interface and the thread thickness have little effect. Based on the results of the parametric studies, the failure mechanism of the DD piles under vertical load is analyzed. Finally, an equation for predicting the ultimate bearing capacities of helical piles based on cylindrical shear failure was used for estimating the bearing capacity of the DD piles, and the calculated results were verified with the numerical results.

Performance-based seismic design provisions for pile-supported piers and wharves highlight the need to evaluate the combined effects of inertial loading, largely associated with the dynamic response of the structure, and kinematic loading resulting from permanent, seismically-induced deformation of the foundation soils. Inertial and kinematic loads on piles are routinely evaluated in an uncoupled manner with the combined load estimated by summation of the peak loads, or a fraction of the peak loads, resulting from the two, independent solutions. This approach requires considerable judgment as both modes of seismic loading involve highly nonlinear soil-foundation-structure interaction (SFSI) therefore superposition of the independent solutions is not strictly appropriate. The evaluation of seismic performance is further complicated when considering the phasing of these non-synchronous load situations. This paper focuses on the results of an investigation of the seismic performance of pile-supported wharves to long-duration ground motions. Dynamic SFSI was evaluated using a 2-D nonlinear geomechanical model that was first calibrated using data from field case histories, physical modeling, and pile load test data prior to application for a terminal wharf at the Port of Los Angeles. The modeling supplements field case histories and physical modeling results, which highlight the need to consider the time- and location-dependent nature of the inertial and kinematic loads on piles, the pattern of accumulated cyclic shear strain in the foundation soils, and soil-pile interaction in rockfill dikes and wave armor layers. Primary geotechnical considerations are summarized with recommendations for practical analysis of pile performance.