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The work at hand proposes a method for assessing, under reasonable hypotheses from an engineering perspective, the failure envelope of a pile group subjected to generalized loading conditions involving a vertical and a lateral force along with a moment. Following different assumptions of increasing complexity, a simple closed-form expression, which is however capable of considering also the strong dependence of sectional yielding moment on the axial force, is derived. The use of such formula, which allows a practical hand calculation of the interaction diagrams at failure, returns conservative yet very accurate results. As a follow up, with reference to reinforced concrete piles, design considerations involving both structural and geotechnical failure under lateral load are reported. It is found that for most cases, if steel reinforcement is established to resist the design bending moment, the geotechnical Ultimate Limit State checks are automatically satisfied.

This work is a numerical investigation of the effect of thermally induced volumetric collapse of normally consolidated clays on the performance of energy piles. A series of coupled thermo‐hydro‐mechanical Finite Element simulations were carried out using the commercial software ABAQUS. These examined a single free‐head energy pile embedded in a normally consolidated clay layer subjected to a constant mechanical load and to a number of heating/cooling cycles, to reproduce operating conditions. The soil behaviour was described with two advanced hypoplastic constitutive models for clays, one of which incorporates the thermally induced volumetric collapse using an ad‐hoc algorithm developed by the authors. Both models predict a cyclic accumulation of settlement and excess pore water pressure, especially when the thermal collapse effect is considered. While the excess pore pressure distribution stabilises within a few cycles, the rate of settlement of the pile head does not show any tendency to decrease from one cycle to another. These results are in agreement with data from small scale tests on an isolated energy pile in normally consolidated clay, indicating that the numerical model developed in this study can be used to investigate the complex soil/pile/raft interaction processes occurring in real piled foundations incorporating energy piles.

This research provides an insight into the previously unexplored aspects of kinematic pile bending, especially for large-intensity earthquakes where the soil behaviour is highly non-linear. In this study, a series of dynamic centrifuge experiments was conducted on pile foundations embedded in a two-layered soil profile to investigate the kinematic effects on pile foundations during model earthquakes. A single pile and a closely spaced 3 × 1 row pile group were used as model pile foundations, and the soil model consisted of a soft clay underlain by dense sand. It was observed that the peak kinematic pile bending moment occurs slightly beneath the interface of the soil layers and this depth is larger for the pile group compared to a single pile. Also, the piles in a group attract lower bending moments but carry larger residual kinematic pile bending moments compared to a single pile. Furthermore, the elastic solutions available in the literature for estimating the kinematic pile bending moments are shown to yield satisfactory results only for small-intensity earthquakes, but vastly underestimate for large-intensity earthquakes, if methods are applied injudiciously. The importance of considering soil non-linearity effects and accurate determination of shear strain at the interface of layered soils during large-intensity earthquakes for a reliable assessment of kinematic pile bending moment from methods in the literature is demonstrated using dynamic centrifuge test data.

This work investigates the role of pile diameter in resisting seismic actions, with reference to two example subsoils, namely a dry sand and a fully saturated NC clay. After a ground response analysis in free-field conditions for different values of peak rock acceleration, mobilized soil stiffness and surface acceleration are used as ingredients for assessing the kinematic and inertial moment in a concrete pile. An optimum pile diameter is identified as the one that, while guaranteeing safety, corresponds to the minimum cost. It is also proven that, with a constant value of reinforcement area and length, increasing pile diameter (i.e. increasing safety factor and cost) leads rapidly to failure. Likewise, if pile reinforcement is designed only for inertial action, increasing pile diameter is severely detrimental.

This work is aimed at furnishing an experimental support to the design of axially-loaded piles, taking advantage of an extensive database of pile load tests carried out in different sites nearby Napoli, in South Italy. Experimental data consist of nearly 400 full-scale pile load tests, some of them reaching large values of settlement. Different construction methods, including Non-Displacement, CFA and Displacement piles, have been used. The main results of the work consist in furnishing experimentally-derived rules and indications for pile design. With regards to failure loads, mobilization curves relating properly normalized values of load and settlement are proposed as function of the installation technique; indications on the bearing capacity of piles as function of geometry and technology are also provided. Initial stiffness of piles is investigated, identifying a rule of thumb for a rapid assessment, function solely of pile diameter and valid regardless of length and specific properties of pile and soil material.

This paper presents the results of a numerical and theoretical study aimed at identifying optimal design solutions for the seismic design of bridge pier foundations in very soft soil deposits. The reference case study consists of the pier foundations of a cross-river bridge designed to complete a highway over the Po Valley (Northern Italy). The subsoil is of sedimentary origin, with alternating layers of clayey silts and clays interbedded by thin layers of silty sand and peat. The mechanical properties of the soils were defined by conventional site and laboratory investigations, including Resonant Column tests carried out to define the dissipative and nonlinear behaviour of the soils. Numerical 2D and 3D models are used to assess the dynamic soil-structure interaction for the bridge piers, focusing both on inertial and kinematic effects. The main goal of the work is to highlight the influence of the type and layout of the foundation system on the overall seismic response of the bridge pier.

A tall r.c. building in the city of Napoli has recently undergone a seismic vulnerability assessment, in order to satisfy its public function fulfilling the requirements of the new Italian Building Code. The study is focused on the inertial response of the building, accounting for soil deformability and damping. To this aim, the overall structure is idealized as a simple oscillator supported on frequency-dependent springs and dashpots.

Gli effetti prodotti da un terremoto sugli edifici dipendono da una moltitudine di fattori, fra i quali le caratteristiche del moto sismico, la stratigrafia e le proprietà meccaniche dei terreni, la tipologia e la rigidezza delle fondazioni e della stessa struttura in elevazione. Un esempio paradigmatico in questo senso è rappresentato da un edificio alto circa 110 m nel Centro Direzionale di Napoli fondato su una palificata progettata in modo convenzionale su terreni vulcanici ed alluvionali deformabili. L’analisi della risposta sismica locale mostra che il moto sismico di free-field in superficie dipende fortemente dal dettaglio stratigrafico, soprattutto nell’intervallo di valori del periodo strutturale di interesse per la tipologia di edificio presa in esame. Nel medesimo intervallo, invece, la modifica del moto sismico free-field dovuta all’interazione cinematica palificata-terreno non produce significativi effetti di filtraggio delle azioni sismiche trasmesse in elevazione. La valutazione dell’interazione inerziale, pur se in forma semplificata, permette invece di apprezzare ulteriori significative riduzioni dell’azione sismica in elevazione per effetto della deformabilità della fondazione. I risultati possono costituire un elemento di orientamento, di carattere più generale, per la verifica sismica di edifici alti fondati su palificate in terreni deformabili.

Nella presente nota viene illustrato un metodo di analisi semplificato dell’interazione piastra-pali-terreno in presenza di carichi verticali. Il metodo tiene conto del comportamento non lineare del contatto piastra-terreno e del gruppo di pali; non consente di prevedere la ripartizione del carico fra i pali, fornendo invece come risultato le curve carico-cedimento della piastra su pali e le due aliquote di carico trasmesse dalla platea al contatto fra questa e il terreno e dal gruppo di pali. Il metodo è stato validato mediante soluzioni di riferimento pubblicate in letteratura.

Kinematic effects at the head of a flexible vertical pile embedded in a two-layer soil deposit are investigated by means of rigorous three-dimensional elastodynamic finite-element analyses. Both pile and soil are idealized as linearly viscoelastic materials, modelled by solid elements, without the restrictions associated with the use of strength-of-materials approximations. The system is analyzed by a time-Fourier approach in conjunction with a modal expansion in space. Constant viscous damping is considered for each natural mode, and an FFT algorithm is employed to switch from frequency to time domain and vice versa in natural or generalized coordinates. The scope of the paper is to: (a) elucidate the role of a number of key phenomena controlling the amplitude of kinematic bending moments at the pile head; (b) propose a simplified semianalytical formula for evaluating such moments; and (c) provide some remarks about the role of kinematic bending in the seismic design of pile foundations. The results of the study provide a new interpretation of the interplay between interface kinematic moments and corresponding head moments, as a function of layer thickness, pile-to-soil stiffness ratio, and stiffness contrast between the soil layers. In addition, the role of diameter in designing against kinematic action, with or without the presence of an inertial counterpart, is discussed.

According to modern seismic codes such as Eurocode 8, pile foundations in earthquake-prone areas must resist two different, yet simultaneous bending actions resulting from kinematic and inertial interaction. Due to the different nature of the two demands, pile must resist seismic actions following different patters, thus leading to different design requirements. In this work, analytical solutions are presented to define maximum and a minimum pile diameters required to resist kinematic and inertial effects in an essentially elastic manner, respectively. It is shown that the range of admissible diameters decreases with decreasing soil stiffness and with increasing design acceleration, collapsing into a single admissible diameter for certain problem configurations. Regions where no pile diameter can guarantee elastic response during strong seismic shaking are identified.

In 2008 a new Building Code (Norme Tecniche per le Costruzioni, D.M. 14/01/2008) was introduced in Italy following the in-troduction of Eurocodes 7 (part 1) and 8 (part 5). Apart from some changes due to the need of adapting the content of the Eurocodes to local practice, the main structure of the latter was held. In the paper some comments are reported reference to the design of piled foundations in seismic areas. Some specific topics are developed, with particular reference to kinematic and inertial interaction, with the aim of pointing out questions which may be worthy of discussion in light of a possible re-examination and updating of Codes.

L’articolo indaga la risposta di pali, immersi in sottosuoli a due strati, soggetti a carichi di natura cinematica. Sulla base di risultati di analisi numeriche agli elementi finiti, viene proposta una nuova interpretazione del meccanismo di flessione generato in corrispondenza dell’interfaccia tra gli strati. Si giunge inoltre a definire una superficie caratteristica rappresentativa di combinazioni di valori di profondità d’interfaccia, rapporto di rigidezza palo-terreno e contrasto di rigidezza tra gli strati, che provocano momento nullo all’interfaccia. Viene quindi proposta una formula semplificata per la valutazione di tali momenti.

During seismic shaking soil movements force piles to deform, resulting in a complex interplay between the two systems commonly referred to as “kinematic interaction”. This interaction generates internal forces along piles even in the absence of a superstructure. Current design practice usually takes into account only forces transmitted to the pile from the superstructure, thus neglecting kinematic interaction. Despite intense research in the topic, few contributions focus on kinematic effects at the pile head in the presence of a stiff pile cap restraining its rotation. The subject may be of importance,for the pile head is subjected both to relevant kinematic and inertial moments, the latter attenuating rapidly with depth. The paper presents the results of an extensive parametric study leading to a simplified formula for evaluating kinematic moments at the pile head in a two-layer soil profile.

Nell’articolo vengono esposte alcune considerazioni sul rapporto relativo tra momenti di natura cinematica e inerziale per fondazioni profonde, alla luce delle prescrizioni normative italiane ed europee. Tra i risultati di maggiore rilevanza, viene mostrato come per terreni scadenti, anche se caratterizzati da rigidezza costante con la profondità, i momenti di natura cinematica sono spesso maggiori di quelli inerziali. Vengono quindi discussi i contenuti delle NTC dell’Eurocodice 8 in materia di interazione cinematica.

The effect of soil inhomogeneity on kinematic response of single flexural elastic piles to vertically-propagating seismic SH waves is explored. The system under consideration consists of a fixed-head long pile embedded in a viscoelastic soil layer underlain by a rigid bedrock; soil stiffness is assumed to increase linearly or constant. Both harmonic and real earthquake motions are employed to investigate soil-pile kinematic interaction in frequency and time domain. Pile response in inhomogcncous soil is analysed in terms of kinematic interaction coefficients relating pile-head to free-field soil lateral motion and compared to its homogeneous counterpart. The problem is tackled numerically by means of both rigorous elastodynamic Finite-Element analyses and Beam-on-Dynamic-Winkler-Foundation (BDWF) formulations. The role of model parameters such as pile diameter, rate at which soil stiffness increases with depth and average shear wave velocity VSi30 referring to soil type C or D according to ECS is elucidated. Results indicate that: (a) the horizontal displacement of fixed-head piles under harmonic excitation is essentially governed by a single dimensionless frequency parameter based on an average Winkler wavenumber incorporating pile-to-soil stiffness ratio, pile slenderness and soil inhomogeneity and (b) piles-induced filtering effect tends to increase by increasing the degree of soil inhomogeneity and pile diameter, revealing a substantially reduced seismic demand on the superstructure compared to that pertaining to die free-field motion. The above filtering action although neglected in seismic codes may of importance in pile design practice.

The paper deals with the analysis and design of energy piles subjected to a cyclic temperature variation under constant mechanical axial load. The problem is first investigated through fully coupled thermo-hydro-mechanical analyses using the finite-element code ABAQUS. A single pile, whose head is either free or restrained, is embedded in a normally consolidated clay obeying different constitutive models. Numerical results are reported and discussed with emphasis on the role of the different constitutive assumptions on the development of the pile axial force due to the thermal load. Further, a design procedure is proposed to derive the maximum thermally induced axial load by using recently developed analytical solutions, worked out to obtain explicit formulae that can be readily employed in a spreadsheet for the direct computation of axial force in a multilayer soil. The method consists of employing these expressions after identifying some rules to: (a) select the soil stiffness profile as a function of the mechanical load and (b) establish the effect of the actual restraint condition at the pile head as a function of the stiffness ratio between the inactive and the active pile subgroups. The main advantage of the proposed procedure is that it requires only the load–settlement curve under the mechanical axial load, which is always assessed in pile design, through analytical, numerical or experimental means. After a comparison with the results of the finite-element analyses, the procedure is also applied to a number of field tests on groups of energy piles available in the literature, and provides a satisfactory match between measurements and predictions.

The effect on seismic demand of the soil-foundation compliance is investigated for a reinforced concrete frame building representative of Italian constructions from the 1970s. Design accounts for regulations, materials, preferred structure and foundation layouts and analysis methods of the period. Inelastic response history analysis for multiple motions at three intensities is carried out. For the compliant-base case, each foundation is replaced with a nonlinear inertial macro-element. Results suggest that the effect of interaction is minor, lower than expected from similar analysis on a new building, due to the larger degree of conservatism associated with foundation design in the considered period and the corresponding lower strength and stiffness of the superstructure.

This research provides an insight into the previously unexplored aspects of kinematic pile bending, especially for large-intensity earthquakes where the soil behaviour is highly non-linear. In this study, a series of dynamic centrifuge experiments was conducted on pile foundations embedded in a two-layered soil profile to investigate the kinematic effects on pile foundations during model earthquakes. A single pile and a closely spaced 3 × 1 row pile group were used as model pile foundations, and the soil model consisted of a soft clay underlain by dense sand. It was observed that the peak kinematic pile bending moment occurs slightly beneath the interface of the soil layers and this depth is larger for the pile group compared to a single pile. Also, the piles in a group attract lower bending moments but carry larger residual kinematic pile bending moments compared to a single pile. Furthermore, the elastic solutions available in the literature for estimating the kinematic pile bending moments are shown to yield satisfactory results only for small-intensity earthquakes, but vastly underestimate for large-intensity earthquakes, if methods are applied injudiciously. The importance of considering soil non-linearity effects and accurate determination of shear strain at the interface of layered soils during large-intensity earthquakes for a reliable assessment of kinematic pile bending moment from methods in the literature is demonstrated using dynamic centrifuge test data.

The paper investigates the problem of Soil-Foundation-Structure Interaction (SFSI) for buildings supported on piles through the comparative analysis between the fixed base and the compliant base assumptions. The structure, a nine-storey residential building (with or without infills), is modelled in non-linear regime while the piled foundation is idealized by means of independent lumped parameters models, either linear or non-linear. In this last case, the soil-foundation system is replaced by an assembly of viscous-dampers, fictitious masses and non-linear springs modelled according to the classical Bouc-Wen formulation, so as to account for the hysteretic behaviour of the foundation. A detailed calibration procedure for both linear and non-linear foundation models is also presented and discussed. Two different natural soil deposits are considered, a pyroclastic deposit and a deep layer of lacustrine clay. The results undertaken in the context of a probabilistic analysis show that SFSI may lead to a significant reduction of the seismic demand in infilled buildings at low and intermediate earthquake intensity levels. Conversely, at higher intensity earthquakes the seismic demand is not affected by the non-linear springs. It is shown that a proper modelling of radiation mechanism at foundation level is crucial for a reliable and sustainable prediction of SFSI effects.

This paper proposes a new simple approach for assessing dynamic soil-structure interaction effects on structures supported by embedded massive foundations. The classical substructure method was revisited by proposing an exact decomposition approach which allows performing the inertial interaction analysis of the superstructure without modeling foundation and soil, which are replaced by properly defined impedances. The proposed approach requires redefinition of simplified formulas for both the dynamic stiffnesses and the kinematic interaction factors, which are referred to the top of the massive foundation. Accurate expressions for the complex impedances were derived based on rigorous finite-element results. The same formulas were used to calibrate a four-spring model for the analysis of the kinematic interaction problem, resulting in different expressions for the kinematic interaction factors depending on the adopted assumptions. The proposed approach, in conjunction with the novel formulas for impedances and kinematic factors, was applied to the case of bridge piers on caisson foundations, and the results were more accurate than those of the existing simplified procedures.

Annular shaped pile groups are a very common foundation layout for onshore wind turbines and other slender structures. In this study, their performance under vertical loads of moderate to high eccentricity, including moment rotation response and bearing capacity, was investigated by centrifuge testing on small scale physical models embedded in kaolin clay. To identify experimentally the capacity of the examined pile groups under different load paths, the model foundations were loaded monotonically until a clear collapse mechanism was achieved. The testing procedure and the proposed interpretation methodology can be easily adapted to load paths or pile layouts other than those considered in the current study. The experimental data can be adopted as a useful benchmark for mathematical models aimed at predicting the response of pile groups to complex load paths. The results of this testing program can also be used to assess the degree of conservatism of current methods adopted by industry for the design of piled foundations subjected to eccentric loads.