Kinematic interaction factors of deep foundations with inclined piles

The beneficial or detrimental role of battered piles on the dynamic response of piled foundations has not been yet fully elucidated. In order to shed more light on this aspect, kinematic interaction factors of deep foundations with inclined piles, are provided for single‐battered piles, as well as for 2 × 2 and 3 × 3 groups of piles subjected to vertically incident plane shear S waves. Piles are modelled as linear‐elastic Bernoulli beams, whereas soil is assumed to be a linear, isotropic, homogeneous viscoelastic half‐space. Different pile group configurations, pile‐soil stiffness ratios, and rake angles are considered. The relevance and main trends observed in the influence of the rake angle on the kinematic interaction factors of the analysed foundations are inferred from the presented results. An important dependence of the kinematic interaction factors on the rake angle is observed together with the existence of an inclination angle at which cap rotation and excitation become out of phase in the low‐to‐mid frequency range. The existence of a small batter angle that provides minimum cap rotation is also shown. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic stiffness of deep foundations with inclined piles

The influence of inclined piles on the dynamic response of deep foundations and superstructures is still not well understood and needs further research. For this reason, impedance functions of deep foundations with inclined piles, obtained numerically from a boundary element–finite element coupling model, are provided in this paper. More precisely, vertical, horizontal, rocking and horizontal–rocking crossed dynamic stiffness and damping functions of single inclined piles and 2 × 2 and 3 × 3 pile groups with battered elements are presented in a set of plots. The soil is assumed to be a homogeneous viscoelastic isotropic half‐space and the piles are modeled as elastic compressible Euler–Bernoulli beams. The results for different pile group configurations, pile–soil stiffness ratios and rake angles are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Kinematic response of single piles to vertically incident P‐waves

Dynamic response of single piles to seismic waves is fundamentally different from the free‐field motion because of the interaction between the pile and the surrounding soil. Considering soil–pile interaction, this paper presents a new displacement model for the steady‐state kinematic response of single piles to vertically incident P‐waves on the basis of a continuum model. The governing equations and boundary conditions of the two undetermined functions in the model are obtained to be coupled by using Hamilton's principle. Then, the two unknown functions are decoupled and solved by an iterative algorithm numerically. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the kinematic response of single piles. It is shown that the effects of the pile–soil modulus ratio, the slenderness ratio of the pile, and the frequency of the incident excitations are very significant. By contrast, the influence of soil damping on the kinematics of the system is slight and can be neglected. Copyright © 2013 John Wiley & Sons, Ltd.     

Influences of type of wave and angle of incidence on seismic bending moments in pile foundations

When analysing the seismic response of pile groups, a vertically‐incident wavefield is usually employed even though it does not necessarily correspond to the worst case scenario. This work aims to study the influences of both the type of seismic body wave and its angle of incidence on the dynamic response of pile foundations. To this end, the formulation of SV, SH and P obliquely‐incident waves is presented and implemented in a frequency‐domain boundary element‐finite element code for the dynamic analysis of pile foundations and piled structures. Results are presented in terms of bending moments at cap level of single piles and 3 × 3 pile groups, both in frequency and in time domains. It is found that, in general, the vertical incidence is not the most unfavourable situation. In particular, obliquely‐incident SV waves with angles of incidence smaller than the critical one, a situation in which the mechanism of propagation of the waves in the soil changes and surface waves appear, yield bending moments much larger than those obtained for vertically‐incident wavefields. It is also shown that the influence of pile‐to‐pile interaction on the kinematic bending moments becomes significant for non‐vertical incidence, especially for P and SV waves. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical model for the dynamic analysis of inclined pile groups

The paper presents a numerical model for the dynamic analysis of pile groups with inclined piles in horizontally layered soil deposits. Piles are modelled with Euler–Bernoulli beams, while the soil is supposed to be constituted by independent infinite viscoelastic horizontal layers. The pile–soil–pile interaction as well as the hysteretic and geometric damping is taken into account by means of two‐dimensional elastodynamic Green's functions. Piles cap is considered by introducing a rigid constraint; the condensation of the problem permits a consistent derivation of both the dynamic impedance matrix of the soil–foundation system and the foundation input motion. These quantities are those used to perform inertial soil–structure interaction analyses in the framework of the substructure approach. Furthermore, the model allows evaluating the kinematic stress resultants in piles resulting from waves propagating in the soil deposit, taking into account the pile–soil–pile interactions. The model validation is carried out by performing accuracy analyses and comparing results in terms of dynamic impedance functions, kinematic response parameters and pile stress resultants, with those furnished by 3D refined finite element models. To this purpose, classical elastodynamic solutions are adopted to define the soil–pile interaction problem. The model results in low computational demands without significant loss of precision, compared with more rigorous approaches or refined finite element models. Copyright © 2015 John Wiley & Sons, Ltd.     

Discrete model for dynamic through-the-soil coupling of 3-D foundations and structures

An efficient discrete model for predicting the dynamic through-the-soil interaction between adjacent rigid, surface foundations supported by a homogeneous, isotropic and linear elastic half-space is presented. The model utilizes frequency-independent springs and dashpots, and the foundation mass, for the consideration of soil–foundation interaction. The through-the-soil coupling of the foundations is attained by frequency-independent stiffness and damping functions, developed in this work, that interconnect the degrees of freedom of the entire system of foundations. The dynamic analysis of the resulting coupled system is performed in the time domain and includes the time lagging effects of coupled dynamic input due to wave propagation using an appropriate modification of the Wilson-θ method. The basic foundation interaction model is also extended to the evaluation of coupled building-foundation systems. © 1998 John Wiley & Sons, Ltd.     

Pile‐head kinematic bending in layered soil

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 semi‐analytical 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. Copyright © 2012 John Wiley & Sons, Ltd.     

Response of seismically isolated structures to rocking‐type excitations

In this paper, the origin of rocking‐type excitations and their effects on the response of base isolated structures are studied. In particular, the role of kinematic interaction in the determination of the rocking excitation is highlighted. The cases of surface foundations subjected to horizontally propagating waves, as well as of embedded foundations under vertically incident shear waves are examined. The validity of the kinematic interaction based on the rigid base mat assumption is discussed. It is shown that, in the case of classical horizontal isolation, rocking input may amplify significantly the response of the lower non‐isolated modes. The examination of full three‐dimensional isolation and active and semi‐active control methods demonstrates the efficacy of these methods to improve the performance of seismically isolated structures subjected to rocking excitations. Copyright © 2009 John Wiley & Sons, Ltd.     

Kinematic bending moments in pile foundations

In this paper the kinematic seismic interaction of single piles embedded in soil deposits is evaluated by focusing the attention on the bending moments induced by the transient motion. The analysis is performed by modeling the pile like an Euler–Bernoulli beam embedded in a layered Winkler-type medium. The excitation motion is obtained by means of a one-D propagation analysis. A comprehensive parametric analysis is carried out by varying the main parameters governing the dynamic response of piles like the soil properties, the bedrock location, the diameter and embedment in the bedrock of piles. On the basis of the parametric analysis, a new design formula for predicting the kinematic bending moments for both the cross-sections at the deposit–bedrock interface and at the pile head is proposed.     

A hybrid time frequency domain formulation for non-linear soil–structure interaction

Methods that combine frequency and time domain techniques offer an attractive alternative for solving Soil–Structure-interaction problems where the structure exhibits non-linear behaviour. In the hybrid-frequency-time-domain procedure a reference linear system is solved in the frequency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the solution scheme explored in this paper, designated as the hybrid-time-frequency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with the unbounded medium represented by frequency-independent springs and dampers. The frequency dependency of the impedance coefficients is introduced by means of pseudo-forces evaluated in the frequency domain at the end of each iteration. A criterion of stability for the HTFD approach is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times required to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approach. © 1998 John Wiley & Sons, Ltd.     

Seismic behaviour of shallow foundations: Shaking table experiments vs numerical modelling

The capability of a simplified approach to model the behaviour of shallow foundations during earthquakes is explored by numerical simulation of a series of shaking table tests performed at the Public Works Research Institute, Tsukuba, Japan. After a summary of the experimental work, the numerical model is introduced, where the whole soil–foundation system is represented by a multi‐degrees‐of‐freedom elasto‐plastic macro‐element, supporting a single degree‐of‐freedom superstructure. In spite of its simplicity and of the large intensity of the excitation involving a high degree of nonlinearity in the foundation response, the proposed approach is found to provide very satisfactory results in predicting the rocking behaviour of the system and the seismic actions transmitted to the superstructure. The agreement is further improved by introducing a simple degradation rule of the foundation stiffness parameters, suitable to capture even some minor details of the observed rocking response. On the other hand, the performance of the model is not fully satisfactory in predicting vertical settlements. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic design of yielding structures on flexible foundations

This paper introduces a simple method to consider the effects of inertial soil–structure interaction (SSI) on the seismic demands of a yielding single‐degree‐of‐freedom structure. This involves idealizing the yielding soil–structure system as an effective substitute oscillator having a modified period, damping ratio, and ductility. A parametric study is conducted to obtain the ratio between the displacement ductility demand of a flexible‐base system and that of the corresponding fixed‐base system. It is shown that while additional foundation damping can reduce the overall response, the effects of SSI may also increase the ductility demand of some structures, mostly being ductile and having large structural aspect ratio, up to 15%. Finally, a design procedure is provided for incorporation of the SSI effects on structural response. Copyright © 2015 John Wiley & Sons, Ltd.     

Effects of the dynamic cross-interaction in the seismic analysis of multiple embedded foundations

A boundary element formulation of the substructure deletion method is presented for the seismic analysis of the dynamic cross-interaction between multiple embedded foundations. This approach is particularly suitable for three-dimensional foundations of any arbitrary geometrical shape and spatial location, since it requires only the discretization of the foundations’ surfaces. The surrounding soil is represented by a homogeneous viscoelastic half-space while the foundations are assumed to be rigid and subjected to incoming SH-, P-, and SV-waves arbitrarily inclined in both the horizontal and vertical planes. The proposed methodology is tested for the case of two identical embedded square foundations for different values of the foundations’ embedment and distance. The effects of the cross-interaction are outlined in the components of the impedance matrix and of the foundation input motion. © 1997 John Wiley & Sons, Ltd.     

Seismic response evaluation of an urban overpass

The seismic response of one section of a 23 km strategic urban overpass to be built in the so‐called transition and hill zones in Mexico City is presented. The subsoil conditions at these zones typically consist on soft to stiff clay and medium to dense sand deposits, randomly interbedded by loose sand lenses, and underlain by rock formations that may outcrop in some areas. Several critical supports of this overpass are going to be instrumented with accelerometers, inclinometers and extensometers, tell tales and end pile cell pressures to assess their seismic performance during future earthquakes and to generate a database to calibrate soil–structure interaction numerical models. This paper presents the seismic performance evaluation of the critical supports located in one section of the overpass. Sets of finite elements models of the soil–foundation–structure systems were developed. Initially, the model was calibrated analyzing the seismic response that an instrumented bridge support exhibited during the June 15th, 1999 Tehuacan (M_w = 7) Earthquake. This bridge is located also within the surroundings of Mexico City, but in the lake zone, where highly compressible clays are found. The computed response was compared with the measured response in the free field, pile‐box foundation and bridge deck. Once the model prediction capabilities were established, the seismic response of the critical supports of the urban overpass was evaluated for the design earthquake in terms of transfer functions and displacement time histories. Copyright © 2010 John Wiley & Sons, Ltd.     

Recursive evaluation of interaction forces and property matrices from unit-impulse response functions of unbounded medium based on balancing approximation

Starting from the unit-impulse response matrix of the unbounded medium, a discrete-time formulation permitting the recursive evaluation of the interaction forces and a continuous-time formulation yielding property matrices corresponding to a model with a finite number of degrees of freedom are discussed. This is achieved using the balancing approximation method which is easily automated, guarantees stability and leads to highly accurate results. © 1998 John Wiley & Sons Ltd.     

System identification for evaluating soil–structure interaction effects in buildings from strong motion recordings

Parametric system identification is used to evaluate seismic soil–structure interaction effects in buildings. The input–output strong motion data pairs needed for evaluations of flexible- and fixed-base fundamental mode parameters are derived. Recordings of lateral free-field, foundation, and roof motions, as well as foundation rocking, are found to be necessary for direct evaluations of modal parameters for both cases of base fixity. For the common situation of missing free-field or base rocking motions, procedures are developed for estimating the modal parameters that cannot be directly evaluated. The accuracy of these estimation procedures for fundamental mode vibration period and damping is verified for eleven sites with complete instrumentation of the structure, foundation, and free-field. © 1998 John Wiley & Sons, Ltd.     

Variations in the dynamic response of structures founded on piles induced by obliquely incident SV waves

Although the seismic actions generally consist of a combination of waves, which propagates with an angle of incidence not necessarily vertical, the common practice when analyzing the dynamic behavior of pile groups is based on the assumption of vertically incident wave fields. The aim of this paper is to analyze how the angle of incidence of SV waves affects the dynamic response of pile foundations and piled structures. A three-dimensional boundary element-finite element coupling formulation is used to compute impedances and kinematic interaction factors corresponding to several configurations of vertical pile groups embedded in an isotropic homogeneous linear viscoelastic half-space. These results, which are provided in ready-to-use dimensionless graphs, are used to determine the effective dynamic properties of an equivalent single-degree-of-freedom oscillator that reproduces, within the range where the peak response occurs, the response of slender and nonslender superstructures through a procedure based on a substructuring model. Results are expressed in terms of effective flexible-base period and damping as well as maximum shear force at the base of the structure. The relevance and main trends observed in the influence of the wavefront angle of incidence on the dynamic behavior of the superstructure are inferred from the presented results. It is found that effective damping is significantly affected by the variations of the wave angle of incidence. Furthermore, it comes out that the vertical incidence is not always the worst-case scenario.     

Seismic response and damage analysis of buildings supported on flexible soils

The investigation reported in this paper studies the effects of soil–structure interaction (SSI) on the seismic response and damage of building–foundation systems. A simple structural model is used for conducting a parametric study using a typical record obtained in the soft soil area of Mexico City during the 1985 earthquake. Peak response parameters chosen for this study were the roof displacement relative to the base and the hysteretic energy dissipated by the simple structural model. A damage parameter is also evaluated for investigating the SSI effects on the seismic damage of buildings. The results indicate that in most cases of inelastic response, SSI effects can be evaluated considering the rigid‐base case and the SSI period. Copyright © 2000 John Wiley & Sons, Ltd.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

The role of soil in the collapse of 18 piers of Hanshin Expressway in the Kobe earthquake

An investigation is presented of the collapse of a 630 m segment (Fukae section) of the elevated Hanshin Expressway during the 1995 Kobe earthquake. The earthquake has, from a geotechnical viewpoint, been associated with extensive liquefactions, lateral soil spreading, and damage to waterfront structures. Evidence is presented that soil–structure interaction (SSI) in non‐liquefied ground played a detrimental role in the seismic performance of this major structure. The bridge consisted of single circular concrete piers monolithically connected to a concrete deck, founded on groups of 17 piles in layers of loose to dense sands and moderate to stiff clays. There were 18 spans in total, all of which suffered a spectacular pier failure and transverse overturning. Several factors associated with poor structural design have already been identified. The scope of this work is to extend the previous studies by investigating the role of soil in the collapse. The following issues are examined: (1) seismological and geotechnical information pertaining to the site; (2) free‐field soil response; (3) response of foundation‐superstructure system; (4) evaluation of results against earlier studies that did not consider SSI. Results indicate that the role of soil in the collapse was multiple: First, it modified the bedrock motion so that the frequency content of the resulting surface motion became disadvantageous for the particular structure. Second, the compliance of soil and foundation altered the vibrational characteristics of the bridge and moved it to a region of stronger response. Third, the compliance of the foundation increased the participation of the fundamental mode of the structure, inducing stronger response. It is shown that the increase in inelastic seismic demand in the piers may have exceeded 100% in comparison with piers fixed at the base. These conclusions contradict a widespread view of an always‐beneficial role of seismic SSI. Copyright © 2005 John Wiley & Sons, Ltd.