Seismic performance of three-dimensional frame structures with underground stories

This paper investigates the seismic performance of moment-resisting frame steel buildings with multiple underground stories resting on shallow foundations. A parametric study that involved evaluating the nonlinear seismic response of five, ten and fifteen story moment-resisting frame steel buildings resting on flexible ground surface, and buildings having one, three and five underground stories was performed. The buildings were assumed to be founded on shallow foundations. Two site conditions were considered: soil class C and soil class E, corresponding to firm and soft soil deposits, respectively. Vancouver seismic hazard has been considered for this study. Synthetic earthquake records compatible with Vancouver uniform hazard spectrum (UHS), as specified by the National Building Code of Canada (NBCC) 2005, have been used as input motion. It was found that soil–structure interaction (SSI) can greatly affect the seismic performance of buildings in terms of the seismic storey shear and moment demand, and the deformations of their structural components. Although most building codes postulate that SSI effects generally decrease the force demand on buildings, but increase the deformation demand, it was found that, for some of the cases considered, SSI effects increased both the force and deformation demand on the buildings. The SSI effects generally depend on the stiffness of the foundation and the number of underground stories. SSI effects are significant for soft soil conditions and negligible for stiff soil conditions. It was also found that SSI effects are significant for buildings resting on flexible ground surface with no underground stories, and gradually decrease with the increase of the number of underground stories.     

Effects of soil cracking on the seismic response of soil–structure systems

A numerical study on the influence that cracks and discontinuities (closed cracks) can have on the seismic response of a hypothetical soil–structure system is presented and discussed. A 2-D finite-difference model of the soil was developed, considering a bilinear failure surface using a Mohr–Coulomb model. The cracks are simulated with interface elements. The soil stiffness is used to characterize the contact force that is generated when the crack closes. For the cases studied herein, it was considered that the crack does not propagate during the dynamic event. Both cases, open and closed cracks, are considered. The nonlinear behavior was accounted for approximately using equivalent linear properties calibrated against several 1-D wave propagation analyses of selected soil columns with variable depth to account for changes in depth to bed rock. Free field boundaries were used at the edges of the 2-D finite-difference model to allow for energy dissipation of the reflected waves. The effect of cracking on the seismic response was evaluated by comparing the results of site response analysis with and without crack, for several lengths and orientations. The changes in the response obtained for a single crack and a family of cracks were also evaluated. Finally, the impact that a crack may have on the structural response of nearby structures was investigated by solving the seismic-soil–structure interaction of two structures, one flexible and one rigid to bracket the response. From the results of this investigation, insight was gained regarding the effect that discontinuities may have both on the seismic response of soil deposits and on nearby soil–structure systems.     

Centrifuge modeling of rocking‐isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil‐footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking‐isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self‐centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Seismic lateral movement prediction for gravity retaining walls on granular soils

At present, methods based on allowable displacements are frequently used in the seismic design of earth retaining structures. However, these procedures ignore both the foundation soil deformability and the seismic amplification of the soil placed behind the retaining wall. Thus, they are not able to predict neither a rotational failure mechanism nor seismic induced lateral displacements with an acceptable degree of accuracy for the most general case. In this paper, a series of 2D finite-element analyses were carried out to study the seismic behavior of gravity retaining walls on normally consolidated granular soils. Chilean strong-motion records were applied at the bedrock level. An advanced non-linear constitutive model was used to represent both the backfill and foundation soil behavior. This elastoplastic model takes into account both the stress dependency of soil stiffness and coupling between shear and volumetric strains. In unloading–reloading cycles, the non-linear shear-modulus reduction with shear strain amplitude is considered. Interface elements were used to model soil–structure interaction. Routine-design charts were derived from the numerical analyses to predict the lateral movements at the base and top of gravity retaining walls located at sites with similar seismic characteristics to the Chilean subduction zone. Thus, wall seismic rotation can also be obtained. The developed charts consider wall dimensions, granular soil properties, bedrock depth, and seismic input motion characteristics. As shown, the proposed charts match well with available experimental data.     

Characterization of rocking shallow foundations using centrifuge model tests

This paper presents new results of centrifuge model tests exploring the behavior of rocking shallow foundations embedded in dry sand, which provides a variety of factors of safety for vertical bearing. The results of slow (quasi‐static) cyclic tests of rocking shear walls and dynamic shaking tests of single‐column rocking bridge models are presented. The moment–rotation and settlement–rotation relationships of rocking footings are investigated. Concrete pads were placed in the ground soil to support some models with the objective of reducing the settlement induced by rocking. The behavior of rocking foundation was shown to be sensitive to the geometric factor of safety with respect to bearing failure, L_f/L_c, where L_f was the footing length, and the L_c was the critical soil‐footing contact length that would be required to support pure axial loading. Settlements were shown to be small if L_f/L_c was reasonably large. Placement of concrete pads under the edges of the footing was shown to be a promising approach to reduce settlements resulting from rocking, if settlements were deemed to be excessive and also had impacts on the energy dissipation and rocking moment capacity. A general discussion of the tradeoffs between energy dissipation and re‐centering of rocking foundations and other devices is included. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of soil parameter uncertainty on seismic demand of low-rise steel buildings on dense silty sand

Focusing on low-rise steel buildings supported by shallow isolated foundations on dense silty sand, this study demonstrates the effect of uncertainty in soil parameters on seismic response of structures. Considering a set of 20 ground motions representing 10% in 50 years hazard level and concentrating on peak base moment, base shear and interstory drift as the demand variables of interest, it is found that uncertainty in soil parameters may result in significant response variability of the structures, especially when vertical factor of safety is low and the structure is relatively stiff. Uncertainty in friction angle results in significant variability of the peak base moment and base shear, while peak interstory drift ratio is found to be virtually unaffected by uncertainty in soil parameters. It is also found that a linear soil–structure-interaction (SSI) model will not be able to predict such response variability under these set of ground motions.     

Integrated foundation–structure seismic assessment through non‐linear dynamic analyses

This paper aims at clarifying the role of dynamic soil–structure interaction in the seismic assessment of structure and foundation, when the non‐linear coupling of both subsystems is accounted for. For this purpose, the seismic assessment of an ideal set of bridge piers on shallow foundations is considered. After an initial standard assessment, based on capacity design principles, the evaluation of the seismic response of the piers is carried out by dynamic simulations, where both the non‐linear responses of the superstructure and of the foundation are accounted for, in the latter case through the macro‐element modeling of the soil–foundation system. The results of the dynamic simulations point out the beneficial effects of the non‐linear response of the foundation, which provides a substantial contribution to the overall energy dissipation during seismic excitation, thus allowing the structural ductility demand to decrease significantly with respect to a standard fixed‐base or linear‐elastic base assessment. Permanent deformations at the foundation level, such as rotation and settlement, turn out to be of limited amount. Therefore, an advanced assessment approach of the integrated non‐linear system, consisting of the interacting foundation and superstructure, is expected to provide more rationale and economic results than the standard uncoupled approach, which, neglecting any energy dissipation at the foundation level, generally overestimates the ductility demand on the superstructure. Copyright © 2016 John Wiley & Sons, Ltd.     

Rocking response of SDOF systems on shallow improved sand: An experimental study

Recent studies have highlighted the potential advantages of allowing inelastic foundation response during strong seismic shaking. Such an alternative seismic design philosophy, in which soil failure is used as a “fuse” for the superstructure has recently been proposed, in the form of “rocking isolation”. Within this context, foundation rocking may be desirable as a means of bounding the inertia forces transmitted onto the superstructure, but incorporates the peril of unacceptable settlements in case of a low static factor of safety FS_v. Hence, to ensure that rocking is materialized through uplifting rather than sinking, an adequately large FS_v is required. Although this is feasible in theory, soil properties are not always well-known in engineering practice. However, since rocking-induced soil yielding is only mobilized within a shallow layer underneath the footing, “shallow soil improvement” is considered as an alternative approach to release the design from the jeopardy of unforeseen inadequate FS_v. For this purpose, this paper studies the rocking response of relatively slender SDOF structures (h/B ratio equals 3 and rocking dominates over sliding), with emphasis on the effectiveness of shallow soil improvement stretching to various depths below the foundation. A series of reduced-scale monotonic and slow-cyclic pushover tests are conducted on SDOF systems lying on a square surface foundation. It is shown that shallow soil improvement may, indeed, be quite effective provided that its depth is equal to the width of the foundation. For lightly-loaded systems, an even shallower soil improvement may also be considered effective, depending on design requirements. The effectiveness of shallow soil improvement is ameliorated with the increase of cyclic rotation amplitude, and with repeating cycles of loading.     

A simplified model for lateral response of large diameter caisson foundations—Linear elastic formulation

The transient response of large embedded foundation elements of length-to-diameter aspect ratio D/B=2–6 is characterized by a complex stress distribution at the pier–soil interface that cannot be adequately represented by means of existing models for shallow foundations or flexible piles. On the other hand, while three-dimensional (3D) numerical solutions are feasible, they are infrequently employed in practice due to their associated cost and effort. Prompted by the scarcity of simplified models for design in current practice, we here develop an analytical model that accounts for the multitude of soil resistance mechanisms mobilized at their base and circumference, while retaining the advantages of simplified methodologies for the design of non-critical facilities. The characteristics of soil resistance mechanisms and corresponding complex spring functions are developed on the basis of finite element simulations, by equating the stiffness matrix terms and/or overall numerically computed response to the analytical expressions derived by means of the proposed Winkler model. Sensitivity analyses are performed for the optimization of the truncated numerical domain size, the optimal finite element size and the far-field dynamic boundary conditions to avoid spurious wave reflections. Numerical simulations of the transient system response to vertically propagating shear waves are next successfully compared to the analytically predicted response. Finally, the applicability of the method is assessed for soil profiles with depth-varying properties. The formulation of frequency-dependent complex spring functions including material damping is also described, while extension of the methodology to account for nonlinear soil behavior and soil–foundation interface separation is described in the conclusion and is being currently investigated.     

Transient kinematic pile bending in two-layer soil

The dynamic response of piles to seismic loading is explored by means of an extensive parametric study based on a properly calibrated Beam-on-Dynamic-Winkler-Foundation (BDWF) model. The investigated problem consists of a single vertical cylindrical pile, modelled as an Euler–Bernoulli beam, embedded in a subsoil consisting of two homogeneous viscoelastic layers of sharply different stiffness resting on a rigid stratum. The system is subjected to vertically propagating seismic S waves, in the form of a transient motion imposed on rock outcrop. Several accelerograms recorded in Italy are employed as input motions in the numerical analyses. The paper highlights the severity of kinematic pile bending in the vicinity of the interface separating the two soil layers. In addition to factors already investigated such as layer stiffness contrast, relative soil–pile stiffness, interface depth and intensity of ground excitation, the paper focuses on additional important factors, notably soil material damping, stiffness of Winkler springs and frequency content of earthquake excitation. Existing predictive equations for assessing kinematic pile bending at soil layer interfaces are revisited and new regression analyses are performed. A synthesis of findings in terms of a set of simple equations is provided. The use of these equations is discussed through examples.     

Effect of earthquake‐induced axial load fluctuations on asymmetric frame–wall–rocking foundation systems

Fluctuations in axial load imposed on a rocking footing will affect its moment capacity, the shape of its moment–rotation hysteresis, and potentially the system's seismic performance. Structural asymmetry increases the likelihood of axial load variation during earthquake excitations. To investigate this issue, a unique centrifuge testing program was carried out on low‐rise frame–wall–rocking foundation systems. In this paper, the seismic behaviors of asymmetric and symmetric models from this test program are systematically compared. Experimental results reveal that placing the lateral force resisting shear wall outboard produces significant axial load fluctuation, which in turn greatly deteriorate the lateral load‐carrying capacity of a foundation rocking dominated frame–wall system, particularly in its weak direction. However, it strengthens the system when loading is towards the shear wall, leading to a highly asymmetric hysteretic response. During earthquake loading, all asymmetric rocking foundation systems observe smaller peak roof accelerations, but larger peak and permanent roof drifts compared with the symmetric systems. Despite these differences in response, the axial load fluctuation and structural asymmetry do not significantly change the relative energy dissipated by the rocking foundations and inelastic structural components within each frame–wall–rocking foundation model. Copyright © 2015 John Wiley & Sons, Ltd.     

Dimensional analysis of structures with translating and rocking foundations under near-fault ground motions

This paper evaluates the inertial soil–structure interaction (SSI) effects on linear and bilinear structures supported on foundation that is able to translate and rock when subject to near-fault ground motions. Through rigorous dimensional analysis, the peak structural responses (e.g. structural drift and total acceleration) of the soil–foundation–structure interacting (SFSI) systems are characterized by a set of dimensionless Π-parameters, which can decisively describe the interactive behavior of SFSI systems. By comparing the normalized structural responses of various structure–foundation systems with their fixed-base counterparts, the study reveals that SSI effects highly depend on the structure-to-pulse frequency ratio, Π_ω, the foundation-to-structure stiffness ratio, Π_k, damping coefficient of foundation impedance, Π_c, the foundation rocking, and the development of nonlinearity in structures. For linear structures, the SSI effects are insignificant when the structure-to-pulse frequency ratio (Π_ω) is smaller than 1.5 and can amplify the structural responses when Π_ω is higher than 1.5. Foundation rocking can shift and enlarge the response amplification zone of SSI. For nonlinear structures, SSI tends to reduce the structural responses for Π_ω<3 while can increase the ductility demands for Π_ω≥3. The bilinear structures may experience more significant SSI effects than linear structures in certain frequency ranges. The numerical simulations on ten real building cases exhibiting significant rocking and a detailed case study on a nine-story frame structure demonstrate the applicability of dimensional analysis results to predict the SSI effects on realistic building structures. The study demonstrates that the dimensional analysis provides a concise and systematic way of evaluating SSI effects.     

Impedance matrices for circular foundation embedded in layered medium

A numerical scheme is developed in the paper for calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme, the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions with unknown coefficients are obtained by solving three-dimensional (3D) wave equations in cylindrical coordinates satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are also obtained by solving the same 3D wave equations satisfying the homogeneous boundary conditions and the prescribed boundary conditions. The prescribed conditions are the interaction tractions at the interfaces between embedded foundation and surrounding soil. The interaction tractions are assumed to be piecewise linear. The piecewise linear tractions at the bottom surface of foundation will be decomposed into a series of Bessel functions which can be easily fitted into the general solutions of wave equations in cylindrical coordinates. After all the analytic solutions with unknown coefficients for both interior and exterior domains are found, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions.     

Embedded foundation in layered soil under dynamic excitations

The critical step in the substructure approach for the soil–structure interaction (SSI) problem is to determine the impedance functions (dynamic-stiffness coefficients) of the foundations. In the present study, a computational tool is developed to determine the impedance functions of foundation in layered soil medium. Cone frustums are used to model the foundation soil system. Cone frustums are developed based on wave propagation principles and force-equilibrium approach. The model is validated for its ability to represent the embedded foundation in layered medium by comparing the results with the rigorous analysis results. Various degrees of freedom, such as, horizontal, vertical and rocking are considered for this study.     

The effect of foundation embedment on inelastic response of structures

In this research, a parametric study is carried out on the effect of soil–structure interaction on the ductility and strength demand of buildings with embedded foundation. Both kinematic interaction (KI) and inertial interaction effects are considered. The sub‐structure method is used in which the structure is modeled by a simplified single degree of freedom system with idealized bilinear behavior. Besides, the soil sub‐structure is considered as a homogeneous half‐space and is modeled by a discrete model based on the concept of cone models. The foundation is modeled as a rigid cylinder embedded in the soil with different embedment ratios. The soil–structure system is then analyzed subjected to a suit of 24 selected accelerograms recorded on alluvium deposits. An extensive parametric study is performed for a wide range of the introduced non‐dimensional key parameters, which control the problem. It is concluded that foundation embedment may increase the structural demands for slender buildings especially for the case of relatively soft soils. However, the increase in ductility demands may not be significant for shallow foundations with embedment depth to radius of foundation ratios up to one. Comparing the results with and without inclusion of KI reveals that the rocking input motion due to KI plays the main role in this phenomenon. Copyright © 2008 John Wiley & Sons, Ltd.     

Footings under seismic loading: Analysis and design issues with emphasis on bridge foundations

The paper provides state-of-the-art information on the following aspects of seismic analysis and design of spread footings supporting bridge piers: (1) obtaining the dynamic stiffness (“springs” and “dashpots”) of the foundation; (2) computing the kinematic response; (3) determining the conditions under which foundation–soil compliance must be incorporated in dynamic structural analysis; (4) assessing the importance of properly modeling the effect of embedment; (5) elucidating the conditions under which the effect of radiation damping is significant; (6) comparing the relative importance between kinematic and inertial response. The paper compiles an extensive set of graphs and tables for stiffness and damping in all modes of vibration (swaying, rocking, torsion), for a variety of soil conditions and foundation geometries. Simplified expressions for computing kinematic response (both in translation and rotation) are provided. Special issues such as presence of rock at shallow depths, the contribution of foundation sidewalls, soil inhomogeneity and inelasticity, are also discussed. The paper concludes with parametric studies on the seismic response of bridge bents on embedded footings in layered soil. Results are presented (in frequency and time domains) for accelerations and displacements of bridge and footing, while potential errors from some frequently employed simplifications are illustrated.     

Single precast concrete rocking walls as earthquake force‐resisting elements

Precast concrete walls with unbonded post‐tensioning provide a simple self‐centering system. Yet, its application in seismic regions is not permitted as it is assumed to have no energy dissipation through a hysteretic mechanism. These walls, however, dissipate energy imparted to them because of the wall impacting the foundation during rocking and limited hysteretic action resulting from concrete nonlinearity. The energy dissipated due to rocking was ignored in previous experimental studies because they were conducted primarily using quasi‐static loading. Relying only on limited energy dissipation, a shake table study was conducted on four single rocking walls (SRWs) using multiple‐level earthquake input motions. All walls generally performed satisfactorily up to the design‐level earthquakes when their performance was assessed in terms of the maximum transient drift, maximum absolute acceleration, and residual drift. However, for the maximum considered earthquakes, the walls experienced peak lateral drifts greater than the permissible limits. Combining the experimental results with an analytical investigation, it is shown that SRWs can be designed as earthquake force‐resisting elements to produce satisfactory performance under design‐level and higher‐intensity earthquake motions. Copyright © 2016 John Wiley & Sons, Ltd.     

钢管混凝土框架-混凝土核心筒减震结构振动台试验研究

某超高层钢管混凝土框架-混凝土核心筒结构因指标超限在设计中采用了耗能减震技术,为了检验该减震结构的抗震性能,制作了1/35的缩尺模型,通过在钢管混凝土框架设置阻尼器或不设置阻尼器,进行模拟地震振动台对比试验,研究了模型结构的动力特性和不同烈度地震作用下的加速度、位移和应变响应。研究结果表明:地震作用下,该钢管混凝土框架-混凝土核心筒减震结构与钢管混凝土框架-混凝土核心筒结构相比,位移、加速度和应变响应均有一定程度的降低;罕遇地震作用下,通过设置耗能减震构件,层间位移角最大值从超过规范要求的1/84减低至满足规范要求的1/130,表明该减震结构具有更优良的抗震性能。     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 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.