Journal of Earthquake Engineering

The characterisation of viscous damping in time history analysis is discussed in this paper. Although it has been more common in the past to use a constant damping coefficient for single-degree-of-freedom time history analyses, it is contended that tangent-stiffness proportional damping is a more realistic assumption for inelastic systems. Analyses are reported showing the difference in peak displacement response of single-degree-of-freedom systems with various hysteretic characteristics analysed with 5% initial-stiffness or tangent-stiffness proportional damping. The difference is found to be significant, and dependent on hysteresis rule, ductility level and period. The relationship between the level of elastic viscous damping assumed in time-history analysis, and the value adopted in Direct Displacement-Based Design is investigated. It is shown that the difference in characteristic stiffness between time-history analysis (i.e. the initial stiffness) and displacement based design (the secant stiffness to maximum response) requires a modification to the elastic viscous damping added to the hysteretic damping in Direct Displacement-Based Design.

Estimation of equivalent viscous damping is an important step in the methodology of the direct displacement based design. Errors in the estimation of this parameter may lead to consequent errors in the ductility demand of the designed elements. Equivalent viscous damping estimated by Jacobsen's approach for steady-state harmonic response are compared with effective damping factors obtained from an iterative procedure using time — history analyses of single-degree-of-freedom systems. In order to separate the effects of elastic-viscous and hysteretic damping the designs and analyses were carried without elastic viscous damping. Six hysteretic models representing a wide range of hysteretic energy absorption characteristics and six artificial records were used in the analysis. It is found that in general Jacobsen's approach overestimates the values for equivalent viscous damping. Based on the analytical results, modified design equations for equivalent viscous damping are proposed.

A displacement-based design (DBD) methodology for structures that are comprised of both frames and walls has been proposed and then tested through examination of several case studies. Strength proportions between walls and frames are decided before any analysis has begun. The various steps required to represent a frame-wall structure as a single-degree of freedom system are identified and a Direct DBD process is then adopted to set the required strength level. To test the design methodology, two sets of 4, 8, 12, 16 and 20-storey reinforced concrete structures are designed, with different proportions of the total strength assigned to the frames. A suite of time-history analyses have then been conducted to validate the methodology, which is seen to perform reasonably well. Finally, improvements to the procedure are outlined and areas for future research are identified.

The Direct Displacement-based Design methodology is applied to six reinforced concrete tube-frame structures and tested using inelastic time-history analyses. Using the established design method inter-storey drifts are found to exceed assumed drift limits, and a series of changes to the design displacement profiles and lateral force distribution are proposed to improve agreement. These changes are then applied to the six frames and further time-history analyses carried out at different earthquake intensities. The inter-storey drift behaviour is found to be significantly improved, with code-based drift limits consistently satisfied. Finally a revised form of the Modified Modal Superposition is proposed to account for higher-mode amplification of column shear forces, while a simple intensity-dependent scaling factor to be applied in the capacity design process is developed for column bending moments. The suggested equations are applied to the frame designs, and found to be in acceptable agreement with time history results at a range of earthquake intensities.

Notwithstanding its potentially high level, the seismic vulnerability of masonry arch bridges has yet to be completely perceived, possibly due to the relatively scarce damage evidence collected after recent earthquakes. The dearth of research studies on this topic is thus one of the main motivations behind the current endeavour, which aims at a better understanding of the dynamic interaction between the arch walls and the filling material of typical masonry arch bridges, and the consequent susceptibility of the latter to out-of-plane collapse mechanisms. Within this framework, a numerical model for the evaluation of the seismic out-of-plane capacity of bridge walls, including the effects of the infill material, is proposed. This methodology can be subdivided into three main components; computation of static earth pressure, evaluation of dynamic soil thrust, assessment of out-of-plane capacity of a masonry wall. In addition, a congruent and relatively simple procedure for the estimation of the seismic demand on the arch wall is described. Finally, a parametric study is carried out with a view to appraise the seismic vulnerability associated to typical masonry arch bridge typologies.

The aim of this paper is to illustrate an analytical model for the assessment of kinematic interaction of large-diameter shaft foundations. The model is derived using recently obtained solutions of soil structure interaction problems of rigid walls and fixed base cylinders subjected to a dynamic excitation. The proposed model constitutes an extension to a deformable base of the elastodynamic solution of a rigid, fixed-base cylinder imbedded in a homogeneous or inhomogeneous soil stratum with different lateral boundary conditions. The analytical model has been validated by means of a finite elements code and it has been implemented in a consistent seismic soil-structure-interaction analysis procedure. An application of the model to a long, multi-span continuous prestressed concrete viaduct with tall piers has been carried out focusing on the importance of kinematic interaction. The main finding of the study is that the foundation input motion is characterised not only by a translational horizontal component which is usually of a reduced amplitude if compared with the free-field ground motion, but also by a rotational component that is responsible for a large seismic demand in the superstructure. The proposed model represents an effective tool to be used in the engineering practice to assess both the seismic actions induced by the ground shaking on the foundation system and the effective input motion of a superstructure founded on massive and large diameter shafts.

It has been observed that after some earthquakes a number of structures resting on spread footings responded to seismic excitation by rocking on their foundation and in some cases this enabled them to avoid failure. Through application to a standard bridge supported by direct foundations, this paper discusses the major differences in response when foundation uplift is taken into consideration. Special focus is given on the modifications of rocking response under biaxial and triaxial excitation with respect to uniaxial excitation. It is found that inelastic rocking has a significant isolation effect. It is also shown that this effect increases under biaxial excitation while it is less sensitive to the vertical component of the earthquake. Finally, parametric analyses show that the isolation effect of foundation rocking increases as the size of the footing and the yield strength of the underlying soil decreases.

The plastic deformation behaviour of embedded-type column bases was experimentally examined. The primary parameters were width-to-thickness ratio and axial load ratio, and results showed significant strength deterioration induced by local buckling that was largely affected by the test parameters. Analytical models of the test specimens were developed. The developed models were applied for nonlinear dynamic analysis of low- and mid-rise steel moment frames. The analysis results showed the importance of considering deterioration behaviour of column bases as it significantly affected the response and the collapse limit. Large dependency of the collapse limit on the width-to-thickness ratio of the column in addition to the strength itself is also noted from the analysis.