Modeling of energy dissipation in structural devices and foundation soil during seismic loading

Though rocking shallow foundations could be designed to possess many desirable characteristics such as energy dissipation, isolation, and self-centering, current seismic design codes often avoid nonlinear behavior of soil and energy dissipation beneath foundations. This paper compares the effectiveness of energy dissipation in foundation soil (during rocking) with the effectiveness of structural energy dissipation devices during seismic loading. Numerical simulations were carried out to systematically study the seismic energy dissipation in structural elements and passive controlled energy dissipation devices inserted into the structure. The numerical model was validated using shaking table experimental results on model frame structures with and without energy dissipation devices. The energy dissipation in the structure, drift ratio, and the force and displacement demands on the structure are compared with energy dissipation characteristics of rocking shallow foundations as observed in centrifuge experiments, where shallow foundations were allowed to rock on dry sandy soil stratum during dynamic loading. For the structures with energy dissipating devices, about 70–90% of the seismic input energy is dissipated by energy dissipating devices, while foundation rocking dissipates about 30–90% of the total seismic input energy in foundation soil (depending on the static factor of safety). Results indicate that, if properly designed (with reliable capacity and tolerable settlements), adverse effects of foundation rocking can be minimized, while taking advantage of the favorable features of foundation rocking and hence they can be used as efficient and economical seismic energy dissipation mechanisms in buildings and bridges.     

Estimation of additional foundation settlements caused by dynamic loading in urban areas

Response of different soils to dynamic loading is of fundamental interest in many engineering, geophysical and environmental studies. Many methods have been proposed to estimate dynamic stability of soils. One more approach, based on laboratory cyclic testing, is discussed in this paper. In our tests, not only the specific features of examined soils, but also different conditions of static and dynamic loading have been taken into account. An analysis of the obtained experimental data explicitly supports the hypothesis of a logarithmic relationship between the axial deformation of soil in cyclic triaxial compression and the number of loading cycles. Evaluation of soil deformation under vibrodynamic loads can also be based on energy approach. The use of critical amount of energy dissipated by soil per its unit volume has been proved to be reliable even in a low dynamic stress range. Convergence of the proposed solution was proved using field measurements and observations. The proposed approach has been applied to evaluate additional settlements of structures founded on the basis of different soil profiles and under various static and dynamic loading conditions.     

Earthquake-induced pounding between equal height multi-storey buildings considering soil-structure interaction

The present paper investigates the coupled effect of the supporting soil flexibility and pounding between neighbouring, insufficiently separated equal height buildings under earthquake excitation. Two adjacent three-storey structures, modelled as inelastic lumped mass systems with different structural characteristics, have been considered in the study. The models have been excited using a suit of ground motions with different peak ground accelerations and recorded at different soil types. A nonlinear viscoelastic pounding force model has been employed in order to effectively capture impact forces during collisions. Spring-dashpot elements have been incorporated to simulate the horizontal and rotational movements of the supporting soil. The results of the numerical simulations, in the form of the structural nonlinear responses as well as the time-histories of energy dissipated during pounding-involved vibrations, are presented in the paper. In addition, the variation in storeys peak responses and peak dissipated energies for different gap sizes are also shown and comparisons are made with the results obtained for colliding buildings with fixed-base supports. Observations regarding the incorporation of the soil-structure interaction and its effect on the responses obtained are discussed. The results of the study indicate that the soil-structure interaction significantly influences the pounding-involved responses of equal height buildings during earthquakes, especially the response of the lighter and more flexible structure. It has been found that the soil flexibility decreases storey peak displacements, peak impact forces and peak energies dissipated during vibrations, whereas it usually leads to the increases in the peak accelerations at each storey level.     

Modelling hysteretic behaviour of coupled walls for dynamic analysis

Modelling techniques for dynamic inelastic response analysis of coupled wall structures are investigated. Emphasis is placed on effects of parameters defining the force-displacement hysteresis loop. Specifically, effects of axial force-moment interaction, strength reduction, shear yielding, pinching, reloading and unloading branches of hysteresis loops are considered. Effects of modelling parameters on selected response quantities are investigated and discussed in detail. A 20-storey coupled wall structure was selected for dynamic analysis. Ranges of parameters characterizing force-displacement hysteresis loops were obtained from laboratory tests under slowly reversed static loading. Previously recorded strong motion accelerograms were used as input motions. Results indicate that wall axial forces and beam strength reduction can have significant effects on response envelopes. Moderate variations in unloading and reloading branches of hysteresis loops and pinching appear to have little effect on dynamic response.     

锈蚀钢筋混凝土圆柱抗震性能的试验研究

对不同锈蚀程度的钢筋混凝土圆柱进行低周反复试验,研究了不同轴压比下的钢筋锈蚀率对钢筋混凝土圆柱滞回曲线、骨架曲线、刚度、延性及耗能能力的影响;给出了试件累积耗能、屈服荷载、极限荷载、荷载最大值和位移延性系数与钢筋锈蚀率和轴压比的关系。研究表明,随着钢筋锈蚀率和轴压比的增大,试件的滞回曲线趋于干瘪,骨架曲线下降段变陡,试件的刚度、延性和耗能能力减小。     

Field testing of stiffened deep cement mixing piles under lateral cyclic loading

Construction of seaside and underground wall bracing often uses stiffened deep cement mixed columns (SDCM). This research investigates methods used to improve the level of bearing capacity of these SDCM when subjected to cyclic lateral loading via various types of stiffer cores. Eight piles, two deep cement mixed piles and six stiffened deep cement mixing piles with three different types of cores, H shape cross section prestressed concrete, steel pipe, and H-beam steel, were embedded though soft clay into medium-hard clay on site in Thailand. Cyclic horizontal loading was gradually applied until pile failure and the hysteresis loops of lateral load vs. lateral deformation were recorded. The lateral carrying capacities of the SDCM piles with an H-beam steel core increased by 3-4 times that of the DCM piles. This field research clearly shows that using H-beam steel as a stiffer core for SDCM piles is the best method to improve its lateral carrying capacity, ductility and energy dissipation capacity.     

Lead-rubber hysteretic bearings suitable for protecting structures during earthquakes

Lead-rubber hysteretic bearings provide in a single unit the combined features of vertical load support, horizontal flexibility and energy absorbing capacity required for the base isolation of structures from earthquake attack. The lead-rubber hysteretic bearing is a laminated elastomeric bearing of the type used in bridge structures, with a lead plug down its centre. Since the invention of the lead-rubber bearing, a total of eleven bearings up to a diameter of 650mm, with lead plugs ranging from 50 to 170mm in diameter, have been tested under various conditions, including vertical loads to 3·15 MN, strokes to ρ 110 mm, rates from 1 mm/h to 100 mm/s, and temperatures of ?35°C to + 45°C. In all of these tests, the lead-rubber bearings behaved satisfactorily and the hysteresis loops could be described reasonably well by assuming that the lead behaved as an elastic-plastic solid with a yield stress in shear of 10·55 MPa. The bearings showed little rate dependence at ～100 mm/s, though at creep rates of ～1 mm/h the force due to the lead dropped to 30 per cent of that at typical earthquake frequencies. The effect of many small displacements has been tested with 11000 cycles at ±3 mm. A total of 92 lead-rubber bearings have been used in New Zealand to base isolate one building and three bridges. They have yet to be used overseas. This paper describes the tests on the lead-rubber bearings, the results and a design procedure for selecting the size of the lead plug.     

Numerical investigation of saturated source area behavior at the small catchment scale

The objective of this research is to explore the relationship between small catchment properties and the temporal growth and decay of saturated source areas (SSA). A simple physics-based hydrologic model, which we call the Sandbox model, is developed for this purpose. A thorough sensitivity analysis is undertaken to evaluate model response to variations in model parameters. Sandbox model output is compared to that from the semi-distributed conceptual model, TOPMODEL, a model with a wide spread acceptance. Plotting the temporal evolution of the extent of saturated source area versus catchment average soil water content during a number of wetting and drying cycles shows a wide variety of trajectories or hysteretic loops. A parametric analysis was performed to quantify the impact of hypothetical catchment properties on the relationship between saturated area extent and basin-average soil water content, revealing hysteretic behavior. It is shown that this hysteresis is the result of changes in groundwater table slope, which is usually less than, and seldom equal to, the land-surface slope in non-saturated areas.     

Finite element analysis and experimental verification of the scrap tire rubber pad isolator

A new base isolation system using scrap tire rubber pads (STRP) has been introduced for seismic mitigation of ordinary residential buildings. The rubber and the steel reinforcing cords used in manufacturing the tire are the alternative materials of the proposed base isolation system. The steel reinforcing cords represent the steel plates used in conventional laminated rubber bearings. These steel reinforcing cords shall prevent the lateral bulging of the rubber bearing. The proposed base isolation system has no bonding between the superstructure and the foundation beam which allows for rollover deformation. In the first part of the study, the STRP layers were just stacked one on top of another without applying the adhesive. This paper presents loading test as well as finite element analysis (FE analysis) of strip STRP isolators that are subjected to any given combination of static vertical and lateral loads. The results of the static vertical and horizontal loading test conducted on STRP isolators were used to calculate the mechanical properties of the isolators, including stiffness and damping values. The load–displacement relationship of STRP isolators were compared between experimental and FE analysis results and the results were found to be in close agreement. The stress state within the STRP isolators was also analyzed in order to estimate the maximum stress demand in the rubber and steel reinforcing cords. These STRP isolators have several advantages over conventional laminated rubber bearings including superior damping properties, lower incurred cost, light weight and easily available material. This study suggests that using the STRP as low cost base isolation device for ordinary residential buildings is feasible.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Response of circular flexible foundations subjected to horizontal and rocking motions

A methodology using modal analysis is developed to evaluate dynamic vertical displacements of a circular flexible foundation resting on soil media subjected to horizontal and rocking motions. The influence of the soil reaction forces on the foundation is considered by introducing modal impedance functions, which can be determined by an efficient procedure with ring elements. The displacements of the foundation can then be easily solved by modal superposition. Parametric studies for modal responses of the flexible foundation indicate that the coupled response of the foundation is significantly influenced by relative stiffness among the foundation and the soil medium, vibration frequency range, foundation mass, and boundary contact conditions. The welded boundary condition should be considered to predict the coupling response while the relaxed boundary condition may be used to predict approximately the vertical displacements. As a foundation with a relative stiffness ratio more than three, it is found that the foundation can be considered as rigid to calculate coupling displacements. For a slightly flexible foundation, considerations of three modes are sufficient enough to obtain accurate foundation responses. Moreover, at low frequencies, the coupling effect due to higher mode can be neglected.     

Non-linear dynamic earth dam–foundation interaction using a BE–FE method

A general, rigorous, coupled Boundary Element–Finite Element (BE–FE) formulation is presented for non-linear seismic soil–structure interaction in two dimensions. The BE–FE method is applied to investigate the inelastic response of earth dams to transient SV waves. The dam body, consisting of heterogeneous materials modelled with a simple non-linear hysteretic model, is discretized with finite elements, whereas the elastic half-space is discretized with boundary elements. The study focuses on the combined effects of the material non-linearity and foundation flexibility. The results show the significant effect of the foundation flexibility in reducing the response through radiation of energy. For excitations with peak ground accelerations from 0·2gto 0·6g, the crest acceleration amplification ranges from 2·5 to 1·4 and seems to be comparable with field observations and results from other studies. Deamplification increasing with strain is reported at the lower part of the dam. The method is computationally powerful and can be used for efficient non-linear analysis of complex soil–structure systems. The efficiency of the BE–FE method allows further improvements with incorporation of a more advanced constitutive model and consideration of the generation and dissipation of pore-water pressures during the earthquake. © 1998 John Wiley & Sons, Ltd.     

Study of vibrating foundations considering soil-pile-structure interaction for practical applications

An investigation of soil-pile-structure interaction is carried out, based on a large reciprocating compressor installed on an elevated concrete foundation （table top structure）. A practical method is described for the dynamic analysis, and compared with a 3D finite element （FE） model. Two commercial software packages are used for dynamic analysis considering the soilpile-structure interaction （SPSI）. Stiffness and damping of the pile foundation are generated from a computer program, and then input into the FE model. To examine the SPSI thoroughly, three cases for the soil, piles and superstructure are considered and compared. In the first case, the interaction is fully taken into account, that is, both the superstructure and soil-pile system are flexible. In the second case, the superstructure is flexible but fixed to a rigid base, with no deformation in the base （no SSI）. In the third case, the dynamic soil-pile interaction is taken into account, but the table top structure is assumed to be rigid. From the comparison beteen the results of these three cases some conclusions are made, which could be helpful for engineering practice.     

Reliability-based load and resistance factor design approach for external seismic stability of reinforced soil walls

Load and resistance factor design (LRFD) approach for the design of reinforced soil walls is presented to produce designs with consistent and uniform levels of risk for the whole range of design applications. The evaluation of load and resistance factors for the reinforced soil walls based on reliability theory is presented. A first order reliability method (FORM) is used to determine appropriate ranges for the values of the load and resistance factors. Using pseudo-static limit equilibrium method, analysis is conducted to evaluate the external stability of reinforced soil walls subjected to earthquake loading. The potential failure mechanisms considered in the analysis are sliding failure, eccentricity failure of resultant force (or overturning failure) and bearing capacity failure. The proposed procedure includes the variability associated with reinforced backfill, retained backfill, foundation soil, horizontal seismic acceleration and surcharge load acting on the wall. Partial factors needed to maintain the stability against three modes of failure by targeting component reliability index of 3.0 are obtained for various values of coefficients of variation (COV) of friction angle of backfill and foundation soil, distributed dead load surcharge, cohesion of the foundation soil and horizontal seismic acceleration. A comparative study between LRFD and allowable stress design (ASD) is also presented with a design example.     

Earthquake response of tension-leg-platforms in steady currents

Dynamic response of tethers of tension-leg-platforms to current and horizontal earthquake excitations is investigated. The static deflected shape of tether under a steady current is firstly identified. Next dynamic analysis for earthquake input is carried out for this deflected tether. The fluid loading due to surrounding water is included in the analysis as an added mass term and a hydrodynamic damping term. The tether is discretized by lumping masses at selected nodes. The platform is represented by a mass at the top end of the tether. The effect of pretension in the tether is taken into account in the form of a geometric stiffness term. At each node three degrees of freedom corresponding to surge, heave and pitch motion are considered. As the vibration modes and hence the responses are likely to be affected by the foundation characteristics, the study is extended to include the dynamic soil–structure interaction. The dynamic equations of motion for the tether–pile–soil system are derived using the substructure method. The natural frequencies and the vibration mode shapes of the total system are determined by eigenvalue analysis. The input ground acceleration is represented by Tajimi–Kanai's power spectrum for stationary conditions. The response analysis is carried out using the frequency-domain random-vibration approach. The coupled axial and lateral responses are evaluated for horizontal ground excitations. Numerical results indicate that the horizontal displacements of the tether increase with the input ground acceleration, but are nearly equal for all the cases of current velocities considered in the study; the vertical displacements however increase rapidly with the increase in current velocity. For the model considered in the present study, the responses are reduced when soil–structure interaction is included in the analysis.     

A versatile index to characterize hysteresis between hydrological variables at the runoff event timescale

This study presents a versatile index for the quantification of hysteretic loops between hydrological variables at the runoff event timescale. The conceptual development of the index is based on a normalization of the input data and the computation of definite integrals at fixed intervals of the independent variable. The sum, the minimum and the maximum of the differences between integrals computed for the rising and the falling curves provide information on the direction, the shape and the extent of the loop. The index was tested with synthetic data and field data from experimental catchments in Northern Italy. Hysteretic relations between streamflow (the independent variable) and soil moisture, depth to water table, isotopic composition and electrical conductivity of stream water (dependent variables) were correctly identified and quantified by the index. The objective quantification of hysteresis by the index allows for the automatic classification of hysteretic loops and thus the determination of differences in hydrological responses during different events. The index was also used to examine the seasonal dynamics in the relation between streamflow and soil moisture and captured the switch in the direction of the loop with changes in event size and antecedent wetness conditions. The sensitivity of the index to the temporal resolution of the measurements and measurement errors was also tested. The index can successfully quantify hysteresis, except for very noisy data or when the temporal resolution of the measurements is not well suited to study hysteresis between the variables. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical analyses of pile performance in laterally spreading frozen ground crust overlying liquefiable soils

Lateral spread of frozen ground crust over liquefied soil has caused extensive bridge foundation damage in the past winter earthquakes. A shake table experiment was conducted to investigate the performance of a model pile in this scenario and revealed unique pile failure mechanisms. The modelling results provided valuable data for validating numerical models. This paper presents analyses and results of this experiment using two numerical modeling approaches: solid-fluid coupled finite element (FE) modeling and the beam-on-nonlinear-Winkler-foundation (BNWF) method. A FE model was constructed based on the experiment configuration and subjected to earthquake loading. Soil and pile response results were presented and compared with experimental results to validate this model. The BNWF method was used to predict the pile response and failure mechanism. A p-y curve was presented for modelling the frozen ground crust with the free-field displacement from the experiment as loading. Pile responses were presented and compared with those of the experiment and FE model. It was concluded that the coupled FE model was effective in predicting formation of three plastic hinges at ground surface, ground crust-liquefiable soil interface and within the medium dense sand layer, while the BNWF method was only able to predict the latter two.     

Masonry infill walls in reinforced concrete frames as a source of structural damping

This paper presents the results of an experimental study on the determination of damping characteristics of bare, masonry infilled, and carbon fiber reinforced polymer retrofitted infilled reinforced concrete (RC) frames. It is well known that the masonry infills are used as partitioning walls having significant effect on the damping characteristics of structures as well as contribution to the lateral stiffness and strength. The main portion of the input energy imparted to the structure during earthquakes is dissipated through hysteretic and damping energies. The equivalent damping definition is used to reflect various damping mechanisms globally. In this study, the equivalent damping ratio of carbon fiber reinforced polymer retrofitted infilled RC systems is quantified through a series of 1/3‐scaled, one‐bay, one‐story frames. Quasi‐static tests are carried out on eight specimens with two different loading patterns: one‐cycled and three‐cycled displacement histories and the pseudo‐dynamic tests performed on eight specimens for selected acceleration record scaled at three different PGA levels with two inertia mass conditions. The results of the experimental studies are evaluated in two phases: (i) equivalent damping is determined for experimentally obtained cycles from quasi‐static and pseudo‐dynamic tests; and (ii) an iterative procedure is developed on the basis of the energy balance formulation to determine the equivalent damping ratio. On the basis of the results of these evaluations, equivalent damping of levels of 5%, 12%, and 14% can be used for bare, infilled, and retrofitted infilled RC frames, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

The local geodynamic test area of CLG-organization and first results of leveling measurement

In 1982, the Central Laboratory for Geodesy (CLG) started a long-term study of the recent crustal movements in a local test area in a mobile region located southwards of Sofia.The recent geodynamic conditions and the deep structure of the Earth's crust in this region are described.Data on the local network of precise leveling are given-the scheme and characteristics of the loops, benchmarks and their monumentation. A first geodynamic analysis of the results of the first and third cycles of measurements is made, a map of the module of horizontal gradient of vertical velocity has been elaborated. The results obtained corroborate the reasons for the selection of this geodynamic test area.