Effect Of Foundation Flexibility Research Articles

Accounting for horizontal torsional vibrations of foundations when calculating seismic load

The article presents a method for calculating in-plane vibrations of building structures under seismic load taking into account the possibility of foundation displacement, which is similar to horizontal torsional vibrations when calculating earthquake forces. The method is illustrated by the structural design of a seven-storey tower-like building with a massive foundation. We develop transfer functions for a massive rigid body, which are subsequently used for calculating the response of the foundation subject to base shears and moments applied to the outer plane of the foundation under seismic forces. The structural calculations conducted for ductile structures with the first frequency of ~2.4 Hz and for more rigid structures with the first frequency of 7.1 Hz showed that, depending on the building stiffness, reduced seismic forces increase by 1.5–2 times. According to the results obtained, when designing structures in areas of high seismic hazard, account should be taken of possible foundation flexibility effects depending on different types of soil and structural solutions of particular buildings.

Effect of Foundation Flexibility on the Seismic Performance of a High-Rise Structure under Far-Field and Near-Field Earthquakes

In this study, the seismic performance of a 20-storey steel structure with a mat foundation located on layered soil is investigated under an array of strong ground excitations, which includes 6 far-fault and 6 near-fault earthquakes. Eight different modes for soil layering have been considered in the numerical simulation. FLAC 2D nonlinear platform has been used to model the near-realistic behavior. To this end, hundred lines of codes and sub-routines have been developed in this platform to perform the analysis. The results of the analyzes include the absolute displacement of the floors, the ratio of the relative displacement of the floors, the shear force, the axial force, and the bending moment of the columns. It was concluded that for a 20-story structure on a mat foundation under both far-field and near-field earthquakes, the most reliable type of soil is the dense sandy soil and the most critical case is the soft clay soil. It was also observed that the near-field strong ground motions have imposed more critical structural responses compared to far-field records.

Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

Seismic Analysis of Open-Top Storage Tanks With Flexible Foundation

The behavior of aboveground storage tanks subjected to seismic excitation was investigated using numerical methods by taking flexibility of foundation into account. The hydrostatic load due to stored liquid has an axisymmetric distribution on the tank shell and base. However, during seismic events, the hydrodynamic load originating from the seismic acceleration of liquid in the tank starts to act in the direction of the earthquake motion. This leads to a nonaxisymmetric loading distribution, which may result in buckling and uplifting of the tank structure. Finite element models were created having nonlinear material properties and large deformation capabilities. Three different tank geometries with liquid height to tank radius aspect ratios of 0.67, 1.0, and 3.0 were selected representing broad, nominal, and slender tanks. These tanks were subjected to two different hydrodynamic loading based on Housner's and Jacobsen–Veletsos' pressure distributions, which forms the basis of design provisions used in American Petroleum Institute API 650 and Eurocode 8, respectively. These pressure distributions were formulated under the assumption of rigid tank wall and base. Furthermore, each tank for a given geometry was subjected to two different foundations: (1) representing a rigid foundation and (2) representing a flexible foundation. The flexible foundation was created using a series of compression-only elastic springs attached to tank base having equivalent soil stiffness. Static analysis corresponding to maximum dynamic force was performed. The finite element results for circumferential and longitudinal stress in the shell were compared with the provisions of API 650. It was found that the effect of foundation flexibility from the practical design point of view may be neglected for broad tanks, but should be considered for nominal and slender tanks.

Controlled-rocking Braced Frame Bearing on a Shallow Foundation

Controlled-rocking braced frames are capable of reducing the drawbacks of conventional frames against seismic loading. This paper examines the effects of soil-foundation modeling on the seismic responses of low-rise controlled-rocking braced frames. For this purpose, dynamic analyses are performed on rocking braced frames and similar conventional frames supported on fixed base and flexible foundations. Structural modeling considerations such as nonlinear constitutive modeling of members, post-tensioned cables, and yielding butterfly-shaped fuses are modeled in OpenSees, and shallow foundations founded on the soil are simulated using the beam-on-nonlinear-Winkler-foundation approach. The effects of modeling and ground motion parameters on seismic performance are investigated from various aspects. Findings show significant foundation flexibility effects in rocking braced-frame archetypes.

Effects of foundation flexibility on seismic demands of asymmetric buildings subject to near-fault ground motions

When the centers of mass and stiffness of a building do not coincide, the structure experiences torsional responses. Such systems can consist of the underlying soil and the super-structure. The underlying soil may modify the earthquake input motion and change structural responses. Specific effects of the input motion shall also not be ignored. In this study, seismic demands of asymmetric buildings considering soil-structure interaction (SSI) under near-fault ground motions are evaluated. The building is modeled as an idealized single-story structure. The soil beneath the building is modeled by non-linear finite elements in the two states of loose and dense sands both compared with the fixed-base state. The infinite boundary conditions are modelled using viscous boundary elements. The effects of traditional and yield displacement-based (YDB) approaches of strength and stiffness distributions are considered on seismic demands. In the YDB approach, the stiffness considered in seismic design depends on the strength. The results show that the decrease in the base shear considering soft soil induced SSI when the YDB approach is assumed results only in the center of rigidity to control torsional responses. However, for fixed-base structures and those on dense soils both centers of strength and rigidity are controlling.

Distribution of strength and stiffness in asymmetric wall typesystem buildings considering foundation flexibility

Architecture constraints in buildings may typically cause irregularities in the distribution of stiffness and mass and consequently causes non-compliance of centers of mass, stiffness and strength. Such buildings are known as asymmetric buildings the distribution of strength and stiffness is one of whose main challenges. This distribution is more complicated for concrete buildings with RC shear walls in which stiffness and strength are interdependent parameters. The flexibility under the foundation is another subject that can affect this distribution due to the variation of dynamic properties of the structure and its constituting elements. In this paper, it is attempted to achieve an appropriate distribution pattern by expressing the effects of foundation flexibility on the seismic demand of concrete shear walls and also evaluate the effects of this issue on strength and stiffness distribution among lateral force resistant elements. In order to understand the importance of flexibility in strength and stiffness distribution for an asymmetric building in different conditions of under-foundation flexibility, the assigned value to each of the walls is numerically calculated and eventually a procedure for strength and stiffness distribution dependencies on flexibility is provided.

Seismic performance of a bridge with tall piers

This paper presents the study of seismic performance evaluation of a proposed railway bridge with tall piers. The study is mainly focused on the central span of bridges having 100-m high piers. The primary aim of the study is to examine the applicability of the response reduction factors, R, given in seismic design codes, for bridges with tall piers. The bridge is designed with increasing values of response reduction factors and its performance is evaluated considering different detailing practices. Moment curvature behaviour and shear resistance of hollow reinforced concrete piers is also discussed. The effect of foundation flexibility on seismic performance of the bridge is explored by performing a sensitivity study with varying modulus of subgrade reaction of the founding soil. It is observed that the response reduction factors prescribed in the Indian code also yield satisfactory performance for tall bridges. In contrast to buildings, currently, displacement is not considered as a design criterion for bridges; however, in most of the cases considered in the present study, the bridges behaved elastically or nearly elastically, with excessive displacement at the top. Foundation–soil flexibility has a significant effect on the displacement of tall bridges, and results in a change of seismic performance level of the considered bridge, in some cases.

Effect of foundation flexibility on response of concrete frame structures under near-fault ground motions

Currently, it is understood that seismic responses of building structures could be changed, owing to the foundation flexibility. The present study is limited to evaluate such phenomenon on non-linear responses of reinforced concrete structures, emphasising their ductility demand distributions. To accomplish this objective, a set of three dimensional reinforced concrete generic frames were modeled as an assemblage of beam/column elements. Utilising substructure method, a set of linearly elastic spring-dashpot model was used to characterise the supporting soil. To estimate ductility demands, non-linear time history analyses as well as pushover analyses were conducted. The foundation–structure system was subjected to an assemblage of ‘ordinary' and ‘near-fault' ground motions. The results indicated soil-structure interaction effects mostly increase ductility demands of the flexible base structures. Consequently, neglecting this phenomenon may lead to erroneous conclusions in the prediction of seismic performance of flexibly supported reinforced concrete frame structures, especially when subjected to near-fault ground motions.

Effect of foundation flexibility on ductility reduction factors for R/C stack-like structures

The most important parameter used to determine force reduction factors in force-based design procedures adopted in the current seismic codes is the structural ductility. For a structure supported on a flexible foundation, the ductility factor could be affected by foundation compliances. The ductility factors given in the current codes are mostly assigned ignoring the effect of SSI and therefore the objective of this research is to assess the significance of SSI phenomenon on ductility factors of stack-like structures. The deformed configuration of stack-like structures is idealized as an assemblage of beam elements considering nonlinear moment-curvature relations, while a linear sway-rocking model was implemented to model the supporting soil. Using a set of artificial records, repeated linear and nonlinear analyses were performed by gradually increasing the intensity of acceleration to a level where the first yielding of steel in linear and nonlinear analyses is observed and a level corresponding to the stack collapse in the nonlinear analysis. The difference between inelastic and elastic resistance in terms of displacement ductility factors has been quantified. The results indicate that foundation flexibility can decrease the ductility of the system and neglecting this phenomenon may lead to erroneous conclusions in the prediction of the seismic performance of flexibly-supported R/C stack-like structures.

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

AbstractComplex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.

Effect of Soil-Structure Interaction on Torsional Response of Asymmetric Wall Type Systems

Generally in the analysis of structures, the base of structures is assumed to be fixed. Whereas, the soil under the structures foundation modify earthquake loading and also change the structural properties. Therefore, considering the fixed base in the structure analysis is not realistic. On the other hand, recent studies have pointed out that for an important class of widely used structural elements such as reinforced concrete flexural walls; stiffness is a strength dependent parameter. This implies that the lateral stiffness distribution in an asymmetric wall-type system cannot be evaluated prior to the assignment of elements’ strength. Consequently, both stiffness and strength eccentricity are important parameters affecting the seismic response of asymmetric wall-type systems. In this study, for different position of stiffness and strength eccentricity, torsional response of asymmetric wall-type system is evaluated. In this evolution the effect of foundation flexibility, is assumed.

The effect of foundation flexibility and structural strength on response reduction factor of RC frame structures

SUMMARYCurrent force‐based design procedure adopted by most seismic design codes allows the seismic design of building structures to be based on static or dynamic analyses of elastic models of the structure using elastic design spectra. The codes anticipate that structures will undergo inelastic deformations under strong seismic events; therefore, such inelastic behaviour is usually incorporated into the design by dividing the elastic spectra by a factor, R, which reduces the spectrum from its original elastic demand level to a design level. The most important factors determining response reduction factors are the structural ductility and overstrength capacity. For a structure supporting on flexible foundation, as Soil Structure Interaction (SSI) extends the elastic period and increases damping of the structure‐foundation elastic system, the structural ductility could also be affected by frequency‐dependent foundation‐soil compliances. For inelastic systems supporting on flexible foundations, the inelastic spectra ordinates are greater than for elastic systems when presented in terms of flexible‐base structure's period. This implies that the reduction factors, which are currently not affected by the SSI effect, could be altered; therefore, the objective of this research is to evaluate the significance of foundation flexibility on force reduction factors of RC frame structures. In this research, by developing some generic RC frame models supporting on flexible foundations, effects of stiffness and strength of the structure on force reduction factors are evaluated for different relative stiffnesses between the structure and the supporting soil. Using a set of artificial earthquake records, repeated linear and nonlinear analyses were performed by gradually increasing the intensity of acceleration time histories to a level, where first yielding of steel in linear analysis and a level in which collapse of the structure in nonlinear analysis are observed. The difference between inelastic and elastic resistance in terms of displacement ductility factors has been quantified. The results indicated that the foundation flexibility could significantly change the response reduction factors of the system and neglecting this phenomenon may lead to erroneous conclusions in the prediction of seismic performance of flexibly supported RC frame structures. Copyright © 2010 John Wiley & Sons, Ltd.

Soil–structure interaction in yielding systems

AbstractThe effects of soil–structure interaction in yielding systems are evaluated, including both kinematic and inertial interaction. The concepts developed previously for interacting elastic systems are extended to include the non‐linear behavior of the structure. A simple soil–structure system representative of code‐ designed buildings is investigated. The replacement oscillator approach used in practice to account for the elastic interaction effects is adjusted to consider the inelastic interaction effects. This is done by means of a non‐linear replacement oscillator defined by an effective ductility together with the known effective period and damping of the system for the elastic condition. To demonstrate the efficiency of this simplified approach, extensive numerical evaluations are conducted for elastoplastic structures with embedded foundation in a soil layer over elastic bedrock, excited by vertically propagating shear waves. Both strength and displacement demands are computed with and without regard to the effect of foundation flexibility, taking as control motion the great 1985 Michoacan earthquake recorded at a site representative of the soft zone in Mexico City. Results are properly interpreted to show the relative effects of interaction for elastic and yielding systems. Finally, it is demonstrated how to implement this information in the context of code design of buildings. Copyright © 2003 John Wiley & Sons, Ltd.

Nonlinear seismic response of reinforced‐concrete free‐standing towers with application to TV towers on flexible foundations

AbstractReinforced‐concrete (R/C) free‐standing towers such as TV towers are often analysed using elastic analyses as fixed‐base cantilever beams, ignoring the effect of soil–structure interaction. To take the capacity of structures after yielding into account, most designers usually prefer to decrease the peak values of the elastic response spectrum for the maximum credible earthquake (MCE) anticipated at the site by a factor called the ductility capacity factor, which varies with the design earthquake level and the structural characteristics of the structure neglecting the effect of supporting soil. To investigate the effect of foundation flexibility on the response of R/C free‐standing towers deforming into their inelastic range during intense ground shaking, a linear sway‐rocking model is applied in numerical modelling of the soil–structure system. The effect of concrete cracking and reinforcement yielding on the elements used in the structure modelling is taken into account by introducing a nonlinear model for R/C frame elements using the moment–curvature (M–ϕ) relation. A method called pseudo‐dynamic analysis is presented to quantify the inelastic seismic response spectrum of a soil–R/C free‐standing system using response spectrum analysis method and push‐over analysis technique. The earthquake responses of cracked and uncracked systems for a practical TV tower and a practical range of soil shear wave velocity are calculated and compared with the objective of understanding how soil–structure interaction influences structural responses. Copyright © 2002 John Wiley & Sons, Ltd.

Effect of foundation flexibility on seismic response of reinforced concrete TV-towers

The analysis of tall reinforced concrete TV-towers is commonly simplified by assuming a fixed base and ignoring the effect of soil–structure interaction. However, the foundation flexibility affects the dynamic characteristics of tall structures and influences their dynamic behaviour. To design these towers for dynamic loading, the fundamental natural periods, base bending moment, and base shear force as the most important parameters are needed and must be evaluated properly. In the current study, a finite element formulation for the response analysis of TV-towers subjected to earthquake ground motion accounting for soil–structure interaction is presented. The effects of foundation flexibility on the dynamic behaviour of TV-towers were evaluated for two different types of foundation, shallow footing and deep foundation, and various soil profiles. A typical example for these towers is analysed and the results for a range of soil dynamic parameters are presented. It was found that the foundation flexibility increases the natural periods, alters the natural mode shapes, and decreases the base bending moment. It was also concluded that the effect of soil–structure interaction may have a large effect on the base shear of the tower and should be considered in the analysis, especially for the design of horizontal reinforcement.Key words: soil–structure interaction, TV-towers, natural period, base forces, foundation flexibility.

Effect of foundation flexibility on seismic response of reinforced concrete TV-towers

Effect of foundation flexibility on seismic response of reinforced concrete TV-towers

On the influence of foundation flexibility on the seismic response of structures

The main objective of this paper is to contribute to a quantification of the effect of foundation flexibility on the most important design variables in the seismic response of building structures with prismatic rectangular foundations. A soil–structure interaction model was used for this purpose. A general continuum formulation was adopted to represent the physical model of the structure and a lumped parameter model was adopted to represent the soil and the interaction mechanisms. Using the implemented models and in view of the objective of the work, a parametric study was made. For this purpose, a group of three structures, three seismic accelerations and seven sets of soil properties will be considered. The results obtained, in view of the large number of uncertainties involved, are presented in a probabilistic format and suggest that the soil–structure interaction can be neglected in the analysis of this class of structures.

Effect of foundation flexibility on the across-wind response of reinforced concrete chimneys with free-standing liners

Chimneys with free-standing liners are often analyzed as fixed base cantilever beams, ignoring the effect of soil-structure interaction on their response. However, soil-structure interaction influences the dynamic response of chimneys in two ways: it alters the natural frequencies, damping ratios, and mode shapes, and it results in coupling of the response of the liner and the shell. In this analysis, the stack was modelled as a continuous cantilever beam with distributed stiffness and mass supported by a flexible foundation. It was found that the relative shell-liner deflection for the flexible foundation case was approximately 35% higher than that for the fixed base case. This increase in deflection may exceed design tolerances for a chimney cap and may lead to liner and (or) shell damage if combined with other adverse conditions such as aerodynamic interference effects with other chimneys. The base forces in the shell decrease significantly due to the foundation flexibility, with values as low as 50% of those of the fixed case. The base forces in the liner were approximately 35% of shell base forces for the fixed base case. These forces are not accounted for in the design of liners using the fixed base assumption. It was concluded that the effects of the foundation flexibility are significant and must be included in the analysis of chimneys with free-standing liners. This is especially true for chimneys in regions with low seismic activity, since the design of the liner would be based on minimal lateral forces.Key words: soil-structure interaction, chimneys, dynamic response, wind.

Effect of foundation flexibility on the across-wind response of reinforced concrete chimneys with free-standing liners

Chimneys with free-standing liners are often analyzed as fixed base cantilever beams, ignoring the effect of soil-structure interaction on their response. However, soil-structure interaction influences the dynamic response of chimneys in two ways: it alters the natural frequencies, damping ratios, and mode shapes, and it results in coupling of the response of the liner and the shell. In this analysis, the stack was modelled as a continuous cantilever beam with distributed stiffness and mass supported by a flexible foundation. It was found that the relative shell-liner deflection for the flexible foundation case was approximately 35% higher than that for the fixed base case. This increase in deflection may exceed design tolerances for a chimney cap and may lead to liner and (or) shell damage if combined with other adverse conditions such as aerodynamic interference effects with other chimneys. The base forces in the shell decrease significantly due to the foundation flexibility, with values as low as 50% of those of the fixed case. The base forces in the liner were approximately 35% of shell base forces for the fixed base case. These forces are not accounted for in the design of liners using the fixed base assumption. It was concluded that the effects of the foundation flexibility are significant and must be included in the analysis of chimneys with free-standing liners. This is especially true for chimneys in regions with low seismic activity, since the design of the liner would be based on minimal lateral forces.Key words: soil-structure interaction, chimneys, dynamic response, wind.