Seismic Inertia Forces Research Articles

Seismic performance of tall pier bridges retrofitted with lead rubber bearings and rocking foundation

Bridges with 40 m or taller piers are commonly constructed in southwest China that is a region of high seismicity. Since it is common practice that the superstructure of such bridges is directly placed on rubber bearings without additional constraints, sliding between the girders and the bearings may occur in the events of strong earthquakes. With the focus on the bridges with tall piers, this paper investigates the effectiveness of different seismic retrofitting measures including lead rubber bearings and rocking foundations in mitigating the seismic responses of bridges. Based on the predetermined damage states for different structural components, the seismic responses of prototype bridge with rubber bearings, as well as retrofitted with lead rubber bearings (LRBs) and rocking foundations, are computed and compared subjected to ground motions with PGA level specified in current Chinese specification. The results show that for the prototype bridge, excessive deformation of rubber bearings and considerable damage of pier columns will happen under strong earthquake motions considered herein. While LRBs are capable of controlling the relative displacement between girders and bearings, reducing the probability of unseating, they cannot suppress the seismic demands of pier columns effectively. On the other hand, when rocking foundations are employed, the dynamic performance of piers is improved significantly, and the piers are expected to remain elastic during strong earthquake excitations. The reason is that LRBs could only reduce the seismic inertial force of superstructure, while the rocking foundation is able to isolate that caused by pier columns as well, which is significant for tall pier bridge. Additionally, once the tall piers start to rock, seismic responses, e.g., deformation of bearings and curvature of piers, tend to be similar and independent of input motions, improving the predictability of post-earthquake state of these bridges.

Seismic damage mechanism of slope and lining in the mountain tunnel portal section

A series of numerical simulations were conducted to study the seismic response in the mountain tunnel portal section. The seismic damage mechanism, including slope cracking and landslide, rockfalls and collapse, and lining cracking were analyzed based on the seismic damage characteristics of the Longxi tunnel during the 2008 Wenchuan earthquake in China. The results show that slope cracking due to the huge horizontal seismic inertial force which exceeds the strength of slope; landslide is caused by the connected cracks where the oblique component of horizontal seismic inertia force exceeds the shear strength of slope; rockfalls and collapse are caused by the cumulative tensile stress in loose soil and rock which exceed the strength of slope; the transverse lining cracks due to the alternate tensile and compressive action of the seismic load along the axial direction, which makes the lining tensile strain accumulates and exceeds the concrete ultimate strength. As for the longitudinal lining cracking, the transverse seismic load makes the bending moment direction in lining alternates, leading to the strength reduction of concrete. Moreover, the circumferential penetrating rupture zone is caused by the large shear force resulting from the slope sliding, which leads to the stress concentration at vault and when the tensile stress exceeds the concrete tensile strength, the vault begins to crack, and then the cracks extend from the arch shoulder to foot.

Seismic bearing capacity factor N γe for dry sand beneath strip footing using modified pseudo-dynamic method with composite failure surface

ABSTRACT An important aspect of studying soil behaviour under seismic loading is the accurate modelling of time-dependent and random seismic forces. The pseudo-static method of analysis is very approximate and although the pseudo-dynamic method considers phase difference and amplification effects, it has certain limitations. The modified pseudo-dynamic method considers the time-dependent behaviour of seismic forces and inherently accounts for the amplification of acceleration, thus making it more realistic. This newly developed method is applied to determine seismic inertia forces for estimating the seismic bearing capacity factor (N γ e) of dry sand underlying shallow strip footings. Limit equilibrium approach is used and a one-sided composite failure surface is considered to be developed under seismic load. The focus of the log-spiral is iteratively determined to give the least value of N γe. The results are presented graphically in non-dimensional form which may be used by geotechnical practitioners for design in seismically active regions.

Seismic performance of a whole Geosynthetic Reinforced Soil – Integrated Bridge System (GRS-IBS) in shaking table test

A scaled plane-strain shaking table test was conducted in this study to investigate the seismic performance of a Geosynthetic Reinforced Soil-Integrated Bridge System (GRS-IBS) with a full-length bridge beam resting on two GRS abutments at opposite ends subjected to earthquake motions in the longitudinal direction. This study examined the effects of different combinations of reinforcement stiffness J and spacing Sv on the seismic performance of the GRS-IBS. Test results show that reducing the reinforcement spacing was more beneficial to minimize the seismic effect on the GRS abutment as compared to increasing the reinforcement stiffness. The seismic inertial forces acted on the top of two side GRS abutments interacted with each other through the bridge beam, which led to close peak acceleration amplitudes at the locations near the bridge beam. Overall, the GRS-IBS did not experience obvious structure failure and significant displacements during and after shaking. Shaking in the longitudinal direction of the bridge beam increased the vertical stress in the reinforced soil zone. The maximum tensile forces in the upper and lower geogrid layers due to shaking happened under the center of the beam seat and at the abutment facing respectively.

Effect of Different Constraint Systems on the Seismic Response of Double-Deck Curved Girder Bridges

Double-deck curved girder bridges can achieve large climb in a short distance, and their seismic response differs from that of regular bridges due to their special structural form. The constraint system of bridges, which consists of bearings and shear keys, has a key influence on the seismic response of the bridge structure. Accordingly, this research aims to develop a reasonable constraint system for double-deck curved girder bridges. A finite element simulation of a double-layer curved steel box girder bridge is also conducted to compare some indexes, which are the displacement of bearings with the curvature of the pier section. The shear bolt is selected as the limit device to study the influence of shear bolts and different bearings on the seismic response of the double-deck curved girder bridge structure. Under the influence of ground motion, the displacement of the upper bearings of double-layer curved girder bridges is generally larger than that of the lower bearings. The double-layer constraint system makes the section curvature and ductility in the middle of the pier smaller than that at the top and bottom of the pier. The spherical steel bearings have a small displacement, whereas the pier has a large internal force. After setting the shear bolts, the displacement of the spherical steel bearings decreases, whereas the damage to bridge piers does not show obvious changes. When the displacement of elastomeric pad bearings increases, sliding occurs under a low ground motion intensity, thereby reducing the degree of damage to the bridge pier. Moreover, the application of shear bolts limits the displacement of bearings and subsequently increases the seismic force being transmitted to the pier whose damage is the most serious. However, the displacement of pot bearings is relatively small, and the displacements of the upper and lower layers are close. In addition, the seismic inertial force of the superstructure is relatively uniform, thereby protecting the piers to a certain extent. After setting the shear bolts, the deformation falls within an allowable range, whereas the damage to the bridge piers slightly increases. Therefore, combining pot bearings with shear bolts creates a reasonable constraint system for double-deck curved girder bridges.

Integrated risk of rail buckling in ballasted tracks at transition zones and its countermeasures

Railway ballasted tracks at transition zones from embankment sections to bridge sections (or the reverse) suffer not only from seismic motions, but also from differential settlements during seismic motions. Therefore, an attempt is made in this study to evaluate the combined effects of hanging sleepers and seismic inertia force on the lateral resistance of ballast in the tracks at transition zones. A series of laboratory tests was conducted on 1/5 scale models to evaluate the lateral resistance characteristics under situations of hanging sleepers or under pseudostatic conditions. The results of the pullout tests revealed that the rail-buckling potential can be underestimated without the consideration of combined effects of hanging sleepers and the seismic inertia force on the lateral resistance. Based on the model test results, the combination of anti-buckling plates and ballast retaining walls is proposed as a new earthquake countermeasure.

Theoretical and experimental studies of seismic resistance of underground passages

In this article theoretical calculations of the construction of the underground passages under the influence of seismic forces are conducted and refined by a series of experiments. As a result of experimental studies, the authors have clarified the value of the active pressure of the ground on the construction and the active seismic inertial forces, taking into account the design. As a result of theoretical and experimental studies of seismic resistance of underground pedestrian crossings at different ground, areas of stress concentration in these constructions have been determined, which allows these sections to provide anti-seismic beams, which ensures the safety of the constructions to an earthquake or significantly reduce the degree of damage.

Computation of sliding displacements of seawalls under earthquake conditions

To understand the serviceability aspects of seawalls, it is essential to study the permanent displacements of seawalls that occur during the earthquakes. Studies in the existing literature have concentrated on displacements of retaining walls with dry backfills; to the authors’ observation there is no specific analytical investigation devoted to the earthquake-induced displacements of retaining walls with submerged backfills. This paper focuses on sliding displacements of gravity type seawall retaining a submerged backfill under active earth pressure condition during the earthquakes. The threshold seismic acceleration coefficients required for initiation of sliding and the amount of sliding displacement due to seismic loading are calculated by adopting Newmark’s sliding block method. One of the prime features of the study is the estimation of seismic inertia forces in the submerged soil and wall applying the modified pseudo-dynamic method. The comparison of the results obtained using the proposed analytical formulation with the existing literature found to be in good agreement. A comprehensive parametric study has been conducted to understand the effects of different parameters such as seismic horizontal and vertical acceleration coefficients, soil and wall friction angles, width of the wall, wall inclination and excess pore water pressure ratio.

The Dynamic Stability Analysis of Shapai Arch Dam Affected by Wenchuan Earthquake

The sliding wedge method and the finite element rigid body limit equilibrium method are combined to analyze the dynamic stability of shapai arch dam affected by wenchuan earthquake, and compared with the pseudo-static method. Analysis indicates that the result got by the sliding wedge method and the finite element rigid body limit equilibrium method is slightly higher than the pseudo-static method of safety coefficient. Because the changes in the size and direction of the arch abutment thrust are taken into account in the sliding wedge method and the finite element rigid body limit equilibrium method, and coincidence coefficient is considered during applying seismic inertia force. So the method referred by this paper can reflect the aseismatic working state of the arch dam. Therefore, it provides a novel means of evaluating aseismatic safety.

Theoretical and experimental studies of seismic resistance of underground passages

In this article theoretical calculations of the construction of the underground passages under the influence of seismic forces are conducted and refined by a series of experiments. As a result of experimental studies, the authors have clarified the value of the active pressure of the ground on the construction and the active seismic inertial forces, taking into account the design. As a result of theoretical and experimental studies of seismic resistance of underground pedestrian crossings at different ground, areas of stress concentration in these constructions have been determined, which allows these sections to provide anti-seismic beams, which ensures the safety of the constructions to an earthquake or significantly reduce the degree of damage.

Seismic Active Thrust on Rigid Retaining Wall Using Strain Dependent Dynamic Properties

An analytical model is proposed for the evaluation of seismic active thrust on retaining wall resting on sandy soil. Foundation and backfill soil is idealized as Kelvin-Voigt solid. The governing differential equation of vertically propagating shear wave is solved by maintaining the displacement continuity and stress compatibility at the interface between backfill and foundation soil. Nonlinear distribution of accelerations induced in the backfill soil is then used to compute the seismic inertia force. Total seismic active thrust is obtained by solving the force equilibrium equation of the triangular failure wedge. The present method computes the strain-dependent shear-wave velocity and damping ratio of sand from its modulus reduction and damping ratio curves using an iterative scheme. Amplification and deamplification of the input excitations in the foundation soil and backfill soil are compared with results of dynamic centrifuge tests reported in the literature. An increase in the magnitude of seismic active thrust is observed when the retaining wall is situated on sandy soil in place of the rigid stratum, and the percentage increase is 18% in comparison to the latest method available in the literature. The seismic active thrust values for long period input excitations are nearly 13 to 17% higher compared to short-period input excitations. The parametric study reveals that depth of backfill and foundation soil, impedance ratio, amplitude, and frequency of input motion dominate the response of the backfill soil under seismic condition. (C) 2018 American Society of Civil Engineers.

Structural Health Monitoring for Performance Assessment of Bridges under Flooding and Seismic Actions

Bridges can be subjected to damaging environmental actions due to flooding and seismic hazards. Flood actions that result in scour are a leading cause of bridge failure, while seismic actions that induce lateral forces may lead to high ductility demand that exceeds pier capacity. When combined, seismic actions and scour can lead to effects that depend on the governing scour condition affecting a bridge. Loss of stiffness under scour can reduce the ductility capacity of a bridge but can also lead to an increase in flexibility that may reduce seismic inertial forces. Conversely, increased flexibility can lead to deck collapse due to support loss, so there exists some uncertainty about the combined effect of both phenomena. A necessary step towards the performance assessment of bridges under flooding and seismic actions is to calibrate numerical models that can reproduce structural responses under different actions. A further step is verifying the achievement of performance goals defined by codes. Structural health monitoring (SHM) techniques allow the computation of performance parameters that are useful for calibrating numerical models and performing direct checks of performance goal compliance. In this paper, various strategies employed to monitor bridge health against scour and seismic actions are discussed, with a particular focus on vibration-based damage identification methods.

Seismic Stability Analysis of Municipal Solid Waste Landfills Using Strain Dependent Dynamic Properties

Seismic stability analysis is an integral part of the design of municipal solid waste (MSW) landfills in the areas of high seismic activity. The conventional pseudo-static methods were used to calculate the factor of safety of MSW landfills. However, these methods didn’t consider the mode change behaviour of the landfill, amplification acceleration of the ground motion and also, neglected the damping properties of MSW. The objective of the present study is to develop an integrated methodology that gives the seismic acceleration profile in the landfill as well as the factor of safety and yield acceleration values for a typical side-hill type geometric configuration. Strain-dependent dynamic properties (shear modulus and damping ratio) of MSW are computed through an iterative scheme and the same shear modulus and damping ratio are used to calculate the seismic factor of safety of landfills. Amplification of base acceleration is observed at low-frequency input motions. The maximum shear strain generated in the landfill is significantly higher for low-frequency input motions, since, at lower frequencies, the seismic inertial forces at all depths are in phase. Whereas, at higher frequencies, those are out of phase. The factor of safety values computed using the present method are on the higher side when compared to the conventional pseudo-static method of analysis for certain combination of input parameters.

Seismic stability of slope using modified pseudo-dynamic method

The paper presents evaluation of factor of safety of slope assuming circular failure surface under seismic loading condition. The centre of most critical circle is located using Fellenius method. Adopting limit equilibrium method, under the influence of weight of potential sliding mass and seismic inertia forces, factor of safety is evaluated applying new pseudo-dynamic method based on visco-elastic behaviour of soil which satisfies zero-stress boundary condition and considers soil amplification inherent to soil properties. Results are presented and compared with available results from literature. Detailed parametric studies are also carried out to observe the variation of safety factor at different soil strength and seismic forces and these can serve as very good criteria for design of slopes.

Seismic Stability of Slope Considering Rayleigh Wave

ABSTRACTIn the present paper factor of safety of slope under seismic loading condition is evaluated assuming circular failure surface. Using Fellenius method the center of most critical circle is located. Adopting limit equilibrium method, under the influence of weight of potential sliding mass and seismic inertia forces, factor of safety is evaluated considering Rayleigh wave along with primary wave and shear wave. Results are presented and compared with the available results from literature. Detailed parametric studies are also carried out to observe the variation of safety factor at different soil strength and seismic forces.

Dynamic Model for Free-Standing Fuel Racks Under Seismic Excitation Considering Planar and Nonslide Rocking Motion

A free-standing (FS) rack is a type of a spent nuclear fuel rack, which is just placed on a floor of a pool. For this characteristic, seismic loads can be reduced by fluid force and friction force, but a collision between a rack and another rack or a wall must be avoided. Therefore, it is necessary for designing an FS rack to figure out how it moves under seismic excitation. In this research, a dynamic model of an FS rack is developed considering seismic inertial force, friction force, and fluid force. This model consists of two submodels: a translation model, which simulates planar translational and rotational motion, and a rocking model, which simulates nonslide rocking motion. First, simulations with sinusoidal inertial force were conducted, changing values of a friction coefficient. Next, to validate this dynamic model, a miniature experiment was conducted. Finally, the model is applied to a real-size FS rack and actually observed seismic acceleration. It is found that translational movement of a rack varies depending on the value of friction coefficient in the simulation with sinusoidal and actual acceleration. Also, simulation results are similar to the experimental results in the aspects of translational and rocking motion provided friction coefficient is selected properly. Through this research, the knowledge is acquired that friction force plays a significant role in a motion of FS rack so that estimating and controlling a friction coefficient is important in designing an FS rack.

Seismic Translational Failure Analysis of MSW Landfills Using Modified Pseudo-Dynamic Approach

For landfills situated in regions of high seismicity, seismic inertial forces may be a triggering factor for the translational stability of municipal solid waste (MSW) landfills. This paper applies a modified pseudodynamic method to the seismic translational stability analysis of landfills. In the present study, a closed-form solution is proposed to obtain the factor of safety and the yield acceleration coefficient for a typical side-hill-type landfill resting on a rigid base using limit equilibrium method. The acceleration ratio obtained in the present study compares well with that obtained using popular ground response analysis software for a given set of input parameters. The acceleration ratio is the ratio of seismic acceleration at the top of the landfill to the seismic acceleration at the base of the landfill. From parametric study, it is observed that the landfill is vulnerable to seismic damage in low-frequency input motions. At low frequencies, the seismic inertia force is in phase at all depths. The seismic force acting on the landfill mass is reduced at higher frequencies, where landfill mass is entering into higher modes of vibration, where some portion of landfill is moving in one direction and the remaining portion is moving in opposite direction. The results obtained are compared with the available literature sharing the same input parameters. The values of the factor of safety obtained in the present study are higher than those calculated using pseudostatic and pseudodynamic approaches. For the input parameters assigned in the comparison, the landfill mass in the third mode of vibration is the reason for the greater values of the factor of safety. Material damping may be also a reason for the higher factor of safety values. (C) 2017 American Society of Civil Engineers.

Effect of dynamic soil properties and frequency content of harmonic excitation on the internal stability of reinforced soil retaining structure

The effect of dynamic soil properties and frequency content of harmonic excitation on the internal stability of reinforced soil retaining structure is investigated. Arc of a log-spiral is considered as the failure surface in the present limit equilibrium analysis. Backfill and reinforced soil is modeled as a visco-elastic material. The whole structure is considered to be resting on a rigid stratum. Backfill soil and the reinforced soil retaining structure are subjected to harmonic shaking at the base. Present methodology satisfies the stress boundary condition at the ground surface. In the present study, amplitude and phase of the horizontal and vertical seismic accelerations change with depth and the variation of accelerations along the depth is found to be time dependent and nonlinear. All the four possible combinations of horizontal and vertical seismic inertia force directions are considered to determine the total reinforcement force and critical length of the reinforcement. In the present study, amplification of accelerations towards the ground surface depends on the dynamic soil properties and frequency content of input excitation. Detailed parametric study is done to understand their implications on the solution. An algorithm is proposed at the end of this paper which uses strain dependent equivalent linear values of shear wave velocity (Vs) and damping ratio (ξ) to compute the total reinforcement force and critical length of the reinforcement. The limitation of equivalent linear based approach is that it only considers vertically propagating shear wave. Comparison of present method with other theories is also presented showing the merit of the present study.

Stability of seawalls using modified pseudo-dynamic method under earthquake conditions

By using the modified pseudo-dynamic method for submerged soils this paper explores the seismic stability of seawall for the active condition of earth pressure. Different forces such as seismic active earth pressure, seismic inertia forces of the wall, non-breaking wave pressure, hydrostatic and hydrodynamic pressures are considered in the stability analysis. Limit equilibrium has been used, and expressions for the factor of safety against sliding and overturning mode of failure have been proposed. The proposed methodology overcomes the limitations of existing pseudo-dynamic method for submerged soils. A detailed parametric study has been conducted by varying different parameters and results are presented in the form of design charts for computation of factor of safety against sliding and overturning mode of failures. It was noticed that the influences of soil friction angle, seismic acceleration coefficient, wall inclination and excess pore pressure are significant when compared to the other parameters. The value of factor of safety against the sliding mode of failure is increasing by about 62% when the value of soil frictional angle is increased from 30° to 40°. It was also found that the factor of safety against overturning mode of failure is decreasing by about 22% as the value of excess pore pressure ratio increases from 0 to 0.75. The proposed method with closed-form solutions can be used for the seismic design of seawalls.

Sliding and overturning stability of breakwater under combined effect of earthquake and tsunami

Powerful tsunami waves were generated by the 2011 off the Pacific Coast of Tohoku Earthquake, and they struck the coast of Japan after few minutes of the main shock. Seismic aftershocks continued for several hours. Many coastal structures such as breakwaters, seawalls were damaged due to the earthquake and tsunami. It may be possible that some coastal structures were hit by the aftershock and the tsunami together. This paper focuses on this fact, and analyzes stability of breakwater under combined effect of earthquake and tsunami. For estimating seismic inertia forces on breakwater, the pseudo-dynamic method was used, which considers seismic waves passing through body of breakwater with respect to depth and time. Stability of breakwater was assessed in terms of factors of safety against sliding and overturning modes of failure. It was found that stability of breakwater reduces drastically under combined effect of earthquake and tsunami as compared to only earthquake and only tsunami. Parameters such as seismic accelerations, height of tsunami wave, seawater level and width of breakwater have significant impacts on stability of breakwater under combined action of earthquake and tsunami. The design charts and tables, presented in this paper, will be helpful for design engineer to design a breakwater under combined effect of earthquake and tsunami in future.