Seismic Coefficient Research Articles

Seismic behavior of steel frames with different joints: Shaking table test and finite element analysis

This paper discusses the effect of different joint types (common joint (CJ), reduced beam section joint (RJ), and cover plate joint (CPJ)) on the seismic behavior of steel frames. Three steel frames (1:2 scale) with different joints were tested under the shaking table. El Centro wave was selected as the input seismic wave. The failure modes, dynamic response, displacement response, strain response, and acceleration response of steel frame specimens under five peak ground accelerations (PGA) were measured and analyzed. The experimental results indicated that the seismic damage of the steel frame specimens was mainly concentrated at the beam-column joints on the first story. The plastic hinge could be achieved shift-away by reinforcing and reducing the flange at the beam end and significantly improving the structure's seismic capacity. In addition, the ductile joints used also affected the overall structural stiffness. The steel frame specimens' dynamic response (seismic shear coefficient, structural capacity curve, and fundamental frequency attenuation curve) was discussed. As the dynamic loading was applied, the seismic shear coefficients of CPJ and RJ steel frame increased continuously, and the structural capacity curves rose steadily, which indicated that the RJ and CPJ had excellent seismic performance and ductility. The finite element analysis was performed to elaborate further on the seismic performance and failure modes of steel frames. The experimental results were verified by the finite element analysis, and the finite element model could be used for the subsequent research on the steel frame.

Seismic stability analysis of heterogeneous slopes reinforced by inclined soil nails

This study aims to propose an effective approach to evaluate the seismic stability of heterogeneous slopes reinforced by inclined soil nails. The modified pseudo dynamic approach is applied to properly describe the characteristics of seismic loads with time and space. The discretization-based failure mechanism generated from the slope crest is divided horizontally into many blocks to incorporate the heterogeneous soil properties and depth-dependent seismic accelerations into the analysis of the stability issue. The critical seismic acceleration coefficient is then determined to assess the slope stability using the kinematic approach of limit analysis. The proposed method is validated by comparisons with existing solutions and numerical results for some available cases. A systematic parametric analysis is conducted to discuss the effects of model parameters on the slope stability. Results show that there exist optimal relative nail lengths and optimal incline angles of soil nails to obtain the maximum critical seismic acceleration coefficient for reinforced slopes. Finally, an application of the proposed model to spatially variable soil strength properties is performed to illustrate that the proposed method has the potential to serve as a benchmark for the slope stability under complex geological conditions.

The multi-dimensional fragility analysis of the underground large-scale frame structure based on the internal relationships of different seismic performance evaluating indexes

In this paper, the seismic performance of the underground large-scale frame structure (ULSFS) is thoroughly investigated aiming at the drift deformation and rotation deformation of vulnerable positions, and the multi-dimensional fragility analysis of the ULSFS is further developed based on the internal relationship of different seismic performance evaluating indexes. Employing the increment dynamic analysis (IDA) method, the seismic performance of the ULSFS is investigated during diverse earthquakes. The interlayer deformation ratio (IDR) and interlayer rotation angle (IRA) are adopted as Damage measures (DM) to assess the drift deformation and rotation deformation, respectively. The internal relationships of two DMs are revealed, and the correlation coefficients are proposed by the correlation analysis. Assuming the DMs subordinated to the joint lognormal distribution, the generalized equations are established to describe performance states of the ULSFS aiming at different seismic failure modes. Considering the seismic thresholds and correlation coefficients of two DMs in different performance limit states, the 2-D fragility curves of the ULSFS are achieved. The results shows that the correlation of seismic evaluating indexes would decrease with the increase seismic intensities due to the structural inelastic damage; and the 2-D fragility curves with considering the reasonable internal relationships of two DMs would be more accurate and conservative. This paper provides the theoretical basis and technical support for the seismic performance assessment of large underground frame structures with complicate seismic failure modes.

Dynamic behavior of gravity segmental retaining walls

AbstractThis work aims to highlight gravity segmental retaining walls with their varied advantages. The paper investigates the dynamic behavior analysis of segmental retaining walls. The stability analysis is conducted on the basis of a pseudo-static Mononobe-Okabe theory that provides safety factors against sliding and overturning failure. The results demonstrate that the crucial safety factor of internal stability is the safety factor against overturning. Moreover, the positive wall inclination angle contributes to an improvement in the stability of the segmental retaining walls and the effect of the vertical seismic coefficient on the stability can be disregarding. Finally, a new equation is proposed for the elementary design of the segmental retaining walls.

Upper bounds for the three-dimensional seismic active earth pressure coefficients

A numerical implementation of the upper-bound theorem of limit analysis is applied to determine two-dimensional (2D) and three-dimensional (3D) active horizontal earth pressure coefficients considering seismic actions through a horizontal seismic coefficient. Results are obtained for vertical wall, horizontal soil, different friction angles of the soil, soil-to-wall friction ratios, horizontal seismic coefficients and wall width-to-height ratios. The few cases for which 3D active earth pressure coefficients are available in the literature using upper-bound methods were used for comparison with the corresponding earth pressure coefficients obtained in this study. This showed a general improvement of these results, which allows expecting a good accuracy for the set of cases studied. The ratios between the 3D and 2D horizontal active earth pressure coefficients are found to be practically independent of the soil-to-wall friction ratio. An equation is proposed for calculating these ratios. This equation can be easily used in the design of geotechnical structures requiring the determination of 3D active earth pressure coefficients.

Thermal cycling effects on the seismic wave propagation coefficients of granite

The seismic wave propagation properties of granite after thermal cycles were experimentally investigated. The granite specimens were subjected to a series of thermal cycles with different thermal cycling temperatures and numbers. Ultrasonic and pendulum impact tests were performed on the granite after thermal cycles. Subsequently, a theoretical study was introduced to explore the wave propagation coefficients of granite after thermal cycles. The effects of the thermal cycling number on the wave attenuation rate, wave velocity, attenuation coefficient, and wavenumber were discussed. The results indicate that the wave velocity and dynamic elastic modulus decrease as the number of thermal cycles increases and that the damage factor increases as the number of thermal cycles increases. However, the variations in wave velocity, dynamic elastic modulus, and damage factor are concentrated mainly in the first thermal cycle. The results further indicate that the wave propagation coefficients, attenuation coefficient, and wavenumber increase as the number of thermal cycles increases. However, they are not significantly influenced by the amplitude and wavelength of impact loading.

STABILITY ANALYSIS OF THE SLOPE SUBJECTED TO THE DYNAMIC LOADING

This paper presents the results of a stability analysis of a slope located in the immediate vicinity of a railway line. The plans for the extension of this railway track include the construction of another line, which would run parallel to the existing one, within a few metres distance. It is expected that intensive goods train traffic will generate both static and dynamic forces in the underlying subsoil. Consequently, seismic vibrations will be generated in the subsoil, propagating mainly not only in the horizontal direction but also in the vertical direction. The method of seismic coefficient of the earthquake intensity determined by a pseudo-static method and horizontal component of acceleration is appropriate and recommended because it is simple, and the safety factor of the slope is calculated in the same way as in conventional stability calculations.

Seismic passive earth pressure resistance for caisson in layered soil using modified pseudo‐dynamic approach

AbstractThe determination of seismic passive earth pressure resistance is of utmost importance during the analysis of geotechnical structures. In the present study, seismic passive earth pressure coefficient for caisson embedded in n‐layered soil is computed using modified pseudo‐dynamic method. Limit equilibrium method of analysis considering poly‐planar failure wedge has been adopted in the study and parametric variation of geometry of failure wedge has also been studied. The current study proposes formulation for variation of horizontal and vertical seismic acceleration profile with depth through various layers and studies the effect of number of layers, relative depths of various layers and relative soil friction angle in those layers, soil‐wall friction angle, horizontal and vertical seismic acceleration coefficients and normalized width of caisson. The study has been extended for submerged soil and the effect of excess pore pressure has been investigated. The results of the present study have been compared with previous theoretical studies and found to be in good agreement. It is observed that the extent of failure wedge formed in front of caisson increases with increasing soil friction angle, soil‐wall friction angle, horizontal seismic acceleration coefficient and width of caisson.

Wall‐diaphragm interactions in seismic response of building systems ii: Inelastic response and design

AbstractAn elastic parametric study of simplified single‐ and multi‐story building models presented in a companion paper shows that seismic building response depends on the period(s) of the vertical lateral force resisting system (vLFRS), the period of the diaphragm (i.e. the horizontal LFRS, or hLFRS) and the mass distribution between the walls and floors. This paper extends the study to include the potential for inelasticity (ductility) in both the v‐ and hLFRS and examines the impact of this inelasticity on the building response. Increased ductility in the vLFRS reduces vLFRS forces, but to what extent are hLFRS (diaphragm) demands reduced? Similarly, ductile hLFRS presumably reduce hLFRS forces, but what about vLFRS forces? Past work has shown that hLFRS forces are difficult to predict. The building model responses indicate wall‐diaphragm interactions may occur between higher modes of the vertical system and the rigid diaphragms causing increased force demands. Ductility demands are observed to be driven by the element (wall or diaphragm) with the larger inelasticity. Significant ductility demands are observed for short period buildings. A simplified formula for an effective ductility seismic force response modification coefficient for the horizontal LFRS is proposed that considers force reductions from both the inelastic vertical and horizontal LFRS.

From an atomistic study of olivine under pressure to the understanding of the macroscopic energy release in earthquakes

• Assessing macroscopic seismic observables from an unusual microscopic perspective. • A common rupture mechanism for intermediate and very deep earthquakes. • Grounds to redefine commonly accepted order of magnitude for seismic efficiency. We present a multi-disciplinary study of the rupture process of deep- and intermediate-depth earthquakes in the subducting slab that develops beneath the Peruvian-Brazilian region. This contemplates the understanding of the atomistic fracture mechanism in an olivine model, its energetics budget, and the bridging of these results to the available seismic observables. A theoretical description of the stress-strain curves for the subducting material is initially provided as a key element to discern whether the rupture mechanism changes with depth or not. To this purpose, atomistic modeling was carried out through ab initio techniques for the forsterite olivine at different pressure ranges. The achieved stress-strain curves were compared to the average moment-scaled functions obtained for 43 intermediate (50 km < h < 200 km) and very deep earthquakes (500 km < h < 700 km) at the Peruvian-Brazilian subduction zone. It is found that at both depths operate a common atomistic rupture mechanism that is based on the gliding of the {001} crystal planes. Although the velocity of stress release changes with depth, this finding helps to clarify the controversial rupture process for very deep earthquakes at subduction zones. Likewise, efforts were directed to quantify the total amount of energy freed during an earthquake. Test calculations were carried out for several deep earthquakes providing rupture energy of six orders of magnitudes larger than the observable radiated seismic energy. This indicates that there might be space for redefining the commonly accepted order of magnitude for the seismic efficiency coefficient.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

Quantum mechanics-based seismic energy absorption analysis for hydrocarbon detection

SUMMARYSeismic attenuation has a considerable impact on resolution reduction and the increase in the dominant frequency period of seismic data. The absorption coefficient estimates, which measure inelastic attenuation, provide a deep understanding of the medium property changes in different geological settings. Conventional absorption coefficient estimation technologies always use time–frequency methods for seismic energy absorption analysis. However, despite continuing efforts to improve the absorption coefficient estimation, the limitation of the time–frequency methods still causes insufficient accuracy of the attenuation estimates, imposing major challenges in oil and gas hydrate exploration. In this study, a quantum mechanics-based seismic absorption coefficient estimation method was proposed for hydrocarbon detection. The seismic data were first projected on a specific basis constructed using the resolution of the Schrödinger equation. Seismic energy absorption analysis was then conducted in the potential-wave function domain. Finally, the quantum absorption coefficient estimates are given by the procedure after using a logarithmic operation and the least-squares fitting method. We examined the merits of these methods using model and field data. The gas reservoir was accurately targeted, which demonstrates that the proposed method has great potential for hydrocarbon detection.

Seismic bearing capacity for strip footings above voids in cohesive-frictional soils

In this article, the seismic bearing capacity for strip footings above square voids in cohesive-frictional soils is presented. A numerical study is performed by using adaptive finite element limit analysis (AFELA), and the pseudostatic approach is employed to consider the earthquake loadings. Both the upper bound (UB) and lower bound (LB) of the seismic bearing capacity for the strip footing are obtained, along with the relative errors, which are found within 8% or less. The results are presented in the form of design tables and charts to be used by designers and practicing engineers. The effects of the location of the voids, the dimensionless strength ratio c/( γB), the soil internal friction angle ϕ, and the horizontal seismic coefficient kh on the seismic bearing capacity are examined. In addition, the failure mechanisms are also discussed, and comparisons with previous studies of static nature are conducted.

Rankine Active Earth Pressure of Unsaturated Filling under Earthquake

The pseudo-static method was adopted to expand the application field of classical Rankine soil pressure theory to the circumstance of infinite inclined backfill acting on the retaining wall under earthquakes. The calculation formula of the active earth pressure for unsaturated soil was deduced by combining the shear strength model of unsaturated soil and the unified strength theory. The effects of matric suction, matric-suction-related friction angle and seismic coefficients on the intensity distribution of Rankine active earth pressure were evaluated, and the resultant action position was discussed. This research shows that rising seismic coefficients lead to a growth of the active earth pressure and an upward movement of the resultant action point; on the other hand, an increasing matric suction and its related friction angle causes a reduction of the active earth pressure and a downward movement of the resultant action. Examples indicate that the suggested formulas in this paper are in good agreement with those of the previous literature subjected to certain conditions. However, compared to the classic Rankine theory, the proposed method extends its application range by considering earthquake, unsaturated soil, inclined rough wall back, non-horizontal backfill surface, and the intermediate principal stress.

Calculation method for reinforcement spacing of bilaterally wrapped reinforced embankments under seismic force

The vertical spacing among reinforcements in geosynthetic-reinforced earth embankment is crucial to its overall stability. Based on the upper bound theorem of plastic limit analysis and pseudo-static approach, an overall stability analysis method for bilaterally wrapped reinforced embankments under strip surcharge and seismic action is put forward in view of the planar and log-spiral failure mechanism of the reinforced embankments, which quantitatively expresses the relationship between the reinforcement spacing and the factor of safety of the embankments. Some examples show that the maximum relative error of the factor of safety between the proposed method and some existing methods is around 10% under a specified reinforcement spacing. The factor of safety is nonlinearly decreasing as the reinforcement spacing increases, and the results by the log-spiral mode are slightly more conservative than those by the planar mode. The proposed method can quantitatively reflect the influence of the filling properties, reinforcement strength, seismic forces, strip surcharge, and embankment geometry on the reinforcement spacing. The nonlinear negative relationship between the factor of safety and the reinforcement spacing is noticeable under different reinforcement strengths. The reinforcement spacing is almost linearly reducing with the increase of the vertical seismic coefficient increases, while it decreases clearly nonlinearly as the horizontal seismic coefficient increases.

Three-dimensional seismic stability of locally loaded slopes under a rotational velocity field

In practical engineering, slopes subjected to local loads, like footings of buildings, are common. This paper aims to give an insight into the effect of seismic force on the stability of locally loaded slopes. Numerical methods can be used to study this problem, but they require much computational time. Contrarily, limit analysis method is an approach to perform slope stability analysis with high computational efficiency. Thus, an accurate approach in mechanical points is proposed for this problem based on limit analysis method herein. In the framework of limit analysis, existing research about this problem used a kinematically translational velocity field. However, the velocity field of the locally loaded slope at failure is proved to be rotational possibly. Thus, to fill this gap, a 3D rotational velocity field is employed herein to obtain limit loads on the slope top, which improves the existing upper-bound solutions obtained by using the translational velocity field. The particle swarm optimization algorithm and the Nelder-Mead simplex algorithm are employed to search the global minimum of the upper-bound estimation of the limit load. Parametric analysis is performed and it shows that the limit load increases with the increase of a/H or the internal friction angle φ but decreases as the slope angle β or the length-to-width ratio (L/t) of the local load increases. Furthermore, the limit load is found to decrease with the increase of the seismic coefficient kh and it is proportional to the seismic coefficient.

Influence of degree of saturation on the dynamic soil properties of a sandy soil

It is commonly assumed that the fully-saturated scenario represents the critical shear strength condition for geotechnical structure design; nevertheless, this is not the case when the dynamic shear strength of unsaturated soil is considered, because the water content affects the transfer of seismic waves through the porous medium and into a structure. It is important to better understand this behavior so the soil response during an earthquake could be established to prevent damage or failure of the structure. A series of cyclic triaxial tests with controlled matric suction was conducted to determine the principal dynamic parameters for a sandy soil for different degrees of saturation. Finally, to assess the influence of soil saturation on the dynamic soil properties of a sandy soil, a dynamic lateral load pile design was performed using Reese’s p-y curve method, and the parameter obtained from the laboratory testing were used to backcalculate the seismic coefficients used for structural design. Structural designs of laterally loaded piles considering different soil degrees of saturation demonstrated that the saturated soil condition while subjected to a dynamic condition does not represent the critical load case for seismic analysis.

Simplified method for three‐dimensional slope stability analysis based on rigorous limit equilibrium

AbstractA simplified procedure is presented for calculating the factor of safety of a slope with a 3‐D slip surface, which satisfies all the six equilibrium conditions for the 3‐D sliding body. By assuming an initial normal stress distribution on the 3‐D slip surface which is then modified by a polynomial function involving five correcting parameters, the six equilibrium equations are established with a prescribed value of factor of safety, which is linear with the five correcting parameters as well as the horizontal seismic coefficient Kc. An iterative procedure is proposed for determining the factor of safety with a prescribed value of Kc, and ensuring that the normal stresses are positive on the whole slip surface. The method is suitable for analyzing 3‐D slope stability, especially with unsymmetric 3‐D shapes, and its application in practical engineering is given, which demonstrates the effectiveness of the present method.

Effect of Openings in Shear wall on Seismic Behaviour of RC Buildings

Shear walls along the exterior perimeter of buildings increase the efficiency of buildings to resist seismic forces. In some conditions, the locations of shear walls are very critical because of the demand of architectural openings like doors and windows in the exterior face of the buildings. The literature has revealed that stiffness and seismic response of the structure is affected by the size of openings and location of openings in shear walls. This paper demonstrates effect of static and dynamic actions on 15 storey RC building having shear walls with openings. 32 building models have been prepared in commercial software STAAD for various inline and staggered openings in shear walls. Seismic coefficient method and Response spectrum method are used for seismic analysis. The analysis is carried out for the seismic zones III and IV for hard and medium soil conditions. The paper compares the response of these building models having shear wall with and without openings on parameters of time period, base shear, storey displacement, storey drifts and surface stress distribution. Uniform stress distribution was observed in shear wall with staggered opening as compared to inline openings.

A State of The Art Review on Soil-Structure Interaction and Seismic Protection System of Nuclear Power Plant

Soil-structure interaction (SSI) is conventionally considered to be advantageous to the seismic response of a structure. Designers proposed that the least consideration of SSI in structural design results in conservative design. Indian Standard codes allow seismic coefficient ignorance or total reduction of SSI. However, advancements made in developing methods by adding SSI in design to avoid the SSI problem becomes a rarity. This paper summarizes several guidelines and techniques related to SSI analysis of structures. Seismic protection systems (SPS) are successfully installed in conventional designs, but most of the nuclear power plants (NPPs) are not equipped with SPS. Besides, considerable research was carried out to comprise SPS in nuclear power plant design. Currently, horizontal isolation is provided in for structures in active seismic zones. This may be insufficient and vertical isolation has also been required. The results of this review indicated that the future construction of nuclear plants in seismic zones should be equipped with advanced SPS to fulfill the standardised design.