Seismicity Factor A-Value and Its Application to Mid-Term Earthquake Prediction in North China

The seismicity factor A-value is defined by synthesizing the seismicity precursors in time, space and magnitude in this paper. The seismicity data of moderate or small earthquakes during 1972 ~ 1996 in North China are used to perform spacial scanning of seismicity factor A-value. The result shows that there are obviously anomaly zones of A-value with better prediction effect in the mid-term of 2~3 years before most moderately strong earthquakes. Some problems regarding the mid-term prediction using A-value have been discussed.

A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves

When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor referred to as the Gaussian dmping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers （PMLs）. This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models： a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio （SNR） than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.

Influences of nonassociated flow rules on seismic bearing capacity factors of strip footing on soil slope by energy dissipation method

Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.

Inelastic displacement ratio of low-to mid-rise BRBFs designed under variable levels of seismicity

Buckling-restrained braces(BRBs)have shown their capability to provide building structures with stiffness,strength,and ductility.Estimating the seismic drifts of buckling-restrained braced frames(BRBFs)is an important design step to control structural and non-structural damage.In current practice of seismic design,the estimation of seismic drifts of BRBFs is performed by using empirical calculations that are independent upon either the type of the structural system or the design level of seismicity.In these empirical calculations,the seismic drifts are estimated by amplifying the reduced elastic drifts obtained under design lateral loading with a displacement amplification factor(DAF).The value of DAF is considered equal to the product of the response modification factor R and the inelastic displacement ratioρ.The goal of the current research is to assess the value ofρfor low-to mid-rise BRBFs designed under low and high levels of seismicity.This goal has been achieved by conducting a series of elastic and inelastic time-history analyses pertaining to an ensemble of earthquake records on 3-,6-and 9-story BRBFs.The results indicate that theρ-ratio increases with an increase in design seismic intensity and an increase in experienced inelasticity.The range ofρfor low seismicity designs ranges from 0.63 to 0.9,while for high seismicity designs this range stretches from 0.83 to 1.29.It has been found that the consideration of a generalρ-ratio of 1.0 is a reasonable estimation for the design of the BRBFs considered in this study.

Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

Seismic force reduction factor(SFRF) spectra of shear-type multi-degree-of-freedom(MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffnessdegradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type(type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two sitespecific characteristic periods. Based on a large number of results, it is found that the peak value of SFRF spectra may also exist for MDOF, induced by large high-mode contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤λk are smaller than those for λF > λk. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λF(= λk0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

SEISMIC RANDOM VIBRATION ANALYSIS OF STOCHASTIC STRUCTURES USING RANDOM FACTOR METHOD

Seismic random vibration analysis of stochastic truss structures is presented. A new method called random factor method is used for dynamic analysis of structures with uncertain parameters, due to variability in their material properties and geometry. Using the random factor method, the natural frequencies and modeshapes of a stochastic structure can be respectively described by the product of two parts, corresponding to the random factors of the structural parameters with uncertainty, and deterministic values of the natural frequencies and modeshapes obtained by conventional finite element analysis. The stochastic truss structure is subjected to stationary or non-stationary random earthquake excitation. Computational expressions for the mean and standard deviation of the mean square displacement and mean square stress are developed by means of the random variable＇s functional moment method and the algebra synthesis method. An antenna and a truss bridge are used as practical engineering examples to illustrate the application of the random factor method in the seismic response analysis of random structures under stationary or non-stationary random earthquake excitation.

Seismic design factors for RC special moment resisting frames in Dubai,UAE

This study investigates the seismic design factors for three reinforced concrete （RC） framed buildings with 4, 16 and 32-stories in Dubai, UAE utilizing nonlinear analysis. The buildings are designed according to the response spectrum procedure defined in the 2009 International Building Code （IBC＇09）. Two ensembles of ground motion records with 10% and 2% probability of exceedance in 50 years （10/50 and 2/50, respectively） are used. The nonlinear dynamic resPonses to the earthquake records are computed using IDARC-2D. Key seismic design parameters are evaluated; namely, response modification factor （R）, deflection amplification factor （Cd）, system overstrength factor （Ωo）, and response modification factor for ductility （Rd） in addition to inelastic interstory drift. The evaluated seismic design factors are found to significantly depend on the considered ground motion （10/50 versus 2/50）. Consequently, resolution to the controversy of Dubai seismicity is urged. The seismic design factors for the 2/50 records show an increase over their counterparts for the 10/50 records in the range of 200%-400%, except for the D~ factor, which shows a mere 30% increase. Based on the observed trends, perioddependent R and Cd factors are recommended if consistent collapse probability （or collapse prevention performance） in moment frames with varying heights is to be expected.

Assessment of seismic design response factors of concrete wall buildings

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modern design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region （UAE）. A large number of Inelastic Pushover Analyses （IPAs） and Incremental Dynamic Collapse Analyses （IDCAs） were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.

Seismic performance evaluation of water supply pipes installed in a full-scale RC frame structure based on a shaking table test

As an important part of nonstructural components,the seismic response of indoor water supply pipes deserves much attention.This paper presents shaking table test research on water supply pipes installed in a full-scale reinforced concrete(RC)frame structure.Different material pipes and different methods for penetrating the reinforced concrete floors are combined to evaluate the difference in seismic performance.Floor response spectra and pipe acceleration amplification factors based on test data are discussed and compared with code provisions.A seismic fragility study of displacement demand is conducted based on numerical simulation.The acceleration response and displacement response of different combinations are compared.The results show that the combination of different pipe materials and different passing-through methods can cause obvious differences in the seismic response of indoor riser pipes.

Relationship between critical seismic acceleration coefficient and static factor of safety of 3D slopes

Many analytical methods have been adopted to estimate the slope stability by providing various stability numbers,e.g.static safety of factor(static FoS)or the critical seismic acceleration coefficient,while little attention has been given to the relationship between the slope stability numbers and the critical seismic acceleration coefficient.This study aims to investigate the relationship between the static FoS and the critical seismic acceleration coefficient of soil slopes in the framework of the upper-bound limit analysis.Based on the 3D rotational failure mechanism,the critical seismic acceleration coefficient using the pseudo-static method and the static FoS using the strength reduction technique are first determined.Then,the relationship between the static FoS and the critical seismic acceleration coefficient is presented under considering the slope angleβ,the frictional angleφ,and the dimensionless coefficients B/H and c/γH.Finally,a fitting formula between the static FoS and the critical seismic acceleration coefficient is proposed and validated by analytical and numerical results.

The MDOF equivalent linear system and its applications in seismic analysis and design of framed structures

This paper reviews the applications of the multi degree-of-freedom(MDOF)equivalent linear system in seismic analysis and design of planar steel and reinforced concrete framed structures.An equivalent MDOF linear structure,analogous to the original MDOF nonlinear structure,is constructed,which has the same mass and elastic stiffness as the original structure and modal damping ratios that account for the effects of geometrical and material nonlinearities.The equivalence implies a balance between the viscous damping work of the equivalent linear structure and that of the nonlinearities in the original nonlinear structure.This work balance is established with the aid of a transfer function in the frequency domain.Thus,equivalent modal damping ratios can be explicitly determined in terms of the period and deformation levels of the structure as well as the soil types.Use of these equivalent modal damping ratios can help address a variety of seismic analysis and design problems associated with planar steel and reinforced concrete framed structures in a rational and accurate manner.These include force-based seismic design with the aid of acceleration response spectra characterized by high amounts of damping,improved direct displacement-based seismic design and the development of advanced seismic intensity measures.The equivalent modal damping ratios are also utilized in the context of linear modal analysis for the definition and construction of the MDOF response spectrum.Furthermore,the equivalent modal damping ratios are employed in a seismic retrofit method for steel-framed structures with viscous dampers.Finally,it is demonstrated that modal behavior(or strength reduction)factors can be easily constructed based on these modal damping ratios for a more rational and accurate force-based seismic design,including the determination of inelastic displacement profiles.

Estimation of quality factors by energy ratio method

The quality factor Q, which reflects the energy attenuation of seismic waves in subsurface media, is a diagnostic tool for hydrocarbon detection and reservoir characterization. In this paper, we propose a new Q extraction method based on the energy ratio before and after the wavelet attenuation, named the energy-ratio method（ERM）. The proposed method uses multipoint signal data in the time domain to estimate the wavelet energy without invoking the source wavelet spectrum, which is necessary in conventional Q extraction methods, and is applicable to any source wavelet spectrum; however, it requires high-precision seismic data. Forward zero-offset VSP modeling suggests that the ERM can be used for reliable Q inversion after nonintrinsic attenuation（geometric dispersion, refl ection, and transmission loss） compensation. The application to real zero-offset VSP data shows that the Q values extracted by the ERM and spectral ratio methods are identical, which proves the reliability of the new method.

Improve Q estimates with spectrum correction based on seismic wavelet estimation

Characterization of seismic attenuation,quantified by Q,is desirable for seismic processing and interpretation.For seismic reflection data,the coupling between seismic wavelets and the reflectivity sequences hinders their usage for Q estimation.Removing the influence of the reflectivity sequences in reflection data is called spectrum correction. In this paper,we propose a spectrum correction method for Q estimation based on wavelet estimation and then design an inverse Q filter.The method uses higher-order statistics of reflection seismic data for wavelet estimation,the estimated wavelet is then used for spectral correction.Two Q estimation methods are used here,namely the spectral-ratio and centroid frequency shift methods.We test the characteristics of both Q estimation methods under different parameters through a synthetic data experiment.Synthetic and real data examples have shown that reliable Q estimates can be obtained after spectrum correction;moreover, high frequency components are effectively recovered after inverse Q filtering.

Characteristics and factors that influenced damage to dams in the M_s 8.0 Wenchuan earthquake

Based on raw data from dams damaged in the Wenchuan earthquake, including many that were severely damaged, characteristics and factors that influenced the damage are discussed in this paper. Findings from this study include： severely damaged dams were densely distributed along the seismologic fault; small dams, especially small earth-rock dams, had the most serious damage that was caused by a variety of factors; the most serious damage was caused by seismic waves; damage was aggregated by aftershocks; and the extent of the damage patterns increased with the seismic intensity. Damage patterns varied in different intensity zones and cracking was the most common type of damage. Most of the dams had a good base with relatively high bearing capacity, and the walls of the earth-rock dams were mostly of clay soil. This type of base and body material mitigated some of the damage to dams. Reservoir maintenance and other factors also have a significant impact on the seismic safety of the dam. Finally, some recommendations to reduce seismic damage to dams are proposed.

Seismic damage of mountain tunnels during the 5.12 Wenchuan earthquake

A number of mountain tunnels suffered significant damage to various extent during the 2008 Wenchuan earthquake in China.Damage ranging from small to heavy cracking was observed both at the portal and inside the tunnels,while some sections close to the faults completely collapsed.A summary of qualitative data collected from reports and papers is presented regarding the behavior of the 55 mountain tunnels near the epicenter during the earthquake.Based on the seismic investigation and data collection of mountain tunnels,the tunnel damage is classified into six most common damage models involving cracking,spalling,shear failure,dislocation,pavement uplift and collapse.Detailed study and discussion are then carried out on the damage models.In order to examine the influencing factors of the damage magnitude of the mountain tunnels,the correlations between epicentral distance,earthquake intensity,overburden depth,geological condition and damage levels are analyzed.The relationships between earthquake parameters and different damagemodels are developed and discussed.Also,suggestions are provided to improve the seismic resistance of mountain tunnels.

Effect of site amplification on inelastic seismic response

The available models for eff ective periods of site and structure are reviewed in context of frequency tuning in the inelastic seismic response of soil-structure system. The eff ect of seismic intensity and ductility demand, on the eff ective periods, is investigated, and inelastic site amplifi cation is shown to be strongly correlated to the normalized eff ective period. Two non-dimensional parameters, analogous to the conventional site amplifi cation factors in codes, are defi ned to quantify the inelastic site amplifi cation. It is shown that the inelastic site amplifi cation factor (i.e. ratio of constant ductility spectral ordinates at soil site to those at rock outcrop) is able to represent the site eff ects more clearly, as compared to the inelastic site amplifi cation ratio (i.e. ratio of inelastic spectral ordinates at soil site to the corresponding elastic spectral ordinates at rock outcrop). Further, the peak in the amplifi cation factor corresponding to the eff ective site period diminishes rapidly with increasing ductility demand.

Study of the seismic response of a recycled aggregate concrete frame structure

Based on six-degree-of-freedom three-dimensional shaking table tests, the seismic response of a recycled aggregate concrete （RAC） frame was obtained. The analysis results indicate that the maximum story shear force and overturning moment reduce proportionally along the height of the model under the same earthquake wave. The story shear force, base shear coefficient and overturning moment of the structure increase progressively as the acceleration amplitude increases. The base shear coefficient is primarily controlled by the peak ground acceleration （PGA）. The relationships between the PGA and the shear coefficient as well as between the PGA and the dynamic amplification factor are obtained by mathematical fitting. The dynamic amplification factor decreases rapidly at the elastic-plastic stage, but decreases slowly with the development of the elastic-plasticity stage. The results show that the RAC frame structure has reasonable deformability when compared with natural aggregate concrete frame structures. The maximum inter-story drift ratios of the RAC frame model under frequent and rare intensity 8 test phases are 1/266 and 1/29, respectively, which are larger than the allowable value of 1/500 and 1/50 according to Chinese seismic design requirements. Nevertheless, the RAC frame structure does not collapse under base excitations with PGAs from 0.066 g up to 1.170 g.

Seismic performance and global ductility of RC frames rehabilitated with retrofi tted joints by CFRP laminates

This paper presents a new FRP retrofi tting scheme to strengthen local beam-column joints in reinforced concrete(RC) frames.The new retrofi tting scheme was proposed following a preliminary study of four different existing retrofi tting schemes.A numerical simulation was conducted to evaluate the effectiveness of FRP-strengthened reinforced concrete frames by bridging behavior of local joints to the whole structure.Local confi nement effects due to varying retrofi tting schemes in the joints were simulated in the frame model.The seismic behavior factor was used to evaluate the seismic performance of the strengthened RC frames.The results demonstrated that the new proposed retrofi tting scheme was robust and promising,and fi nite element analysis appropriately captured the strength and global ductility of the frame due to upgrading of the local joints.

Stochastic seismic response of multi-layered soil with random layer heights

This paper deals with the effect of layer height randomness on the seismic response of a layered soil. These parameters are assumed to be lognormal random variables. The analysis is carried out via Monte Carlo simulations coupled with the stiffness matrix method. A parametric study is conducted to derive the stochastic behavior of the peak ground acceleration and its response spectrum,the transfer function and the amplification factors. The input soil characteristics correspond to a site in Mexico City and the input seismic accelerations correspond to the Loma Prieta earthquake. It is found that the layer height heterogeneity causes a widening of the frequency content and a slight increase in the fundamental frequency of the soil profile,indicating that the resonance phenomenon is a concern for a large number of structures. Variation of the layer height randomness acts as a variation of the incident angle,i.e.,a decrease of the amplitude and a shift of the resonant frequencies.

Numerical simulation of roadbed slope under seismic action in permafrost regions

The deformation and strength characteristics of roadbed slope under seismic loading in permafrost regions are simulated numerically. The seismic response of roadbed at different positions and inclinations of a slope section was analyzed. Results show that, roadbed slope damage is mainly led by lateral displacement, and the deformation gradually decreases with increasing depth; roadbed and foundation displacement and plastic strain increases with the magnitude of slope angle, hence the roadbed safety factor will be reduced.