Amplification of in-plane seismic ground motion by group cavities in layered half-space (Ⅱ): with saturated poroelastic soil layers

As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and saturated poroelastic soil layers. The influence of poroelastic layers on the amplification of seismic ground motion is studied both in frequency domain and time domain using indirect boundary element method （IBEM）. It is shown that for the example of a saturated poroelastic site in Tianjin under the excitation of Taft wave and E1 Centro wave, the amplification of seismic ground motion in poroelastic case is slightly smaller than that in the elastic case, and the amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum）.. can be increased up to 38.8% and 64.6%; the predominant period of response spectra in poroelastic case becomes shorter to some extent compared with that in the elastic case. It is suggested that the effect of underground group cavities in poroelastic half-space on design seismic ground motion should be considered.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Amplification of in-plane seismic ground motion by group cavities in layered half-space (Ⅰ)

Amplification of in-plane seismic ground motion by underground group cavities in layered half-space is studied both in frequency domain and time domain by using indirect boundary element method （IBEM）, and the effect of cavity interval and spectrum of incident waves on the amplification are studied by numerical examples. It is shown that there may be large interaction between cavities, and group cavities with certain intervals may have significant amplification to seismic ground motion. The amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum） can be increased up to 45.2% and 84.4%, for an example site in Tianjin, under the excitation of Taft wave and E1 Centro wave; and group cavities may also affect the spectra of the seismic ground motion. It is suggested that the effect of underground group cavities on design seismic ground motion should be considered.

Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.

Estimation of Seismic Ground Motion Induced by the 23 January, 2005 Earthquake in Palu Region, Central Sulawesi, Indonesia

On January 23rd 2005, a strong earthquake with moment magnitude （Mw 6.3） hit the Palu City （Central Sulawesi area）. The earthquake involved an area more than 800 km along the Palu Koro fault zone. In order to characterize the seismic ground motion of alluvium layers existing in the Palu City, eight sites of mierotremor array measurements were performed. The shear wave velocity of the top layer is ≤ 300 m/s. Palu City had deposited on a thick alluvial layer in the coastal area. The subsurface geology also changes slowly from soft sedimentary layers in the coastal area to igneous intrusion and metamorphic rock in the mountains. Seismic strong ground motion was predicted based on the statistical Green＇s function method. Considering the damage produced by the 2005 Palu earthquake （Mw 6.3）, we also estimated peak ground acceleration distribution at Palu City, with values ranging from 100 gal up to 500 gal on the PGA （peak ground acceleration） scale. Peak ground velocity becomes more than 0.3 m/s in some areas, which may likely lead to severe damage to buildings.

Seismic Ground Motion Zoning Maps of the Pangxi Region

The seismotectonic environment and seismic activity in Southwest China region were studied based on new data and new results obtained during the Eighth and Ninth Five-Year Plans, the seismic areas and zones and potential seismic source zones were determined, and the relation between seismic activity parameters and ground motion attenuation was determined. Finally the seismic ground motion zoning maps of the Pangxi region was compiled by using the multi-parameter and multi-scheme method.

Study on the Relationship of Seismic Design Ground Motion at Different Fortification Levels in the Xinjiang Region

The seismic risk analysis results of 79 cities in Xinjiang are presented, and the bedrock peak ground accelerations under three seismic levels and their ratios are discussed. Then, the relationship between earthquake environments and the seismic risk analysis results of different exceeding probabilities are researched. The results show that minor and major earthquake motion parameters calculated from moderate earthquakes do not have a consistent probability and the ratio of bedrock peak accelerations under different exceedance probabilities are dosdy correlated with earthquake environments.

The Relationship Among Bedrock Seismic Ground Motion Parameters with Different Exceedance Probabilities in the Panxi Area

Based on the calculation of the bedrock effective peak acceleration (EPA) zoning map in the Panxi area, the ratios of EPA with exceedance probabilities of 63%, 5%, 3%, 2% and 1% over 50 years to that of 10% in 50 years are 0.302, 1.30, 1.55, 1.76 and 2.14, respectively. The seismic effect will be conservative and safe if taking this zoning map as the earthquake resistant fortification level and following the relevant rules of the Code for Seismic Design of Buildings (GBJ11 89) to calculate the seismic effect. Furthermore, the main factors that influence the A10/A63 ratios have been found to be the attenuation relationship of seismic ground motion, the division of seismic potential source regions and the seismicity parameters. These achievements are helpful to the spreading and applying of the zoning map.

Amplification Effect of Peak Ground Motion Acceleration in ClassⅡ and Ⅲ Sites over Shandong Province

In this paper, the amplification factor （ks ） of peek ground motion with different exceedance probability in class Ⅱ and Ⅲ sites over Shandong Province was estimated by analyzing the seismic response data of soil layers collected from 358 boreholes of class Ⅱ sites and 140 boreholes of class Ⅲ site. From the results, one can conclude that： （1） The scatter plot of ks generally obeys a normal distribution ; （2） ks decreases with the increase of the strength of input ground motion, which is more apparent in Class Ⅲ site than in class lI site; （3） for class Ⅱ site, with the increase of depth of the bedrock interface where ground motion inputs, ks increases gradually until to a stable value when the depth reaches up to approximately 20 meters or larger. Yet, for class Ⅲ site, ks is insensitive to the depth; （4） the average of ks for class Ⅱ site is 1.47, slightly larger than that used in the Seismic Ground Motion Parameters Zonation Map of China （ GB 18306-2001 ）. Also, ks in class Ⅱ and Ⅲ sites at different levels of peak ground acceleration over Shandong Province is preliminarily discussed in the paper.

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.

Observations on the application of artificial neural network to predicting ground motion measures

Application of the artificial neural network （ANN） to predict pseudospectral acceleration or peak ground acceleration is explored in the study. The training of ANN model is carried out using feed-forward backpropagation method and about 600 records from 39 California earthquakes. The statistics of the residuals or modeling error for the trained ANN-based models are almost the same as those for the parametric ground motion prediction equations, derived through regression analysis; the residual or modeling error can be modeled as a normal variate. The similarity and differences between the predictions by these two approaches are shown. The trained ANN-based models, however, are not robust because the models with almost identical mean square errors do not always lead to the same predictions. This undesirable behaviour for predicting the ground motion measures has not been shown or discussed in the literature; the presented results, at least, serve to raise questions and caution on this problem. A practical approach to ameliorate this problem, perhaps, is to consider several trained ANN models, and to take the average of the predicted values from the trained ANN models as the predicted ground motion measure.

Analysis of structural fuzzy random seismic response

The earthquake loads specified for the aseismic structure design depend mainly on the predicted seismic intensity and the site soil classification.Earthquake excitation not only has evident randomness but also has strong fuzziness owing to the imprecision in the definition and evaluation norms of seismic intensity and site soil classification.A realistic analysis and design of structural systems subjected to such earthquake excitations must account for the uncertainty arising from both randomness and fuzziness simultaneously in a consistent and rational manner.In this paper,the models of stationary and nonstationary filtered white noise fuzzy stochastic processes of the earthquake ground motion are set up.And then the analysis methods for fuzzy random seismic response of single degree of freedom and multi degree of freedom systems are put forward by the theory of fuzzy stochastic dynamical systems(Zhang,1991;Zhang and Wang,1993).

Characteristics of Far-field Seismic Radiated Energy from the Five Earthquakes with MS≥5. 0 in the Earthquake Swarm Sequence of 2013,MS5. 8,Qianguo,Jilin Province,China

The Qianguo Ms5. 8 earthquake swarm of 2013 occurred in Qianguo, Jilin Province, China. There are five earthquakes with Ms ≥5. 0 in the Qianguo earthquake swarm, with magnitudes of Ms 5. 5, Ms 5. 0, Ms 5. 3, Ms 5. 8 and Ms 5. 0. In this study, the far-field seismic radiated energy characteristics of the earthquakes are compared based on the source spectrum and the ground motion spectrum of the earthquake swarm. The ground motion spectrum of the five earthquakes at Changchun seismic station （CN2）, which is the national standard station, is first investigated with the recorded ground motions, and then the far-field seismic radiated energy is calculated and combined with the relationships of the source spectrum to describe the variable characteristics of the Qianguo earthquake swarm. Research results indicate that the second earthquake （No. 2） with Ms5. 0 is the key event of the earthquake swarm, which occurred on October 31, the same day following the first Ms5. 5 earthquake （No.l）. In fact, the magnitude of event No. 2 decreased compared to event No.l, which did not agree with its large far-field seismic radiated energy. It needs to be pointed out that event No. 2 was the turning point event of the Qianguo earthquake swarm, as being a significant transition before the largest Ms5. 8 earthquake.

Generation of endurance time excitation functions using spectral representation method

In this study,application of the spectral representation method for generation of endurance time excitation functions is introduced.Using this method,the intensifying acceleration time series is generated so that its acceleration response spectrum in any desired time duration is compatible with a time-scaled predefined acceleration response spectrum.For this purpose,simulated stationary acceleration time series is multiplied by the time dependent linear modulation function,then using a simple iterative scheme,it is forced to match a target acceleration response spectrum.It is shown that the generated samples have excellent conformity in low frequency,which is useful for nonlinear endurance time analysis.In the second part of this study,it is shown that this procedure can be extended to generate a set of spatially correlated endurance time excitation functions.This makes it possible to assess the performance of long structures under multi-support seismic excitation using endurance time analysis.

A random physical model of seismic ground motion field on local engineering site

This paper presents a random physical model of seismic ground motion field on a specific local engineering site.With this model,artificial ground motions which are consistent with realistic records at SMART-1 array on spatial correlation are synthesized.A two-scale modeling method of seismic random field is proposed.In large scale,the seismic ground motion field on bedrock surface is simplified to a two-dimensional spherical wave field based on the seismic point source and homogeneous isotropic media model.In small scale,the seismic ground motion field on the engineering site has a plane waveform.By introducing the physical models of seismic source,path and local site and considering the randomness of the basic physical parameters,the random model of seismic ground motion field is completed in a random functional form.This model is applied to simulation of the acceleration records at SMART-1 array by using the superposition method of wave group.

The space and time distribution characteristics of the shear stress field for the sequence of the Wuding earthquake

Follow Chen and Duda's model of spectral fall-off of ω~3, the dependence of peak parameters of ground motion, peak displacement d_m, peak velocity vin and peak acceleration a_m, upon the environment stress τ_o-values are studied using near source seismic digital recordings for the sequence of the Wuding, Yunnan, M = 6.5 earthquake, in which, as a new thought, the peak parameters are assumed to be related to the medium Q-value. Three formulae for estimating the environment stress τ_o-values by the peak parameters of three types of ground motions are derived. Using these formulae, the environment stress τ_o-values are calculated for the sequence of the Wuding earthquake. The result show that τ_o-values calculated by the three formulae are constant largely, the averages of τ_o are in the range of 5.0-35 MPa for most earthquakes. It belongs to the high-stress earthquakes sequence: the high-stress values are restricted to the relatively small area closely near to the epicenter of the main shock. The fine distribu tion structure for the contours of the environment stress τ_o-values is related closely to the strong aftershocks. The analysis of spatial and temporal feature of To-values suggests that the earthquakes sequence in a rupture process generated at the specific intersection zone of seismo-tectonics under high-stress background.