Journal of Engineering Geology

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Evaluation of strong ground motion up beneath the construction is important in both geotechnical engineering (site effect) and earthquake engineering aspects (analysis of earth behavior). The common methods of microzonation in geotechnical engineering are based on one dimensional dynamic analysis, in which ground surface is assumed to be horizontal. However in many cases, because of variety of topography conditions, recorded responses are different on the top of hills and their corners. In this study, FLAC 2D software, as finite difference software, is used to analysis the trapezoidal hill with different shape ratios. These topography models are analyzed by far field earthquake records, and their dimensionless amplification ratios are compared with the obtained results of one dimensional analysis. Assessment of these two analyses methods in some points on the topography and around it, demonstrated considerable differences that show the necessity of two dimensional analysis in earthquake geotechnical engineering.

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Direct observation and experience of past earthquakes together with modeling carried out by researchers, has shown that ground motion acceleration and frequency is affected by the nonlinear behavior of site soil. In the process of assessing the seismic response of structures and lifelines, it is essential to understand the nonlinear behavior of the soil and how it can affect the results. In this paper, the nonlinear behavior of Urmia's subsurface soil is studied by performing one dimensional nonlinear site response analysis in time domain. Artificial acceleration time histories that were synthesized based on the result of seismic hazard analysis, conducted over three return periods, are used as input motion. Spectral acceleration at the ground surface is compared with those calculated for seismic bedrock, and spectral acceleration amplification curves are obtained. These curves show that, the amplification is greater in the central and eastern regions of the city than those for other regions of the city because of a deeper soil profile. The results show that the maximum amplification for higher return period is smaller because of greater soil nonlinear behavior

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Introduction
Local site conditions considerably influence all characteristics of the ground strong motion including the domain, frequency content, and duration. The level of such an effect could be considered as a function of geometry, properties of the materials embedded in the underlying layers, the site topography, and properties of excitement. Site effect fall into two categories: a) the effect of the surface soft layers triggered by the shear velocity differences between the soil layers and b) the surface and subsurface topography effects that lead to the wave reflection and refraction based on the site geometry, and subsequently enhance the level of amplification.
Since most cities have been constructed in the vicinity of or on sedimentary basins, geotechnical earthquake engineering devotes particular attention to effects of the sedimentary basins. Basin edge curvature deposited with soft soils are capable to trap the body waves and generated surface waves within the deposit layers. Such waves could create stronger and lengthier vibrations than those estimated in a 1D analysis that assumes the shear waves to be vertically propagated.
Although critically important, the 2D effect of the site has not been included in seismic codes and standards of the world. This might be due to the fact that the site effect depends on a number of parameters such as the site geometry, the type of wave excitement, properties of the materials, etc. that in return make it almost out of the question to make predictions about the effect. This study was an effort to compare the responses of four sedimentary basins with hypothetical geometries of rectangular, trapezoidal, elliptical, and triangular shapes in order to examine the effect of the geometrical shape of the basin on its responses and the extent of the response sensitivity to the excitation frequency of the wave. The study assumed the edge to depth proportion to be both constant and equal in all four basins so that the effect of the geometrical shape could be equally examined and compared in all four basins.      
Material and methods
In order to validate the results of the sedimentary basin modeling, firstly, ABAQUS finite element software was used to create a free field motion of a semi-circular alluvium valley in accordance with Kamalian et al. (2006) and Moassesian and Darvinsky (1987).  Then, the results from the model were compared with those from the above mentioned studies. The following descriptions are to present the model in details.
To evaluate the geometrical effect of the sedimentary basin on its response, the authors relied on the software to examine four sedimentary basins with the fundamental frequency (2.04 Hz). The basins enjoyed rectangular, trapezoidal, elliptical, and triangular geometrical shapes with a constant edge to depth proportion (49m to 300m respectively). The implicit method was also applied to perform the dynamic analysis. The materials were all viscoelastic and homogeneous. The soil behavior/treatment model was considered to be of a linear nature.  The Rayleigh damping model was used to specify the damping level. The soil element was a plane strain and SV waves (the Ricker wavelet) were used for seismic loadings in a vertical dispersion. The side boundaries (right and left) of the model were of a combinational type (viscous and free field boundaries); the down side boundary was composed of viscous. To achieve higher levels of wave absorptions, heavy columns were used as the free filed columns.
Next, it was the time to conduct the 1D analysis of the site. Three waves were in use in order to examine the effect of the frequency content of the excitation load on the basin response: 1) a wave with the dominant frequency of 1Hz that was out of the frequency range of all basins (2.04 Hz), a second wave with the dominant frequency of 2Hz that was close to the fundamental frequency of all basins, and a third wave with the dominant frequency of 4Hz. The waves were applied to a 2Dmodel. The results were compared with those obtained from a 1Dmodel in terms of the timing.
Then, the basin responses to all three waves (1, 2, and 4 Hz) were subjected to an individual analysis in order to examine the sensitivity of each basin response to its geometrical shape. Results indicated that while the responses of the rectangular and trapezoidal basins were significantly more sensitive to the excitation frequencies, the elliptical and triangular basins showed more stable behaviors to such frequencies. The final stage of the study was dedicated to examine the site 2D effect during the ground motion.
Results and Conclusions
According to the results of the present study, it could be suggested that the geometrical shape of the sedimentary basin has a significant effect on the responses of the field of seismic waves and that it could result in so different responses from the ones attained after a 1D analysis of the site. In addition, the pattern of the seismic waves’ responses is highly dependent on the geometrical shape and the frequency content of the seismic load. Also, the location where the maximum horizontal acceleration occurs along with the sedimentary basin depends on the excitation wave and varies accordingly. Further, it could be suggested that the site 2D effect results in both considerable amplification and an increase in the length of ground motion.
The results of the 2D analysis showed remarkable differences with their 1D counterparts: a 1.45 larger response for the rectangular basin, a 1.28 larger response for the trapezoidal basin, a 1.22 larger response for the elliptical basin, and a 1.19 larger response for the triangular basin.
With the frequency of 1 Hz where the excitation frequency is out of the basin range (i.e. the excitation frequency is below the lowest frequency of basin), the sedimentary basin did not show any signs of amplification and chaos (unlike two other frequencies); instead, it was a cause for de-amplification.
The frequency of 2 Hz that is subject to resonance resulted in amplifications (absent in 1D analysis) and there are traces of a reduction in the acceleration responses near to the edges of the basins. The proportion of the amplification (in the center of the basins) in 2D to 1D analysis was 1.4 for the rectangular basin, 1.28 for the trapezoidal basin, 1.22 for the elliptical basin, and 1.15 for the triangular basin.
 

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Introduction
Every year, numerous casualties and a large deal of financial losses are experienced due to earthquake events. The losses incurred by an earthquake vary depending on local site effect. Some well-known examples include the earthquake in Caracas 1967, Mexico city 1985, Kalamata 1986, Loma Prieta 1989, Roodbar 1990, Bam 2003, Jammu and Kashmir 2005, Sichuan 2008 and Haiti 2010. Therefore, in order to conquer drastic effects of an earthquake, one should evaluate urban districts in terms of the local site effect. Various methods are available for the evaluation of site effect. One of the most common methods includes ambient noise survey. Today, this approach is being used as fast, applicable, cost-effective method. Ambient seismic noise are feeble ground motions with displacement amplitudes of about 0.1–1 μm and that can be detected by seismograph with high magnification. Many investigations have been conducted to determine the nature of ambient noise. One of the possible sources of ambient noise can be human activity, such as traffic, industrial noises and nature activity, such as wind, ocean waves. The Babol city is one of the largest cities in the north of Iran (Mazandaran province). It lies on alluvium beds in the region presenting a high seismic potential. Therefore, comprehensive studies are necessary to introduce suitable solutions for minimizing earthquake damage and loss of life. For this reason, in Babol city, ambient noise survey has been performed at 60 stations and the obtained data were analyzed with Nakamura or H/V method (1989). The results were compared with local geological, geotechnical and seismic data to confirm their reliability for a seismo-stratigraphic.
Methodology and data collection
The analysis of ambient noise was initially proposed by Kanai and Takana (1961). Since then, many researchers have used ambient noise for site effect evaluation. As it is said before, one of the most popular techniques for estimation of site effects in the regions with low seismicity is ambient noise survey by Nakamura or H/V method (1989). Based on the literature review, the Nakamura method (1989) has been used in many places. Many theoretical and experimental studies show that, this method has the capability of estimation of fundamental frequency. Ambient noise survey was carried out at 60 stations in Babol city. Ambient noise was recorded using a velocity meter SARA. Two horizontal and a vertical components of ambient noise at each location are recorded for duration of 15 min with 100 samples per second. Because the environmental noise has an effect on ambient noise they are recoded between 10 p.m. to 6 a.m. The locations were determined by using GPS at the sites. The ambient noise survey in this study was made in compliance with the guidelines of SESAME (2004).
Results and discussion
The maximum and minimum values of fundamental frequency of the present research are 11.4 and 0.65 Hz, respectively. Also, the maximum and minimum values of amplitude of H/V peaks have been calculated as 3.71 and 1.19, respectively. The most significant point is that the fundamental frequency of the major part of Babol city is smaller than 1 Hz in agreement with the previous knowledge of the city geological setting. Another relevant point is the presence of some stations with very high (> 5 Hz) fundamental frequencies. In these cases, ambient noise recording and data analysis were repeated, but similar results were obtained. Considering the lack of sufficient geotechnical data (in some stations), the above phenomena need to be integrated with other methods. For this purpose, the data of electrical resistivity tomography (ERT) were used. The ERT showed that small regions of the north-west, west, and south areas have high resistance values probably related with the presence of hard deposits in the shallow subsoil. Babolrood river diversion in the west part and its return to the previous direction in the northern section is possibly due to the existence of these relatively hard deposits. By comparing these two tests, we observed that the ERT results correlate with the ambient data analysis. Therefore, we can conclude that the high-frequency peaks measured are reliable, but we need direct investigation to associate them to a specific shallow geological layer. To validate the results, fundamental frequencies obtained from ambient noise survey were compared with geotechnical data, numerical analysis and seismic data in the study area. A general review shows that the geotechnical data, equivalent-linear analysis results and seismic data have an acceptable conformity with the results of ambient noise survey.
Conclusion
The results show minimum and maximum fundamental frequencies 0.65 and 11.4 Hz, respectively. Assessment also reveals that the major parts of Babol city have the fundamental frequencies less than 1 Hz, which are in conformity with that of previous research. According to the results of seven cross sections, it can be concluded that fundamental frequency variations are in line with the geotechnical and geological data in the study area. It means that this method is the appropriate way to assess the local site effect in the Babol city. It is also observed that besides the soil layers, the soil stiffness and its shear wave velocity are effective factors in changing the fundamental frequency. Site frequencies were also estimated by preliminary 1-D site modeling using the equivalent-linear method. In general, a reasonable correspondence between the methods was obtained. Using seismic data, the HVSR of two strong ground motions have been calculated and the results have been compared with the nearest ambient noise recording station. Analyzing the spectral ratios demonstrates that the value of the fundamental frequency obtained by the H/V method (1.06 Hz) is very close to that of frequencies obtained by the seismic data (0.95 and 0.90 Hz)../files/site1/files/124/6rezaee%DA%86%DA%A9%DB%8C%D8%AF%D9%87.pdf

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Introduction
Past research studies have demonstrated that seismic ground motion can vary significantly over distances comparable to the dimensions of long span engineering structures. The accurate determination of earthquake ground motion at the base of long span structures such as dams and bridges whose piers are located on the valleys surface is one of the most important issues in earthquake engineering. In this paper, the spatially variable earthquake ground motions are generated at stations located on the valley slopes, considering the topography effect of a triangular valley. To this end, the simplified geometry of the valley of Masjed Soleyman embankment dam has been used for numerical modeling. The spatially varying ground motions are simulated by using spectral representation method. According to this methodology, the generated time histories are compatible with prescribed response spectra reflecting the wave passage and loss of coherence effects. This method assumes that the response spectrum is identical for all stations i.e., they have the same amplitudes and frequency content. This assumption is not valid for stations located on valley surface in which the amplitude and frequency content of the seismic waves are changed considerably by topography features. It is concluded that the proposed method in this study can lead to artificial spatially variable earthquake ground motions which can be readily reflect the amplification pattern of 2D triangular valleys.
Material and methods
In the first part of this paper, seismic response of a triangular valley is investigated through time history analysis conducted by using FLAC2D computer program. The geometry of the valley analyzed in this paper is chosen close to the valley of the Masjed Soleyman embankment dam. Dynamic analysis is conducted using an artificial earthquake generated by spectral representation method. The material properties are obtained based on the results of a comprehensive study carried out to identify the dynamic characteristics of two large embankment dams in Iran. Spectral amplification functions of seismic waves are calculated by dividing the response spectra of stations located on the slope of the valley to that in base of the valley. These functions are then used as target quantity for generation of spatially variable ground motions at points located on the valley. In this study, spectral representation method, the most widely accepted method for generation of spatially variable ground motions, is developed to take into account the topography effect. According to this methodology, the generated time histories are compatible with prescribed spectral amplification functions reflecting the wave passage and loss of coherence effects. The Harichandran-Vanmarcke coherency model is used to simulate spatially variable seismic ground motions.
Results and discussion
Based on the obtained results the maximum and minimum values of peak acceleration are yielded at the base and at the edge of the valley, respectively. The results indicate considerable increase of the acceleration RMS at points near the edge of the valley. Maximum spectral amplification is also observed at the edge of the valley. For all points located on the valley, the first peak spectral amplification occurred at frequency of 1.15Hz, which can be readily interpreted as the natural frequency of the valley. In order to evaluate the accuracy of the proposed method, the RMS and spectral amplification functions of artificial earthquakes are compared to target quantities. A very good consistency between the spectral amplification of artificial earthquakes and target spectral amplifications was observed in terms of both amplitude and frequency content.
Conclusion
The following conclusions were drawn from this paper.
- Artificial earthquakes generated using proposed method of this paper are in a very good agreement with the amplification pattern of the valley.
- The results of this study can be readily used to investigate the influence of spatial variability of earthquake ground motion on structures like bridges and dams whose supports are located inside the valley and are subjected to multi-support earthquake excitation.
- The proposed method of this paper is not limited only to the valley topography, but it can be effectively used in the generation process of non - uniform artificial earthquakes for stations located on other topography features. The latter can be carried out by establishing the spectral amplification functions of other topography features such as slopes and hills resulted from field or numerical studies.