بررسي اثرات توپوگرافي در ساختگاه سد پاكويما با روش اجزاي مرزي سه‌بعدي در حوزه زمان

Topography Effects in Pacoima Dam Site Using Time-Domain Three-Dimensional BEM

توپوگرافي ناهموار يكي از عوامل ايجاد تفاوت جنبش در نقاط تكيه‌گاهي سازه‌هاي بزرگ نظير سدها مي‌باشد. در اين مقاله از روش عددي اجزاي مرزي سه‌بعدي جهت حل پاسخ لرزه‌اي دره محل سد پاكويما استفاده شده و نتايج حاصله در كنار تحليل‌هاي ارائه شده، با مقادير ثبت شده طي زمين‌لرزه سال 2001 سد پاكويما مقايسه شده است. از مؤلفه‌هاي افقي زمين‌لرزه واقعي ثبت شده در كف دره پس از پردازش‌هاي لازم، به‌عنوان موج ورودي جهت تحليل استفاده گرديده و تاريخچه تغيير مكان و بزرگنمايي نقاط مختلف دره محل سد ارائه و بررسي شده است. نتايج نشانگر آن است كه دامنه بيشينه تغيير مكان با افزايش ارتفاع نقاط در دو سوي دره كاهش مي‌يابد؛ با اين حال در حوزه فركانس، بزرگنمايي در فركانس‌هاي بالا با افزايش ارتفاع نقاط دره افزايش مي‌يابد. نسبت دامنه تغيير مكان‌ها در طول دره محل سد تا حدود 3 نيز مي‌رسد كه اين مسئله لزوم توجه به جنبش‌هاي غيريكنواخت در سازه‌هاي بزرگ را نشان مي‌دهد.

The reliable estimation of seismic loads on a structure is required in order to earthquakes resistant design of the structure. The difference in seismic loading in different support points of the structure is important in large and long structures. In general, the lack of access to the reliable time histories in different support points of the structure is the main problem of performing non-uniform excitation analyses. Numerical analyses and calculation of ground motion at different points of the foundation of the structure is one of the ways to achieve the non-uniform support excitation. This paper aims to evaluate the seismic response of Pacoima dam site by performing three-dimensional boundary element analyses in the time domain. The pattern of displacement and amplification due to seismic waves scattering in the dam site are evaluated, and calculated results are compared to the recorded ground motions. The numerical modeling has been executed using the time-domain boundary element that is based on the boundary integral equation of the wave motion. To transform the governing integral equation into the ideal form, it has been discretized in both time and spatial domains. Finally, the obtained equations have been expressed in the matrix form and have been implemented in a computer code named as BEMSA. Earlier, several different examples of wave scattering have been solved in order to show the accuracy and efficiency of the implemented BE algorithm in carrying out the site response analysis of topographic structures. Pacoima dam is a concrete arch dam located in the San Gabriel Mountains in Los Angeles County. The height and the length of the crest of the dam are 113 m and 180 m, respectively. The dam is instrumented by use of 17 accelerometers at different elevations on the dam body and its abutments. For site response analyses, the dam site has been subjected to vertically propagating recorded motions of the Pacoima dam 2001 earthquake with a magnitude of 4.3, depth of about 9 and epicentral distance of about 6 km south of the dam. The medium assumed to be homogeneous linear elastic with density of 2.64 ton/m3, shear wave velocity of 2000 m/s and Poisson's ratio of 0.25. The 3D topographic model has been generated up to a radius of 5000 meters, using 1218 eight-node quadrilateral isoparametric elements with the average effective element size of 25 m in the center part of the model. In order to investigate the seismic response of the canyon, a couple of points at four levels have been considered on both sides of the canyon and the results analyzed in time and the frequency domains. Despite the actual record earthquake motions, which includes the effects of the interaction between the foundation and the dam structure as well as the lake behind the dam, the calculated motions include only the wave scattering by the topography of the canyon. Therefore, although the exact matching of the recorded and calculated motions are not expected, comparison of the motions show that the patterns of the displacements are close together. This phenomenon indicates the importance of valley shape and its important contribution to the dynamic response of the dam site. Assessment of the displacement time histories in various points at both sides of the canyon indicates that the amplitude of the motions decreases when the height of the point increase. Besides, the comparison between the motions of the left and right sides points show have a higher frequency content and a higher shear-wave velocity. 4) In all ten soil groups, the shear wave velocity that due to the non-symmetricity of the canyon, displacement amplitudes in the left side are larger than the right side. Based on the calculated displacements on the various points, the maximum amplitude along the canyon would be changed up to three times. In the frequency domain, different points of the canyon surface have generally the similar amplification patterns. There are two main peaks of amplification in the frequency range of 3-5 Hz and the frequency range of 6-8 Hz. In both sides of the canyon by increasing the height of the points amplification is increased, especially in the frequency range of 6-8 Hz. Moreover, at the same elevation points, the amplification value in the left side is higher than the right side. Comparison of amplification curves of recorded and calculated motions, show the appearance of new peaks of amplification in higher frequency, which could be related to the real conditions of the dam site. Finally, although the motion amplitude in time domain decreases by height increasing on both sides of the canyon, as expected, the amplification in the frequency domain, especially in high frequencies, increases. This insists that the amplification characteristics of a site should be considered and interpreted as a frequency dependence phenomenon. Moreover, the results indicate the spatial variation of the motion due to the topography effect along the canyon, in which the amplitude of peak ground displacements along the canyon has been changed up to three times.