ﺑﺮﺭﺳﯽ ﺍﺛﺮﺍﺕ ﺗﻮﭘﻮﮔﺮﺍﻓﯽ بر روی جابه‌جایی افقی و قائم تپه‌های ﻧﻴﻢ‌ﺳﻴﻨﻮﺳﯽ تحت برخورد ﺍﻣﻮﺍج ﺭﯾﮑﺮ

این پژوهش مطالعه ای است روی رفتار لرزه‌ای تپه های نیم‌سینوسی شکل که در معرض امواج برشیِ قائمِ ریکر قرار گرفته‌اند. برای مدل‌سازی از نرم‌افزاری که بر مبنای روش تفاضل محدود می‌باشد، استفاده شده است. چون تمرکز بر روی تاثیرات توپوگرافی است، از پارامتر ضریب شکل (نسبت ارتفاع به نیم‌پهنای تپه) و پارامترهای زمین به‌عنوان متغیر استفاده شده است. رفتار محیط مدل‌سازی الاستیک خطی در نظر گرفته شده است؛ در نتیجه تپه های شبه‌سینوسی با ضریب شکل های متفاوت (0/1، 0/4 و 0/8)، در زمین با جنس های متفاوتِ تیپ i، ii و iii (که تفاوت آنها طبق استاندارد 2800 در چگالی و سرعت موج برشی در محیطِ پیوسته است) مدل شده‌اند که هرکدام از آنها تحت موج ریکر با فرکانس ثابت قرار گرفته‌اند. در این تحقیق جابه‌جایی‌های افقی و عمودی برای نقاط مختلف روی تپه  محاسبه شده اند. همچنین بزرگنماییِ جابه‌جایی با توجه به مدل میدان آزاد به دست آمده است. نتایج نشان‌دهنده‌ی این مطلب است که با افزایش ضریب شکل، هم جابه‌جایی افقی و هم جابه‌جایی قائم و درنتیجه بزرگنمایی در تمام موارد افزایش می یابد. همچنین از نمودارهای حاصله می توان دریافت که با تغییر جنس زمین از تیپ i به تیپ ii جابه‌جایی ها کاهش می‌یابد.

Evaluation of the Effects of Topography on the Horizontal and Vertical Displacement of Semi-Sine Shaped Hills against Ricker Waves

This study presents the results of a numerical study on seismic behavior of twodimensional semisine shaped hills that were subjected to vertically propagating incident SV wave of the Ricker wavelet. In the case of 2D response analysis of hills, different researchers studied the seismic response of triangular shaped hills under vertically propagating SH waves. Earthquakes are natural events that can have considerable economic and social injuries and have effects on people life and their environment. Geotechnical earthquake engineering has been noticed particularly in recent decades. Soil mass and soil structure response analysis against earthquake movements is one of the most important practical concepts in geotechnical earthquake engineering. This paper used finite difference method and represented that topography has specific effect on acceleration distribution in different points of roughness. The finite difference software is used to model and analyze the different sizes of the hills. Concentration is on topographic effects, so parameters such as the shape factor (the ratio of the height to half width of the hill) and the type of ground took into account in this research. The medium was assumed to have a linear elastic constitutive behavior. An important factor that affects on numerical results is the shape factor of the hills. Therefore, we modeled semisine hills with different shape factors (0.1, 0.4 and 0.8) subjected to Ricker wavelet with constant frequency on grounds with different properties that differ from each other in density and shear velocity (three types). The finite difference software used to run the numerical analyses was Flac 2D. The aim of this project was to investigate the response of topography effects on semisine shaped hills under Ricker wavelet, which is the second derivative of Gauss function. In this research, the horizontal and vertical displacements of different points on hills were calculated. Also, amplification factors were calculated from the ratio of horizontal components of motion to displacements of freefield model. The results are shown that both horizontal and vertical displacements were increased with a change in the shape factor as well as the amplification. It is shown that changing ground type from one to three, the displacements were reduced. Obtained results show that most horizontal displacement occurs in the top of the hill and as we reach the lowest height of the hill, this displacement decreases. Thus it can be seen that most amplification occurs in the top of the hill for different numerical models. The vertical displacement in top of the hill is zero and with decreasing the height of the hill, this vertical displacement increases and then decreases. Based on obtained results, the most vertical displacement occurs in the height between the top and down of the hill for different finite difference numerical models. Another important result is that these vertical and horizontal displacements depend mostly on soil geotechnical behavior of the hill. It is obvious that the shape factor of the hill affects on the obtained numerical results. An important factor that is studied in this research is the shape factor of the hill. Another important factor on which results are dependent is input motion frequencies. It is clear that when natural frequencies of the hill and the input motion frequencies are near to each other, the vertical and horizontal displacement increases. When the hill steep increases, the obtained results increase because of gathering most energy on top of the hill in a narrow band area.