آثار شرايط مرزي در دقت و كارايي روش المان محدود براي تحليل نابه جايي گسل درون نيم فضاي ارتجاعي همگن

The Effects of Boundary Conditions on Accuracy and Efficiency of Finite Element Analysis for Fault Dislocation within Homogeneous Elastic Half-Space

در اين پژوهش، ميدان جابه جايي سطح آزاد زمين براثر نابه جايي گسل در نيم فضاي همگن ارتجاعي با روش المان محدود بررسي شده است. مرزها بر روي نتايج حاصل از روش المان محدود تاثير شاياني دارند، به ويژه اگر دامنه مسيله داراي مرزهايي بي نهايت باشد. بنابراين بايد تدابير مناسبي براي افزايش كارايي و دقت روش انديشيده شود. براي دستيابي به نتايج جامع در اين زمينه، مدل سازي مرزها در اين مقاله با دو رويكرد انجام شده است. رويكرد اول از المان هاي رايج براي مرزها استفاده مي كند، اما رويكرد دوم از المان هاي نامحدود بهره مي جويد. براي راستي آزمايي نتايج، هر مسيله با چند شبكه گوناگون بررسي شده تا تاثير شبكه نيز ديده شده و پاسخ هاي عددي با روابط تحليلي اوكادا مقايسه مي گردد. در كنار اثرات نوع مدل سازي مرزها تاثير شبكه نيز ديده شده تا بتوان بر اين اساس به رويكرد مناسب مدل سازي كه با تعداد المان كمتري منجر به نتيجه مطلوبي مي شود، دست پيدا كرد. در روند مدل سازي براي شبيه سازي نابه جايي گسل، از المان هاي تماسي استفاده شده است. نتايج بدست آمده حاكي از آن است كه استفاده از المان نامحدود نه تنها براي مسايل نابه جايي لازم است بلكه موجب افزايش كارايي و دقت روش المان محدود مي شود، به طوري كه با شبكه هاي درشت تر مي تواند به نتيجه مناسبي منجر شود.

Surface deformation of the earth due to earthquake fault dislocation is very important for predicting ground motions. There are many studies on kinematic modeling of earthquake faults in both analytical and numerical methods. However, suitable investigations on improving usefulness and efficiency of those numerical methods are still necessary for relevant researchers. In this paper, displacement fields for free surface of the earth due to fault dislocation in homogeneous elastic half-space have been investigated by finite element method. Boundary conditions have significant effects on the results of finite element method, especially when the domain of the problem has infinite boundaries (half-space). Therefore, appropriate cares should be taken to increase the efficiency and accuracy of this method. In order to achieve a comprehensive study on this topic, boundaries have been modeled by two approaches here. The first approach uses common elements for infinite boundaries, while the second one uses infinite elements for those boundaries. To verify the results, each problem has been examined by several meshes and numerical solutions have been compared to Okada’s analytical solutions. In addition to the effects of the boundary modeling, the discretization effects have been investigated in order to find a suitable approach to reduce computational efforts and to increase the accuracy and efficiency of finite element method. In the modeling process, contact elements have been employed to impose fault dislocation. Three numerical examples have been provided for these finite element analyses. Each example includes four analyses without infinite elements and three analyses with infinite elements which are also compared together. The results show that not only infinite elements are necessary for quasi-static fault dislocation problems, but also they improve the performance of finite element method, so that with finer meshes and smaller dimensions of a domain, analytical solutions can be captured by numerical solutions with suitable accuracy.