5 .1 Earthquake Source
Chapter 6 Chapter 6 Validation of Simulation Software
6.4 Discussion
The results from the finite-element simulation show close agreement with those from the discrete- wave-number technique and the static analysis. The absorbing boundary effectively prevents con- tamination of the solution in the interior of the domain from reflections off the lateral sides and the bottom of the domain. Comparison of the velocity time histories also suggests that we cannot use the ground motions at the absorbing boundaries for any analyses because the dampers distort the time histories. Additionally, the static displacements near the edges of the domain have limited ac- curacy, as a result of the lack of stiffness provided by the absorbing boundary. Hence, the simulation software provides accurate results as long as we ignore the ground motions very close to the edges of the domain.
In the above validation we use homogeneous material properties. We also want to simulate the ground motions in heterogeneous domains with the same confidence in the accuracy of the
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-20
-30 -30 -20
0 FEM
0 Static -10 0 10 20 30
West-East (km)
Figure 6.6: Horizontal components of the final (static) displacements along two lines on the ground surface. The dotted line indicates the projection of the fault plane onto the ground surface. The north-south line passes though the center of the domain, and the east-west line along the top of the fault. The thin, solid lines show the original locations of the lines. The displacements have been scaled by a factor of 50,000.
because the absorbing boundaries do not model the stiffness of the truncated portion of the domain as discussed in section 2.3.3. This leads to a slightly slower decay with distance from the source in the final displacements of the finite-element model compared to the analytical solution. The east-west displacements exhibit excellent agreement across the domain.
6.4 Discussion
The results from the finite-element simulation show close agreement with those from the discrete- wave-number technique and the static analysis. The absorbing boundary effectively prevents con- tamination of the solution in the interior of the domain from reflections off the lateral sides and the bottom of the domain. Comparison of the velocity time histories also suggests that we cannot use the ground motions at the absorbing boundaries for any analyses because the dampers distort the time histories. Additionally, the static displacements near the edges of the domain have limited ac- curacy, as a result of tltP. lac:k of stiffnP.ss prnvklP-rl hy thfl ::ih::orhing boundary Hence, the simulation software provides accurate results as long as we ignore the ground motions very close to the edges of the domain.
In the above validation we use homogeneous material properties. We also want to simulate the ground motions in heterogeneous domains with the same confidence in the accuracy of the
54
20
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10 Static
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-10
-20 -30 -20 -10 0 10 20 30
South-North (km)
Figure 6.7: Vertical and north-south components of the final (static) displacements on the ground surface along the north-south line passing though the center of the domain. The dotted line indicates the projection of the fault plane onto the vertical slice. 'rhe displacements have hP.en ~r.::ilPd hy a factor of 50,000.
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-30 -20 -10 0 10 20 30
West-East (km)
Figure 6.8: Vertical and east-west components of the final (static) displacements on the ground surface along the east-west line along the top of the fault. The dotted line indicates the projection of the fault plane onto the vertical slice. The displacements have been scaled by a factor of 50,000.
ground motions. Because we assume homogeneous material properties within an element, varying the material properties involves simply setting the properties in each element according to some specified spatial distribution. As discussed section 2.3, the node spacing governs the accuracy of the ground motions, so we limit the errors in the simulation by adjusting the node spacing with the material properties. In other words, in order to handle heterogeneous material properties with the same level of accuracy, all we need to do is to insure that we maintain the appropriate node spacing throughout the domain.
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-10
-20 -30 -20 -10 0 10 20 30
South-North (km)
Figure 6.7: Vertical and north-south components of the final (static) displacements on the ground surface along the 11orth-imutJ1 line passiug Lhuugh Lhe ceuLer uf Lhe domain. The dotted line indicates the projection of the fault plane onto the vertical slice. The displacements have been scaled by a factor of 50,000.
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-20 -30 -20 -10 0 10 20 30
West-East (km)
Figure 6.8: Vertical and east-west components of the final (static) displacements on the ground surface along the east-west line along the top of the fault. The dotted line indicates the projection of the fault plane onto the vertical slice. The displacements have been scaled by a factor of 50,000.
ground motions. Because we assume homogeneous material properties within an element, varying the material properties involves simply setting the properties in each element according to some
specified spatial distribution. As discussed section 2.3, the node :spacing governs the accurncy of the ground motions, so we limit the errors in the simulation by adjusting the node spacing with the material properties. In other words, in order to handle heterogeneous material properties with the same level of accuracy, all we need to do is to insure that we maintain the appropriate node spacing throughout the domain.