Landslides - Causes, Types and Effects.pdf

212 Tsuyoshi Ichimura and Muneo HoriHowever, it is difficult to carry out such 3D simulation since it requires its huge computationalcost; the spatial resolution required for the structure analysis is in the engineeringlength-scale, say, 10 −2∼0 m, while the target domain size is in the geological length scale,say, 10 2∼5 m. In most cases, an approximate simulation is made which computes wavepropagation in the geological length scale neglecting soft surface layers and then input resultingwaves into the surface layers to analyze structure responses. This approximation israther crude, and hence the analysis of soil-structure interaction is often simplified; a simpleparallel layer model is used for surface layers, and two-dimensional state of plane strain isassumed. By its own nature, the approximate simulation is not applicable to a large-scalestructure as mentioned above.Recently, studies of earthquake motion prediction are conducted for practical engineeringpurposes (e.g., [1]), and remarkable progress of 3D seismic wave propagation simulationis being achieved (e.g., [2, 3, 4, 5, 6, 7, 8]). Also, in the field of computationalmechanics, 3D numerical simulation with finer spatial discretization is being studied to analyzedynamic response of structures (e.g., [9, 10, 11]). Therefore, it can be expected thatan efficient approach to carry out 3D numerical simulation of strong ground motion andstructure response can be made by combining these two advanced simulations.In this article, we present a multi-scale analysis for the 3D numerical simulation. Thekey idea of this analysis is to rationally link numerical simulation in the geological lengthscaleto that in the engineering length-scale; see Fig. 1-b). The rationality of the link isdue to the mathematical theory that takes advantages of the singular perturbation expansion;this theory is established for analysis of general heterogeneous media [8, 12, 13].Separately carrying out two numerical computations, the multi-scale analysis drasticallyreduces computational cost for the 3D simulation of strong ground motion and seismicstructure responses.The contents of this article are as follows: First, in section 2., multi-scale analysis isformulated for the 3D simulation of strong ground motion and seismic structure response.Next, we present an example of applying the multi-scale analysis in section 3.. The targetproblem is an underground shaft which connects a large-scale tunnel to the ground; theshaft runs through soft soil deposit. The results of the multi-scale analysis are comparedwith the direct analysis that is obtained by the huge-scale numerical computation, and itis shown that the agreement of the multi-scale analysis with the direct analysis is morethan satisfactory. Some discussions are made for the potential usefulness of the multi-scaleanalysis in order to estimate strong ground motion and seismic structure responses of largeinfrastructures.2. Formulation of Multi-Scale AnalysisIn this section, we present the multi-scale analysis for the 3D numerical simulation of strongground motion and seismic structure responses. The target problem is a fault-infrastructuresystem, denoted by D, as shown in Fig. 1-a). Since the formulation is used for the numericalcomputation, we start from a discretized wave equation by a finite element method (FEM)in spatial domain, i.e.,[M][ü]+[C][ ˙u]+[K][u] = [0] (for D). (1)