FINITE DIFFERENCE SIMULATION OF BASIN EDGE INDUCED AND TRANSDUCED SURFACE WAVES

Abstract

Quantification and understanding of local site effects on ground motion characteristics is very important for seismic microzonation and cost effective earthquake engineering. Study of local site effects needs an efficient and accurate numerical method. A second order accurate in time and fourth order accurate in space (2, 4) SH-wave and P-SV wave staggered grid finite difference (FD) algorithms are developed (Madariaga, 1976; Virieux, 1984; 1986; Levander, 1988; Graves, 1996; Pitarka, 1999; Narayan 2001a&b; Moczo et al., 2002; Narayan and Kumar, 2008). In order to reduce the required computational memory and time, variable grid size with continuous grid mesh is used (Miyatake, 1980; Moczo, 1989; Oprsal and Zahradnik, 1999 & 2002; Pitarka, 1999). Error free simulations were carried out with a maximum grid spacing ratio of the order of 12.5 and 6.0 in case of SH-wave and P-SV wave algorithms, respectively. Both the Clayton and Engquist (1977) and Israeli and Orszag (1981) absorbing boundary conditions are implemented on the model edges. We inferred on the basis of iterative numerical experiments that the stability condition for both the algorithms is V, At < 0.71 • The required minimum number of grid points (5-6 grid points) min(Ajc,Az) per-shortest wavelength to avoid the grid dispersion is the same as reported by Levander (1988) and Moczo et al. (2000). The VGR-stress imaging technique, variable grid size and better stability limit are the superiority attributed to these algorithms. In staggered grid scheme, if stress imaging technique (Levander, 1988; Graves, 1996) is used as the free surface boundary condition, the effective thickness (ETH) of the first soil layer become less by one-half of vertical grid-size than the assigned thickness (ATH). Based on various numerical experiments, it was inferred that the stress imaging technique suffers with soil thickness discrepancy. This thickness discrepancy causes error in the computation of fundamental frequency of soil deposit. Apart from the thickness discrepancy, there is another problem associated with stress-imaging technique, dispersion of Rayleigh waves in a homogeneous half-space (Kristek et al., 2002). So, in order to avoid the above mentioned error/problems, we have proposed a new technique for the planer free surface boundary condition. This new technique is IV based on the vertical grid-size reduction above the free surface during the explicit computation of free surface boundary condition. We have proposed "VGR-stress imaging technique" name for this new technique, where VGR is acronym for 'vertical grid-size reduction' (Narayan and Kumar, 2008). Adetailed study ofthe performance of VGR-stress imaging technique in avoiding the significant dispersion of Rayleigh wave and thickness discrepancy of the first soil layer is carried out. Simulated results revealed that the proposed VGR-stress imaging technique is efficient enough to avoid both the thickness discrepancy and dispersion ofRayleigh wave. The preserved shape of elliptical path of particle motion with travelled distance in case of VGR-stress imaging technique further supports the performance ofVGR-stress imaging technique. Acomparison of numerically and empirically obtained F0 for the layered soil deposit revealed that the available empirical relations (Dobry et al, 1976) are inadequate to predict the same. The computed F0 of a closed basin of different width revealed that the Fo of basin based on ID response should be only used if the width/length of a closed basin is more than four times the thickness of soil in the basin. The performance ofan approach similar to that of Graves (1996) for incorporation of damping in the time domain simulation is also studied by comparing the computed amplification factor at F0 with using an empirical relation (AF = -j-^—) for different Q and the impedance contrast (IC). The quantitative results not only verified the implementation procedure of damping in time domain simulation but also the accuracy of the developed SH-wave FD algorithm. The simulated results revealed that both the strong lateral discontinuity (SLD; slope=90°) and basin-edge (slope=45°) induce Love waves (Bard and Bouchon, 1980a&b; Moczo and Bard, 1993; Narayan, 2005). To incorporate 2D site effects in seismic microzonation aggravation factor was computed (Chavez-Garcia and Faccioli, 2000). The maximum ground displacement, average aggravation factor (AAF) and the strain level were obtained near the edge of basins. An increase of AAF and maximum strain with impedance contrast was obtained. AAF and strain level was more in basinedge model due to edge slope effect (Narayan, 2005). The analysis of the computed strain for different spans reflected that the even small span structures may suffer more damage in a basin. Effects of soil layering on the fundamental frequency (F0) of soil deposit, characteristics of edge induced surface waves and associated spatial variability and aggravation factor was studied. Surface waves were induced in both the two and three soil layer basin-edge models. The lower cut-off frequency for surface wave generation is equal to the F0, even there is alot of variation in the F0 depending on the material parameters ofthe two and three soil layer basin-edge models. The amplitude of induced Love waves and associated strain was inversely proportional to the impedance contrast between soil layers in both the increasing and decreasing velocity with depth cases. But, AAF was inversely proportional to impedance contrast between soil layers in case of increasing velocity with depth basin-edge models and was proportional to impedance contrast in case of decreasing velocity with depth basin-edge models. On an average, strain was more in case of increasing velocity with depth model but AAF was more in case ofdecreasing velocity with depth basin-edge models. The generation of Rayleigh wave in homogeneous model was studied and the results revealed Rayleigh wave generation up to certain focal depth only. Largest spectral amplitude was obtained in that wavelength for which the ratio of focal depth to wavelength of Rayleigh wave was around 0.17 in case of P-wave source and 0.9 in case of SV-wave source. An exponential decrease of spectral amplitude of Rayleigh wave was obtained with the departure of ratio of focal depth to the wavelength of Rayleigh from above mentioned constants. The effects of basin edge geometry and soil parameters on the basin transduced Rayleigh wave (BTR-wave) is studied in detailed. Acomplex mode transformation of BTR-wave after entering in to the basin from the surrounding rock is observed (Kawase, 2002). Fundamental and first modes of BTRwave inferred in the basin were retrograde vertically and horizontally polarised, respectively. Amplitude of first mode of BTR-wave was more than that of fundamental mode. Qualitatively, it was inferred that amplification of horizontal component of BTR-wave was around twice to that of the vertical component. An increase of amplitude of BTR-wave with increase of impedance contrast was obtained. Achange of polarisation of first mode of BTR-wave with increase of Poisson's ratio of soil was observed. Aconsiderable effect of edge slope was obtained only on the horizontal component of BTR-wave.