FINITE-DIFFERENCE SIMULATION OF TOPOGRAPHY EFFECTS ON THE GROUND MOTION

Abstract

The imçact of earthquake disaster on the manmade society very much depends on the ground 111ion characteristics which in turn are largely affected by the local site condition. The damage pattern in particular basin may he highly variable from one place o anothet ue to the various factors like single and double resonance effects (Dobry and Vacetic. i'87; Narayan ci al.. 2002 Kumar and Narayan, 2008), basin-edge induced surface waves (Kawase. 1996; Graves ci al.. 1998; Narayan. 2005), basin-transdued surface waves (Bakir et al., 2002; Narayan. 2012) and basement focusing effects (Gao et al,, 19). The post earthquake damage survey and ground response analysis have revealed thai basement focusing was responsible for the selective damage to unreinforced brick :hmr.ys in west Seattle. Washington during the 2001 Nisqually earthquak of magnitude 6.8 (Booth et al., 2004). Another classic example regarding basement focusing is the very 2ecu1iar damage pattern observed in Santa Monica area, Los Angeles basin during Northridge earthquake of 1994 (Gao et al., 1996; Alex and Olsen. 1998). I - Similady. H the hilly areas. highly variable damage patterns have been reported during past ithqiakes due to the presence of ridges, valleys and slope variations (Celebi. 1991; Nara'an and Rai, 2001). As far as we know, most of the studies on the ridge effects were limited to the simple shapes of homogeneous ridges (Ccli el al., 1988; Sanchez-Ssma and Canpilo, 1991; Narayan and Rao. 2003; Karnalian ci al., 2006). Further, very limited vcrk is carried out to quantify the combined effects of ridge-weathering and shap-ratic on the ground motion and associated differential ground motion (DGM) (Ccli et al. - Q8;). The DGM has an important impact on the seismic response of structures since it irduces significant additional stresses in the structures than the ones induced if the ioUO:5 at the supports were considered to he identical. The damage patterns during recent Lncian earthquakes calls for an estimation of local site effects for the consideration in the design ground motion (Narayan and Rai. 2001; Narayan et al., 2002). kealistic quantification of local site effects on the ground motion characteristics requires an eficien1 numerical method (Moczo et al.. 1997; Narayan. 2001 a&b; Narayn and Kurnai. 2008; Zeng et al.. 2012). The finite difference (FD) method is the most popular and extensively used numerical method for the study of local site effects (Madariaga, 1976: Pitarka, 1999: Moczo et al., 2002). The accuracy of FD method very much depends on the implementation of the absorbing boundary conditin (Clayton and Engquist, 1977; Israeli and Orszang, 1981), free-surface boundary cond tion (Levander, 1988: Narayan and Kumar, 2008; Zeng et al.. 2012) and anelastic damping, particularly in the time-domain simulations (Emmerich and Korn. 1987; Kristek and Moczo, 2003). A fourth-order accurate SH-wave and P-S V-wave staggered-grid viscoelastic FD algorithms with a variable grid size have been developed based on the GMB-EK rheological model (Ernrnerich and Korn, 1987). There is provision to implement either VGR-stress imaging technique (Narayan and Kurnar. 2008) or an improved vacuum formulation (Zeng et al.. 2012) as a free surface boundary condition. The accuracy cfthe developed FD algorithms is validated by comparing the numerical grid-dispersion curves for a homogeneous elastic medium with the analytical one as well as comparing the numerically computed spatial spectral damping, phase velocities and quality factors in a homogeneous viscoelastic medium with the same obtained using Futterman's relations (Futterman, 1962) and the GMB-EK model (Emmerich and Korn, 1987). In order to find out the answer to the question why only unreinfbrced brick chimneys were selectively damaged during the 2001 Nisqually eLrthquake in west Seattle. a combined effects of synclinal basement topography (SBT) and the sediment damping on the characteristics ol'the SI-I- and P-SV waves is studied in details. In order to separate the SBT focusing effects from the free surface effects, Llnbounled model is considered. An increase olspectral amplification was inferred with an increase of both the frequency and distance from the tip of the SBT towards the tbcus point in case of response of an elastic SBT model (Davis et al. 2000). The amplification of SV-wave caused by SBT focusing was lesser than that of the SH-wave. In addition to this, ar increase of rate of spectral amplification with frequency was inferred towards the focus point of the SBT. However, the sediment damping masked the increase of spectral amplfication with an increase of frequency. The study of combined effects of sediment damping and anticlinal basement topography (ABT) on the SH-wave and P-SV wave characteristics revealed that the de-amplification caused by the ABT dc-focusing is not frequency dependent in contrast to the SBT focusing (Davis, et al., 2000). Finally, it is concluded that a particular frequency may be maximally amplified for a particular set of value of the SBT focal length, distance of a site from the tip of the SBT and sediment damping. This maximally amplified frequency may cause selective damage it' it matches with the natural frequency of a behind the repocd selective damage to unreinforced structure. This may be the reason brick chimneys in west Seattle during Nisqually earthquake. in case of shallow to deep large scale hounded SBT models, the variation of amplitude ampliflcflion ASA and ASAF with SBT depth does not reveals an increase of SBT focusing with an increase of the depth of SBT. However. AAF of the transmitted wave reflected an increase of SBT bcusing with an increase of depth olthc SBT. This finding aggravtcs the conclusion of Stephenson et al. (2006) who reported that focusing of the direct wave was responsible for the selective damage ofthe chimneys in west Seattle during Nisqually earthquake. The simulated responses of small to large scale BST models depicted that a shallow small scale SBT may cause anomalous damage pattern (means intense and no damage pattern), which cannot be explained using the soil amplification and associated resonance (Hartzell, et al., 1997). A comparative analysis of the SI-I-wave and SV-wave responses of various SBT models revealed that the width of zone of amplTied ground motion is more in case of SI-I-wave as compared to the horizontal comionent of the SV-wave. To study the combined effects of the ridge- shape ratio and the ridge-weathering on the groLnd motion characteristics, SF1-wave and P-SV wave responses of various models with different shape-ratio and weathering thickness have been computed. An improved vacium formulation proposed by Zeng et al. (2012) is used as a free surface boundary cordition, which fully satisfies the free surface boundary condition by using an appropriate combination of the staggered-grid and a parameter averaging scheme proposed by Moczo et al. (2002). The simulated results revealed an increase of amplification of SH-wave but a decrease of amplification of SV-wave with an increase of rioge-shape ratio. Amp lilication of both the SF!- and SV-waves was larger in the low frequency range (wavelength larger than the width of base of a ridge) as compared to the h:gh frequency range in both the weathered and non-weathered models. The computed [GM for the SV-wave along the ridge flank was lesser in case of weathered ridge as mpared to the non-weathered ridge but reverse was the case for the DGM developed by H-wave. Finally, the weathering aggravation factor revealed that the weathering effect is sser than the expectations and it is least ticar the base of the ridge.