Response Spectral Amplification Ratios Model Of Trapezoid Mountain

Many post-earthquake damage surveys and research results in China and abroad suggest that topography, such a moderate ground swell and a moderately high hill, can modify strong-ground motions and cause more severe damages to engineering structures than the ground motions on a flat site. The topography effect on ground motions is an important part of site effect and the proper modeling can provide a vital scientific basis to modify the design spectrum for structures.There are three methods to model topography effect, including empirical method based on the analysis on the strong-motion records that contains topographical effect, analytical solutions based on simplified topography model and numerical simulation method. Empirical method requires a large number of strong-motion records with strong topographical effect and it is not possible for most parts of the world. Analytical solutions are usually given in the frequency domain and cannot be used directly for an engineering design. Also numerical method is ideal for a specific case but the traditional frequency amplification/deamplification ratios cannot be used for an engineering design.Seismic design load on a structure can be described by a 5% damped response spectrum which is usually presented in a continuous but smoothed segments as a function of spectral periods in many design codes. A code design spectrum does not explicitly include any topographical effect even though some of the records that are used to derive the design spectrum may come from sites with steep topography. To design a structure on a slope or the top of a hill, the topography effect is usually ignored. This design practice should not be used for structures on a site with a steep topography.In this thesis, we will use numerical modelling to construct a set of simulated acceleration time histories at sites with topography subjected to rock site strong-motion records and then built an "empirical" model based on the response spectral ratios from these time histories over the corresponding rock site time histories. The response spectral ratios can then be used to modify the rock site design spectrum and the modified spectrum can then be used to design structures at a site with a quantified topography effect.In this study, one special topography from a small or moderately high hill is addressed. For many hill ranges, the topography effect is much more significant in the transverse direction than in the longitudinal direction along the hill range. This property of the hill range allows the use of two-dimension (2-D) models that can be analyzed efficiently with moderate computing power and the effort of model setting up can be greatly reduced. The 2-D model is in a trapezoidal shape, with only 4 parameters. Elastic response was assumed.It is known that response spectral amplification ratios for an elastic model still depends on the frequency contents of the rock site records, e.g. the response spectral ratios from two rock-site records with different frequency contents differ significantly. In order to include the effect from this type of variability, a large number of rock site records from earthquakes with different magnitude, source distance and tectonic types were used. Also, two main parameters representing frequency contents of a records, earthquake magnitude and source distance were also used as model parameters.Finite element computer package ABAQUS was used to carry out full modeling for one strong-motion records and then a transfer function approach were used to increase computing efficiency. The work was carried out according to the following steps:1) 65 finite element model and the corresponding one-dimension free-field model were be built, with each model having 11 monitoring points along the slope and at the top of the hill subjected to 473 horizontal components of rock site records.338195 spectrum ratios (473 seismic records×65 models×11 monitoring points) at each of 36 spectrum periods were obtained.2) The regression model parameters were determined using a random effects model and each parameter was statistically tested. Using the random effects methodology, residuals were divided to two parts:between-model standard deviation and within-model standard deviation, so that trade-off effects between model parameters and earthquake parameters can be minimized.3) A step-by-step method was used to smooth the model parameters with respect to the logarithm of spectral periods without any significant loss of statistical goodness-of-fit parameter.4) The distribution between-model and within-model residuals with respect to all model parameters was checked to ensure the distribution is not biased.The final model for the response spectral amplification ratios has a small number of parameters and can be used to modify code design spectrum for the design of structures that are located in a trapezoidal hill.