近断层浅层盆地地震动响应

SEISMIC RESPONCE OF A SHALLOW BASIN FROM

EARTHQUAKE ON A BLIND ACTIVE FAULT BENEATH

X. X. Tao

School of Civil Engineering, Harbin Institute of Technology, China.

Institute of Engineering Mechanics, China Earthquake Administration, China.

X. D. Sun H.M. Liu P. Li

School of Civil Engineering, Harbin Institute of Technology, China

ABSTRACT:

Many cities in the world are located in basins. Basin can amplify ground motion

significantly by the soft sediment, buried rock topography and edge effect in it. Hundreds

of papers have been published on this effect for decades. Seismic waves are adopted as

inputs in the analysis. Near field ground motion is governed predominantly by earthquake

source. A hybrid source model is introduced in this paper, which combines Asperity

model and K square model to take into account the physical nature and ignorance on the

slip distribution on the faulting plane. The ground motion in short period range is

synthesized by a random method in which dynamic corner frequency is applied in each

sub-source model. The ground motion in the basin is further calculated by means of 1D

equivalent linearization procedure. Two steps are carried out for the long period motion.

Firstly, the displacement field at the top of buried crystal base rock surface is calculated

by analytical Green Function method. Then the ground motion at ground surface is

calculated by 3D wave propagation finite element method with input from the first step.

The two parts of ground motion are finally superposed. For illustration, the result of a

shallow basin from an earthquake with magnitude 6 on the blind fault beneath is shown

and the distribution pattern of the response motion is summarized.

1 INTRODUCTION

With the developments of modern cities, more and more structures with large horizontal dimensions such as long span structures, over crossing bridges and buried pipelines have been built up in urban area. Damages of these structures in earthquake will cause severe loss to the city. Therefore, earthquake disaster risk assessments and reductions for cities, especially for those located near to active fault become a stress in earthquake engineering. The problem must be complicated if the city locates on a basin since it can amplify ground motion significantly by the soft sediment, buried rock topography and edge effect. In this paper, a case study is presented for seismic response of a shallow basin from an earthquake with magnitude 6 on blind active fault just beneath the basin. A hybrid finite fault source model is adopted to describe the slip distribution on the faulting plane. Stochastic synthesis procedure and numerical Green function are applied to generate ground motion in high frequency range (1Hz f >) and low frequency (1Hz f <) range respectively.

2 HYBRID SOURCE MODEL

Finite fault model (FFM) is currently adopted in strong ground motion simulation to describe near-fault rupture directivity effect and hanging wall effect. It is convenient to describe the inhomogeneous distribution of the dislocation on the rupture surface. In the model, the faulting plane is divided into many sub-sources, and the specified dislocation energy is assigned to each one of them, as point source. Tao and Wang (2004) developed a hybrid finite fault source model. The main idea of the

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Keywords: stochastic model ；numerical Green function;equivalent linearization;shallow basin

model is to combine asperity model (Somerville et al , 1999) and k square model (Herrero and Bernard, 1994), in which the slip distribution on the finite fault is determined by the superimposition of the slip of long wave length from asperity model and the slip of short wave length from k square model. Parameters in the model consist of three parts, global source parameters (fault location, size, and orientation, i.e. strike, dip and dip angle; rupture area, length and width; and average slippage), local source parameters (the area, location and slippage of asperity on the fault and the rupture starting point) and spatial corner wave numbers in two directions along strike and dip directions respectively. The stress drop is considered as a global parameter and can be estimated from regional seismological study, even though it was considered varying on the rupture surface and/or varying with magnitude. The fault length can be estimated from geological mapping, fault width can be estimated from regional thickness of the seismogenic zone which generally shown by the regional seismicity distribution in depth. The orientation of the blind fault beneath the basin is N43°W ，dip to northeast with angle 65°, and total length 30km, depth to 12km. From scaling laws (Wang and Tao, 2003, 2004), the expected rupture area is 90km2，average slippage 37.6cm ，length 11-14km, width is about 6km, K CX and K CY are 0.079 and 0.117 respectively. 30 source models are constructed from parameters with the above mean and statistical deviation of normal distribution (Sun, 2005). The rupture start point is presumed at the southeast end with depth 10km. The rupture process is governed by a constant rupture velocity, which can be taken as depth independent at a value of 0.8 times the shear wave velocity generally at the half depth of the source in regional crust. The crack in a FFM element is triggered when the rupture reaches its center. A random component, especially needed when the elements are on regular

grids, can be added to the rupture velocity. Figure1. shows one example of 30 source models.

Fig.1. An example of hybrid source models for M w 6.0 earthquake on the blind fault

3 CALCULATION OF LONG PERIOD MOTION

Numerical Green function is adopted herein to estimate ground motion in low frequency (1Hz f <) range. The whole volume 30km×35km×6km to be calculated, consists of two parts, the homogenous zone that contains the source and inhomogeneous zone from the ground to the top of crystal base rock which is treated as 200m ×200m ×D finite element grids as shown in figure 2 southward. D is about 200m assorts with the topographies of ground and the interface in the crust. The shear wave velocities are from 402m/s at ground to 3230m/s to the crust deep, and the densities from 1.9 to 2.5 g/cm 3, in average.

Firstly, displacement time history at each node on the bottom of grids caused by each sub-source is calculated by the space-time convolution of the rise time function and 3-order Green function from the superimposition of those corresponding 9 earthquake moment tensors, as shown in Eq.(1). The displacement time histories at each node from all sub-sources are superposed to provide the input field for the following finite element numerical analysis.

11m n

P np i j F G F G ??η==×=×∑∑ (1) Secondly, displacement time histories at ground nodes layer are calculated by means of a space-time

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decoupling explicit finite element calculation with the second-order local artificial transmitting

boundary (Liao et al, 1984, 2001, 2002).

Fig.2. Computing model for numerical Green function

4 SYNTHESIS OF SHORT PERIOD MOTION

In high frequency range, the ground motion is synthesized by stochastic procedure (Boore, 1983, 1987; Anderson, 1984; Atkinson, 1984, 1997, 2000). The acceleration Fourier spectrum of ground motion caused by a sub-source can be written as following.

()00(,,),()(,)()()FA M f R S M f G R D R f A f P f =???? (2)

where ()0,S M f is source spectrum; ()G R represents geometric attenuation; (,)D R f stands for inelastic attenuation; ()A f is surface amplification factor; ()P f is a high pass filter. The acceleration time history at a given site are summed by those from all sub-sources with time delays in time domain.

()()1W

L N N ij ij i j a t a t t ==?∑∑ (3)

where L N and W N are numbers of sub-sources along strike and dip directions respectively; ij t is the time delay of the ij th sub-source determined by the distances from sub-source to the rupture start point and to the site. In order to eliminate the effects of sub-fault size on high frequency radiant energy, dynamic corner frequency (Motazedian and Atkinson, 2005) is adopted, which makes the acceleration spectrum from the ij th sub-source have the following form.

()()202021ij ij ij ij CM H f A f f f π=????+?????????? (4)

where C is a coefficient independent on frequency, 0ij M is the moment of the ij th sub-source, ij H is a compensative factor to keep the high frequency radiant energy conservation, 0ij f is dynamic corner frequency which depends on the rupture area at some time and changes as the rupture propagates. 5 SEISMIC RESPONSE OF THE SHALLOW BASIN

The seismic response of a basin may be obtained from finite element simulation with a smaller element size to meet the frequency resolution and to describe the complexity of 3-D velocity structure of the basin. However, the minification of element size must result in the increase of computing

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amount. The maximum thickness of soil in the basin is less than 40m and the area taken into account is 13.6km ×16.6km, as shown in figure 3. Even the element with size less than 10 meters also may not able to describe the variation of shear wave velocity in shallow soil layer, and the complexity of sediment in the basin sufficiently. So small element size will result in unacceptable computing amount. Therefore, 1D equivalent linearization analysis is applied instead of more detailed finite element simulation in the seismic response analysis of the basin. The progress is as follows:

(1) Zone the basin according to some given depth intervals.

(2) Calculate the transfer function for each zone by means of 1D equivalent linearization analysis with shear wave velocity profile in the zone.

(3) Multiply ground motions at 50 m deep beneath the basin by the corresponding transfer function instead of the surface amplification factor ()A f in Eq.(2) to get the ground motions at the same notes of 200m ×200m grid in the basin.

Finally, the ground motions are superposed with low frequency ground motions in time domain, after the high and low pass filtered respectively.

Fig.3. The contour map of soil depth in the basin and its vicinity

The location of the blind reverse fault is shown in figure 5. Figure 4 shows the zonation of soil condition in the basin (left) and the corresponding average transfer functions (right). The zone I is

referred as rock site in which the short period ground motions are calculated from Eg.(2) directly.

A m p l i f i c a t i o n Period Fig.4. Zonation of soil condition and the corresponding transfer functions in the basin and its vicinity As a result, the PGA zoning map is worked out, as shown in figure 5. Those with subscript 1 are at

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