Four layer ground model
In A15 vertical array, the downhole accelerometers are located at depths of 5.3 m, 15.8 m, 26.3 m and 52.6 m, respectively. From the results of geological explorations as shown in Figure 3, it is known that the LSST site has a quite simple geological profile, a sand layer of thickness 5 m overlying a very thick gravel formation. The shear wave velocities shown in this figure are the results measured from the geophysical survey (PS-logging). They are usually regarded as the small strain velocity. Based on that, it is reasonable to adopt a simple ground model, as shown in Figure 6, for wave velocity identification. From ground surface to the depth of 52.6 m, the ground is divided into 4 layers according to the depths of downhole accelerometers. Each layer has thickness hi and mass density ρi. The underlying soils are regarded as a half-space.
The ground motions excited by earthquakes are rather complex in nature. However, for engineering applications, it is often assumed that the horizontal ground motions are mainly produced by vertically propagating SH waves, i.e., the 1-D shear beam model can be applied. By substituting the predominant frequencies identified previously into the characteristic equations of SH wave traveling in the associated soil layers, the shear wave velocity of each layer can then be identified subsequently. It is noted that the damping ratio of soil has very little effect on the modal frequency of ground.
Therefore, it is convenient to assume that the damping ratios of soils are all equal to zero in deriving the characteristic equation of soil layers. This leads to a real-valued characteristic equation which is much easier for calculation purpose.
Based on the theory of wave propagation, the characteristic equation of transfer function between different soil layer can be derived as follows.
Single Layer Over a Half-Space
For a single layer on top of an elastic half-space as shown in Figure 7(a), the transfer function can be written as
⎟⎟⎠
Let f21 be the predominant frequency as identified from the transfer function between the first downhole station and the surface station, then the equivalent shear wave velocity for the first layer can be estimated by
For a system of two layers of soil on top of an elastic half-space as shown in Figure 7(b), the transfer function can be written as
⎟⎟⎠
The characteristic equation corresponding to the predominant frequency f31 is
1
Multi-Layer System
For the system of 3 soil layers on top of an elastic half-space as shown in Figure 7(c), the upper two layers can be regarded as an equivalent uniform single layer of thickness h1 and velocity Cs1 where
h1 =h1+h2 (6)
Cs1 =4h f1 13. (7)
Now regard the upper three layers of soil as two layers of soil with thicknesses h1 and h3 and shear wave velocities C and Cs1 s3, respectively, as shown in Figure 7(d). Then Cs3 can now be solved based on Eq.(5) when the predominant frequency f41 is given from Table 2. For a system having more layers of soil, the same procedure can be used recursively to calculate the shear wave velocity for each layer.
Figure 6. Ground model used for system identification
(a) Single layer model (b) Two layer model
(c) Three layers model (d) Equivalent two layer to system (c) Figure 7. Idealized model for calculation of shear wave velocity
Table 3. Shear wave velocities for each layer identified
Shear wave velocities identified
Based on the procedure described above and the predominant frequencies shown in Table 2, the shear wave velocities for Layer L1(0~5.3m), Layer L2(5.3~15.8m), Layer L3(15.8~26.3m), and Layer L4(26.3~52.6m) can be calculated layer by layer. For all cases, the velocity profile identified from the NS and EW ground responses are summarized in Table 3. It shows that the velocities identified from the EW responses are smaller than those from the NS responses in general. It is as expected because the predominant frequencies obtained from spectral analyses have lower values in EW direction.
Gunturi et al.(1998) had used the data of two earthquakes (Events 4 and 5 of this paper) to identify the shear wave velocities of soils by method of cross-correlation function, and similar results to this study were obtained except for the deepest layer.
Shear wave velocity vs. magnitude of ground shaking
To correlate the shear wave velocities with the magnitude of ground shaking, the shear wave velocities identified in Table 3 are plotted with respect to the PGA recorded at the depth of the top of each layer, as shown in Figures 8(a)~(d). It can be clearly seen that the shear wave velocity of each layer is decreased with the value of PGA recorded at the top of each layer, i.e., with the magnitude of ground shaking. This is due to the effect of nonlinearity of soil when it is subjected to larger shear strains. It can also be observed from those figures, the shear wave velocities identified have lower values in the EW direction as compared to the results in the NS direction. It is attributed from the effects of soil an-isotropy. The same trend had been obtained from previous study (Hsu and Chen, 2003).
CONCLUSIONS
Based on the results obtained, some conclusions can be deduced as follows:
1. The method of phase spectrum identification is very effective to deduce the predominant frequency of vibration of soils by using the transfer function of earthquake responses recorded.
2. The predominant frequency of transfer function between the downhole earthquake response and the ground surface response will decrease with respect to the value of PGA at the ground surface.
This is due to the effects of soil nonlinearity when the ground is subjected to larger excitations.
3. For the Hualien site, the shear wave velocity of each layer identified from the earthquake responses is decreased with respect to the value of PGA recorded at the top of each layer.
4. Both the predominant frequency of transfer functions calculated and the shear wave velocity of soil layers identified from earthquake responses show that the ground of Hualien site is anisotropic in two horizontal directions.
A15~D11 (0m ~ 5.3m)
0 50 100 150 200 250 300 350
0 20 40 60 80 100 120 140
A15 PGA(gal.)
Cs (m/s)
EW NS
D11~ D12 (5.3m ~ 15.8m)
0 100 200 300 400 500 600
0 20 40 60 80 100 120 140
D11 PGA(gal.)
Cs (m/s)
EW NS
(a) A15~D11 (b) D11~D12
D12~ D13 (15.8m ~ 26.3m)
0 100 200 300 400 500 600
0 20 40 60 80 100
D12 PGA(gal.)
Cs (m/s)
EW NS
D13~ D14 (26.3m ~ 52.6m)
0 150 300 450 600 750 900
0 20 40 60 80
D13 PGA(gal.)
Cs (m/s)
EW NS
(c) D13~D14 (d) D14~D15 Figure 8. Shear wave velocity vs. PGA at the top of each layer
AKNOWLEDGEMENTS
Earthquake data provided by the Taipower company and financial support by the National Science Council of Taiwan (NSC – 90 - 2811 – E - 002 – 034) are deeply appreciated.
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