ABSTRACT

INTRODUCTION
The range of applicability of the ground response characterization based on the low strain soil properties, is determined by the rate of strength degradation with increasing strain. Most of the soil types encountered in urban areas in Japan [7] are found to begin exhibiting strength degradation at fairly low strain levels. Consequently, nonlinearity during large earthquakes can be expected to be substantial, particularly at medium and soft sites. Soil nonlinearity is closely linked with the level of excitation, and the type and depth of soil deposit, and, broadly speaking, can affect the seismic threat to structures in two ways. Firstly, the incident motion can be characteristically modified in terms of amplitude and frequency content. Secondly, the excitation can cause ground failure resulting in the The present investigation is concerned with the first type of seismic loss of support. effect. As the level of excitation increases, the stiffness degradation effectively results in elongation of site period [9]. Consequently, the long period components tend to play increasingly dominant role in ground response [2].  Recognition and evaluation of such effects are essential for the assessment of hazards and risks related seismic microzonation. The incident motion is characterized by defining the appropriate response spectra at stiff sites. Three lev¬ els of incident motion response spectra considered f here correspond to the frequent, medium, and ex¬ 400 treme levels of excitation defined for the seismic mi¬ crozonation case study of Sendai area [2], and are shown in Fig. 1. In Japan, the Ohsaki standard spec¬ tra defined in the period range 0.02 to 2.0 seconds forms part of the recommendations for nuclear power Figure 1: Incident Motion Spectra plant design. The response spectra in Fig. 1 are de- fined to include relatively long periods of up to 10 seconds by considering a combination of Ohsaki standard spectra, and the estimation based on the prediction of large earth- quakes from seismograms of small carthquakes, by the so called empirical Green's function method [1]. The small earthquake records from the dense strong motion observation array system in Sendai are utilized for this purpose. Response spectra compatible time histories are generated by a two step iterative scheme, first in frequency domain, and then in time domain. Artificial earthquake time histories are initially generated to match approximately the response spectra in Fig. 1 based on the Equation:
Here, Mc is the number of control Table 1: Parameters of Envelop Function. period points satisfying the condition Level C t1 t2 To given by Equation 2 [8], and E(t) is 16.0 0.164 5.0 Frequent 30.0 the envelop function given by Equa- 20.0 0.115 5.0 tion 3 defining the overall character Medium 40.0 24.0 52.0 0.082 of the ground motion in time domain. Extreme 4.0 The total durations TD of the respec- tive incident motions are based on the nuclear power plant design practice in Japan. The parameters of the envelop function in Equation 3 are shown in Table 1.
Utilizing the close relation between the Fourier spectra amplitude and the response spectral velocity ordinates, mj in Equation 1 are initially replaced by spectral velocity ordinates Sv(wj) at the corresponding control frequencies ω; of the target response spectra in Fig. 1, giving the initial time history a(t) from Equation 1 for subsequent iterations. The phase angles ψ ; are assumed to vary uniformly between 0 and 2π, and uniform random numbers generated in the range (0.0, 1.0) are utilized for this purpose. The response spectral ordinates of a(t) calculated at the Me control period points are compared with the corresponding target spectral ordinates. The discrete Fourier amplitudes mi in Equation ·1 are then modified by multiplying by the ratio between the target and the calculated spectral ordinates. This itcrative scheme for modification of the time history is continued until a reasonable level of matching is achieved. The time domain iterative scheme of localized perturbation [2, 4] in the time history at the end of frequency domain iterations is utilized to achieve a closer compatibility to the respective target response spectra. The three levels of incident motion time histories are shown in Fig. 2. The extent of compatibility to the corresponding target spectra can be seen in Fig. 3. The time domain itcrative scheme is remarkable in achieving the desired extent of compatibility of the time histories initially generated based on the frequency domain iterations discussed above.
NONLINEAR RESPONSE ANALYSIS
Selection of Soil Profiles for Investigation The ground profiles from Sendai are used in this investigation. Altogether 336 soil pro- The shear wave velocity for different soil types is estimated from files are analized. the correlation of initial shear modulus Go with standard penetration test N-values, Go=1200xNo.8 (t/m2) [7]. The soft rock underlying the Sendai area is assumed to be the base layer. Sites are assumed to be horizontally layered, and the soil profiles are modeled as a series of lumped masses connected by shear springs and dashpots. The fundamental ground period TG of each site is computed from the mass matrix, and the stiffness matrix based on the initial shear modulus Go of the lumped mass model. The sites are classified Table 2 shows Table 2: Site classification and data content. site classification into six groups of different TG ranges [10]. The TG range used for No. of Grouping in Soil corresponding classification recom- data Japanese code Group grouping mended in the Japanese code for 193 1 (Hard) Tc ≤ 0.20 1 earthquake resistant design of build- 0.2 < T G  > 0.35 2 67 ings is also shown. 2 (Medium)し0.35 < TG < 0.55 41 The stiffness of soil layers dur- 26 0.55 < TG < 0.75 4 ing the inelastic time domain re- 8 5 0.75 < Tc < 1.00 sponse was determined by the hys- 3 (Soft) 1.00 < TG 6 teretic model. The dependence of the shear modulus, and the equivalent damping factor, is based on the Masing's type The soil types in the selected soil profiles are Model developed by Ohsaki et al. [6]. broadly divided into three types: (a) clayey soils, (b) sandy soils, and (c) sandy gravel.
Nonlinear Response Analysis
The hysteretic model parameters α, β, and Go/Su, for the three soil types, are shown in Table 3. The correspond- ing shear stress-strain hysteretic plots, for a simple sinosoidal strain history with increasing amplitude, are shown in Fig. 3. The constants of the hysteretic model for clay and sand are as given by Ohsaki et al. [6], and that for gravel is arrived at by interpolation. The non- linear time domain response analysis is carried out by step-by-step numer- ical integration using the Wilson's θ- method developed by Ohsaki [5]. Vis- cous damping of 3% is assumed to rep- resent damping in soil at initial con- ditions. The input motion is assumed to be incident at an exposed surface of base layer by considering a transmit- ting boundary [5].
RESULTS OF THE INVESTIGATION
Maximum Surface Acceleration
A section across ground in Sendai is shown in Fig. 5. Distribution of maximum surface response accelerations, corresponding to the frequent, medium, and extreme levels of in- cident motions, are also shown. The dotted line is the fundamental ground period TG of sites. For a given incident motion, the maximum surface acceleration is seen to decrease towards the bay area, due to increased nonlinearity at medium and soft sites [9].
Response Spectra of Surface Response
Fig. 6 shows the response spectra of surface response corresponding to the three incident motions in Fig. 2. Response spectra at three of the sites, numbered 6, 11, and 19 in Fig. 5, representing stiff, medium, and soft sites respectively, are compared, together with the incident motion response spectra, in each case. The incident motion response spectra are modified least by the stiff site, particularly at lower level of excitation. The response spectra are very significantly modified by the medium and soft sites, characterized by increased dominance of long period components with the level of excitation.
Average Response Spectra
Following the method utilized for seismic microzonation study of Tokyo [10], the ground conditions are classified into six groups in Table 2. It is noted from Table 2 that most of the bore-hole data used in this investigation are from stiff sites. Attempt is made to develop site dependent response spectra for each group of sites represented by mean plus one standard deviation of the ordinates. Fig. 7 shows one such response spectra for group 3 sites, where it is seen that the response spectral ordinates all the way up to about 3.0 seconds are affected by sites in this group.
CONCLUSIONS
The effect of the different levels of excitation on the nonlinear response of different site conditions is inves¬ tigated. The effect of the increase in the level of ex¬ citation on the spectral characteristics of the incident motion is noted to be dependent on the site conditions as well as on the level of excitation. There is clear in- dication that the level of excitation tends to stand out as an independent variable in the nonlinear response of medium and soft sites. The increasing domination of the long period components shows the need to give adequate consideration to the long period components in defining the incident motion for seismic microzona- tion.