MODERN MICROZONATION METHODOLOGIES FOLLOWED BY UPSL

1. Prediction of Ground Motion

   Prediction of ground motion is the first step of earthquake damage assessment. Many local governments in Japan have done this kind of assessment, and prediction of ground motion is generally consists of two processes as shown in Fig. 1.1. The first process is prediction of ground motion on seismic bedrock and the second process is evaluation of soil effects. When both processes are calculated, ground motion at surface can be predicted. There are cases where the second process is divided into two processes further.

   

   Fig. 1 Schematic illustration of wave propagation through seismic bedrock and soil surface

   The 1st Process: Wave propagation in seismic bedrock
   The 2nd Process : Wave propagation in soil surface

   1. Ground Motion on Seismic Bedrock

       

      On the first process as shown in Fig. 1.1, ground motion on seismic bedrock are predicted for a hypothetical source. The method of this process is classified into two groups.

      (a) The method that considers rupture pattern of fault
      
      (b) The attenuation formula for ground motion 

      In the group (a) hypothetical seismogenic fault is divided into subfaults, and rupture pattern can be considered. Therefore, the method of this group explains the phenomenon that the observed waveform at the same distance from source are different each other according to rupture pattern. However, there is a problem that it has uncertainty on setting rupture direction for hypothetical earthquake that have never occurred.

      In the group (b) the empirical relationship is derived from regression analysis for the observed data. This is an easy method to calculate ground motion and there are many attenuation formulas for each ground motion index such as peak acceleration, peak velocity, response spectrum and so on . Recently the observed data near source is used for regression analysis and attenuation formula can be adapted to calculation of ground motion near source region. There are attenuation formulas that can consider rupture direction also. However the attenuation formula can’t fully explain the distribution of strong motion because the actual earthquake has complex rupture process.

      1. Midorikawa and Kobayashi (1979, 1980)

         1. Input/Output

            1. Pre-Condition

1. Outline of the Method

   In this method, fault plain is modeled to consist of small subfaults as shown in Fig. 1.2 (a), and seismic waves are radiated when rupture front arrives at each subfault.

   The chracteristic of this method is as follows:

   1) Evaluate ground motion with velocity response envelope
   2) Divide fault plain into small subfaults and think of subfault as point source
   3) Deal with S wave with period of approx. 0.1-5 sec.

    

   

   Fig. 2 Schematic illustration of round motion prediction using response envelopes
   (Midorikawa and Kobayashi, 1979)

   (a) Dividing fault plain into small subfaults
   (b) An approximate model of response envelope for ground motion
   (c) Superpositon of response envelopes from each subfault

   Response envelopes from each subfault are illustrated as shown in Fig. 1.2 (c).
   When the size and rupture velocity of subfault is , respectively, duration of response envelope is given by

   .

   Envelope has coda duration as a result of scattering effect on ray as follows:

   

   where is proportional coefficient to express the time lag that is the difference between arrival time of first arrived wave and arrival time of last arrived wave from subfault.

   Peak amplitude for each response envelope from subfault is given by

   .

   Total response envelope at observation is calculated by superposition of response envelopes from each subfault in consideration of travel time and delay time by rupture propagation. Velocity response is given by attenuation formula for velocity response spectrum as follows:

   

   Duration is given as

   .

   In this method calculation output is velocity response spectrum. According to Kawasaki City (1988) peak ground acceleration is given as

   

   .

2. Note

   This method provides velocity response spectrum with damping factor of 5% on seismic bedrock in which S-wave velocity is approx. 3 km/s.

   Analyzed data in this method don’t contain record observed near source region and the shortest distance between source and observation is no less than approximate 50km. Therefore this method cannot explain ground motion near fault. When this method is used near source region, the calculation result overestimated.

   In order to solve this problem, other attenuation formula for response spectrum is used. For example, Miyagi Prefecture (1996) uses the following formula that is calibrated by the recorded data for the 1995 Southern Hyogo Prefecture Earthquake.

   

1. Irikura (1986)

   1. Input/Output

      1. Pre-Condition

• Seismic moment of hypothetical earthquake
• Seismic moment of element earthquake
• Seismogram of element earthquake (=)
• Rise time (=)
• Rupture velocity
• S-wave velocity in propagation-path
• Position of observation point

1. Outline of the Method

   Ground motion for large earthquake, which reflects rupture pattern, ray path and site effect, can be synthesized by convolving waveform of small event which is observed at same location from same fault area as follows:

   

   is corresponding to summation with respect to number of elements. indicates summation with respect to time in rupture process. is dislocation time function at point on fault. is time lag between origin time and rupture starting time of element. is delay time related with rupture propagation. is the Green’s function from point on fault to observation point , and indicates convolution with . In this Empirical Green’s Function method, the observed record for element earthquake is used as .

2. Note

   To estimate ground motion by this method, it is necessary that observed waveform for small event that occurs near hypothetical source is recorded. But it is rare that necessary waveform was recorded. In this case, Green’s function is obtained by using numerical calculation or statistical technique.

   For example, there is Somerville (1993) technique as deterministic method. In that method, Green’s function is estimated by use of ray tracing method and source time function calculated from observed data.

3. Reference

1. Goto et al. (1995)

   1. Input/Output

      1. Pre-Condition

1. Outline of the Method

   Goto et al. (1995) computes peak ground acceleration on seismic bedrock by multiplying acceleration that is obtained by attenuation formula (Joyner and Boore, 1981) and coefficient of directivity effect corresponding to rupture pattern together.

   When directivity effect is not considered, horizontal peak ground acceleration on seismic bedrock can be calculated by attenuation formula of Joyner and Boore (1981) as follows:

   

   where is peak ground acceleration in gal, is the closest distance to the fault rupture in km and is moment magnitude

   1. Case of bilateral faulting

      In this case rupture propagates along fault line toward both the ends from hypocenter that is located center of the fault line. Then peek ground acceleration is given by

      

      

   2. Case of unilateral faulting

   In this case rupture propagates along fault line toward the end from hypocenter that is located another end of the fault line. Then peak ground acceleration is given by

   

   

   Azimuth is the angle that is measured clockwise from the direction of rupture propagation to the direction of observation , and is 0.72 that is given as average value.

    

2. Note

   Joyner and Boore already modified their attenuation formula from Joyner and Boore (1981).

1. Fukushima and Tanaka (1990, 1991)

   1. Input/Output

      1. Pre-Condition

1. Outline of the Method

   Fukushima and Tanaka (1990, 1991) proposes the attenuation formula of peak ground acceleration, which is derived from ground motion data recorded in Japan, the United States and so on. This attenuation formula showed the good agreement also with observed data for the 1995 Southern Hyogo Prefecture Earthquake.

   

   

   Fig. 4 Analyzed data and attenuation relation for peak horizontal acceleration
   (Fukushima and Tanaka, 1991)

2. Note

   Since this formula calculates peak acceleration at the surface, correction is required when this formula is applied to estimating ground motion on bedrock. For example, it is possible to use the ratio of the observed acceleration to predicted acceleration for each soil type, which is described at the original paper.

3. Reference

1. Annaka et al. (1997)

   1. Input/Output
      1. Pre-Condition

• Set hypothetical hypocenter (or seismogenic fault)

1. Outline of the Method

   This method provides peak ground motion on engineering bedrock in which S-wave velocity is the range from 300m/s to 600m/s. Compared with other attenuation formulas, the characteristic of this method is that the focal depth is taken into consideration.

   

   Table .1 Regression coefficients 

   Parameters	Cm	Ch	Cd	C0
   Peak acceleration [gal]	0.606	0.00459	2.136	1.730
   Peak velocity [cm/s]	0.725	0.00318	1.918	-0.519

2. Note

   ---

1. Midorikawa (1993)

   1. Input/Output

      1. Pre-Condition

1. Outline of the Method

   Since it is thought that there is a high correlation between earthquake damage and peak ground velocity, in Midorikawa (1993) method, peak ground velocity is used as a measure for ground motion severity. This method provides peak ground velocity on stiff site with S-wave velocity of 600m/s.

   

   

   

   

2. Note

   According to the magnitude range of analyzed data, it is valid to use this formula for earthquakes with moment magnitude of 6.5 to 7.8

3. Refference

1. Evaluation of Soil Effects

   The following methods are generally used as response analysis of soil surface in earthquake damage assessment.

   (a) Multi-reflection theory
   (b) Equi-linearized technique
   (c) Calculation to apply Multi-reflection theory to deep subsurface and apply equi-linearized technique to shallow subsurface

   Multi-reflection theory is basic method in response analysis, and built in early 1960s (e.g. Haskell, 1960). This method can explain that ground motion tends to be amplified at soft-soil site. However if incident wave has large amplitude, ground motion at soft-soil site is weaker than at stiff site. This phenomenon is called nonlinear behavior of soil and observed when large earthquake occurred, but multi-reflection theory can’t explain this phenomenon.

   In order to take nonlinear behavior into consideration, equi-linearized technique was developed. In earthquake damage assessment, SHAKE (Schnabel et al., 1972) has been often used as equi-linearized technique, but recently the method which can consider frequency-dependent effect of shear modulus and damping factor, e.g. FDEL (Sugito et.al., 1994), is used more and more.

   On the other hand there are simple methods for evaluating site amplification factor. For example, Matsuoka and Midorikawa (1994) can calculate site amplification factor from geomorphological unit or geology, altitude and the shortest distance from a river. The advantage of this method is that it does not need detailed parameters about soil which is obtained from field investigation such as boring data. On the other hand, the disadvantage is that it cannot explain nonlinear behavior of soil.

   1. Multi-Reflection Theory

      1. Input/Output

         1. Pre-Condition

1. Outline of the Method

   As shown in Fig. 1.5, soil surface is modeled as the horizontal layered media.

   変位	S波速度	剛性率	密度	層厚	層
   u1	V1	μ1	21	d1	1
   u2	V2	μ2	22	d2	2
   ：	：	：	：	：	：
   um	Vm	μm	2m	dm	m
   ：	：	：	：	：	：
   un-1	Vn-1	μn-1	2n-1	dn-1	n-1
   un	Vn	μn	2n	dn	n

   Fig. 5 Soil model with horizontal layered structure

   Displacement amplitude of incident S wave at upper boundary of th layer (=bedrock) is given by

   ,

   where is the angular frequency and is a constant. Displacement in any th layer is expressed with summation of downward transmitting wave and upward transmitting wave . Because is expressed by and , displacement and stress in th layer is given by

   ,

   where is depth from upper boundary of th layer and .

   Derived from continuity condition of displacement and stress between th layer and ()th layer,

   

   ,

   where is called layer matrix.

   By using this recurrence formula iteratively, displacement and stress at ground surface can be computed by

   .

   Stress at ground surface is zero and displacement amplitude of incident S wave is given by , then an above equation is developed as

   .

   Therefore frequency-transfer function, it is the ratio of surface to incident amplitude in frequency domain, is given by

   .

   Taking intrinsic attenuation parameter into consideration, you have to substitute complex shear modulus for shear modulus in above-mentioned equations.

2. Note

   Because this method does not consider nonlinear behavior of soil, predicted amplitude at soft-soil sites, particularly sand deposit, is overestimated compared with observed amplitude when incident S wave has large amplitude.

   This method need many parameters for each layer, but it is exceptional that parameters such as S-wave velocity is observed in research area even if there are many boring data. So it is necessary to infer unknown parameters using conversion formulas with N value as input, because N value is usually recorded in boring data in Japan.

3. Reference

1. Equi-Linearized Technique

   1. Input/Output

      1. Pre-Condition

1. Outline of the Method

   In general, soil has characteristic that shear modulus decreases and damping factor increase as shear strain increases. In this method, to consider this characteristic calculation is executed with following process (see also Fig. 1.6).

   Process 1
   Set up soil structure model with parameters necessary for calculation. Then compute shear modulus and damping factor on the assumption that shear strain is slight.

   Process 2
   Do response analysis for given incident waveform and calculate time series of shear strain for each layer.

   Process 3
   Calculate new shear modulus corresponding to 60 percent of maximum shear strain which is given by response analysis, using strain-dependent curves of shear modulus and damping factor.

   Process 4
   Calibrate soil structure model with newly gained shear modulus and damping factor.

   Process 5
   Iterate calculation from process 2 to process 4 until shear modulus and damping factor converge.

    

2. Note

   The nonlinear technique called SHAKE (Schnabel et.al., 1972) is one of the typical methods which consider strain-dependency in physical properties of soil. The nonlinear technique is more suitable to actual behavior of soil than multi-reflection theory as described in 1.2.1. However, predicted amplitude at soft-soil sites, particularly sand deposit, is underestimated compared with observed amplitude, because shear strain become too large when incident S wave has large amplitude.

   To improve this problem in SHAKE, in FDEL (Sugito et.al., 1994) the frequency dependent effect of shear modulus and damping factor is taken into consideration.

   These methods need many parameters for each layer, but it is exceptional that parameters such as S-wave velocity is observed in research area even if there are many boring data. So it is necessary to infer unknown parameters using conversion formulas with N value as input, because N value is usually recorded in boring data in Japan.

3. Reference

1. Matsuoka and Midorikawa (1994), Midorikawa et.al. (1994)

   1. Input/Output

      1. Pre-Condition

         ---

      2. Input Data

1. Outline of the Method

   Using the observed strong motion data for the 1987 Chiba-ken-toho-oki, Japan earthquake, Midorikawa et al. (1994) proposes the following equations which can calculate the site amplification for peak ground acceleration () and velocity () with the time-weighted average shear wave velocity to a depth of 30m ( in m/s) as input.

   

   Where is given by the following equation for each soil type (Matsuoka and Midorikawa, 1994).

   

   

   The regression coefficients of are summarized in Table 1.2.

   Table .2 Regression coefficients for each soil type (Matsuoka and Midorikawa, 1994)

   Geomorphological unit or Geology					Data #
   Reclaimed Land	2.23	0	0	0.14	132
   Artificial Transformed Land	2.26	0	0	0.09	7
   Delta, Back Marsh ()	2.19	0	0	0.12	36
   Delta, Back Marsh ()	2.26	0	0.25	0.13	57
   Natural Levee	1.94	0.32	0	0.13	18
   Valley Plain	2.07	0.15	0	0.12	26
   Sand Bar, Dune	2.29	0	0	0.13	13
   Fan	1.83	0.36	0	0.15	20
   Loam Plateau	2.00	0.28	0	0.11	95
   Gravel Plateau	1.76	0.36	0	0.12	12
   Hill	2.64	0	0	0.17	22
   Other Geom. Units (e.g. Volcanic Mountain)	2.25	0.13	0	0.16	10
   Pre-Tertialy	2.87	0	0	0.23	3

   Peak ground acceleration (or velocity) at surface can be obtained by multiplying the amplification factor and peak ground acceleration (or velocity) on bedrock together. In this method bedrock indicates the layer with .

2. Note

   Because this method derived from the dataset mainly recorded in Kanto district in Japan, calculation result is not compensated except Kanto district.

   In order to be able to use this method in other area in Japan, Geological Survey of Japan (1996) decided maximum and minimum value for , , for each geomorphological unit or Geology.

   Table .3 Maximum and minimum value for , ,
   (Geological Survey of Japan, 1996)

   Geomorphological unit or Geology	VS	H	D
   Reclaimed Land	170	－	－
   Artificial Transformed Land	180	－	－
   Delta, Back Marsh ()	155	－	－
   Delta, Back Marsh ()	155～250	－	0.5～4.0
   Natural Levee	160～250	5～30	－
   Valley Plain	165～300	10～500	－
   Sand Bar, Dune	195	－	－
   Fan	180～450	15～200	－
   Loam Plateau	170～400	10～150	－
   Gravel Plateau	200～500	30～400	－
   Hill	435	－	－
   Other Geom. Units (e.g. Volcanic Mountain)	200～400	5～500	－

3. Reference