EARTHQUAKE ENGINEERING ASSIGNMENT #1

The Centre of Kathmandu city is located in the vicinity of ten independent seismic sources represented by source zone 1 to 10. These source zones in reality are active faults, and they are characterized as given in table 1 given below. For simplicity, all the source zones are considered as point sources. Perform the probability seismic Hazard Analysis for the site using separately the following Attenuation Relationships. (Note: The mean annual occurrence rate of earthquake of magnitude larger than the threshold magnitude v calculated for each source using the given a and b values shall be divided by 16).

Table 1

Source zone	EQ zone (Fault)	Fault name	Fault type	Assumed Ms,max	Assumed Mw,max	a-value	b-value	Source-to- Site distance (Km)	Mean annual rate of occurance (νi)
1	HFF-1 10	Narayani River	R/RL	6.7	6.6	4.17	1	83	0.02923
2	HFF-1 15	Dalkebar	R	7.2	6.8	3.38	1	84	0.00474
3	MBT-2 3	Arung Kh	R,N down	7.5	7	4.24	1	140	0.03435
4	MBT-2 4	Narayani	R	7	6.7	4.17	1	78	0.02923
5	MBT-2 5	Hetauda	R	7.3	6.9	4.17	1	38	0.02923
6	MCT-3 3	Gosai Kunda	R	7.5	7	4.17	1	21	0.02923
7	HFF-1 13	Amlekhgunj	R	7	6.7	4.17	1	47	0.02923
8	LH-4 10	Sunkoshi-Roshi Kh	Rt-lat-st-sl	8.7	6.5	4.17	1	68	0.02923
9	MBT-2 6	Udaipur-Sunkoshi	Rev norm	8	7.3	4.23	1	104	0.03356
10	LH-4 7	Saptakoshi-Doomal	R	7.6	7.1	4.24	1	185	0.00947

Attenuation relationship given is

Kawashima et. al. (1986)

PGA= 232.5x10^0.313M(R+30)^-1.218

Where PGA is in gal (cm/sec²), and σ_{log PGA} = 0.224

Step 1: Sources

 Identification and Characterization of Earthquake Sources which are capable of producing damaging ground motions at a site is done. Since, all sources are considered as point sources, P(R) = 1 for all cases.

Threshold magnitude is assumed to be 4.5 as earthquake of magnitude less than 4.5 shall not be considered significance as magnitude less than 4.5 do not contribute to seismic hazard and mean annual rates is calculated as-

For source 1 : ν₁ = 10^{(4.17-1 x 4.5)}/16 = 0.02923

This value is shown in the table and similar calculation is done for other sources and shown in the

Table 1. As per the question mean annual rates is divided by 16.

Step 2: Magnitude (size uncertainty)

Probability of the magnitude is calculated (Table 3) using where M_min<m<M_max

F_M(m)=  

M_max is the maximum earthquake that a source can produce. The continuous distribution of magnitude is transformed into a discrete set of magnitudes.

P(M=m_j) = F_M(m_j+1) - F_M(m_j)

Where, m_j are discrete magnitudes such that m_j< m_j+1

As long as the discrete magnitudes are narrowly spaced, the approximation will not affect numerical results. From minimum value, increment of 0.25 is done.

Step 3 : Ground motion Intesity (Effect uncertainty)

Ground motion prediction models forecast the probability distribution of ground motion intensity as a function of numerous variables such as magnitude, distance, etc.

Attenuation law used for Peak ground motion (in units of g) is

Kawashima et. al. (1986)

PGA= 232.5x10^0.313M(R+30)^-1.218

Where PGA is in gal (cm/sec²), and σ_{log PGA} = 0.224

The is modeled  and seen to be well characterized by Normal-distribution.

 Standard deviation is taken constant for all magnitude.

                                P[PGA>x(M,R)]=               1-z(  )

Step 4 : Combine all information

The mean annual rate of exceedance  λ* of a PGA is given by PSHA as:

λ* =

where,

vi = average rate of threshold magnitude exceedence =

 = Probability that the parameter (here, PGA) is greater than a value y*