ground motion characteristics

7/23/2019 Ground Motion Characteristics

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Introduction

Fukushimaearthquake occurred in 2011 was considered for the study. At each station

only horizontal ground motions were considered. Mechanism of earthquake was

reverse fault for both the events. Details of magnitude of the earthquake are given

below.

S. No Earthquake Name YEAR Station Name Sequence Number Station ID No

1 Fukushima Hamadori 1 2011 HIRATA 2436 FKSH122 Fukushima Hamadori 1 2011 HITACHI 2499 IBR003

3 Fukushima Hamadori 1 2011 KOORIYAMA 2435 FKSH094 Fukushima Hamadori 1 2011 KOHRIYAMA 2430 FKS0185 Fukushima Hamadori 1 2011 KATSURAO 2418 FKS006

Velocity and displacement indices considered are vRMSand dRMS. Their definition issimilar to aRMS, replacing acceleration with respective response quantity.

Q1

S. No PGA PGV TBracket TTri_Bra aRMS AI CAV vRMS dRMS

m/sec2 m/sec sec sec m/sec2 m/sec m/sec m/sec m

1 1.61 0.027 19.85 32.67 0.21 0.25 3.16 0.015 0.25

2 1.62 0.027 19.90 32.90 0.17 0.15 2.60 0.013 0.24

3 2.67 0.031 19.60 30.80 0.22 0.25 2.64 0.012 0.19

42.00 0.033 19.37 30.71 0.16 0.14 1.96 0.006 0.095 2.24 0.029 19.65 35.79 0.18 0.19 2.42 0.010 0.18

6 1.80 0.031 19.41 35.81 0.16 0.15 2.32 0.022 0.45

7 4.17 0.064 19.61 36.04 0.28 0.49 4.08 0.008 0.13

8 4.75 0.069 21.98 36.05 0.45 1.22 5.95 0.013 0.26

9 3.57 0.071 19.76 34.20 0.35 0.69 4.96 0.042 0.80

10 3.07 0.077 19.84 34.27 0.34 0.66 5.06 0.040 0.68

Q2

Correlation coefficients between two horizontal ground motions for events.

S. No Ccorrelation

1 0.034

2 -0.009

3 -0.047

4 -0.179

5 -0.185


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Q3

S. No

Mw R PGA PGV TBracket TTri_Bra aRMS AI CAV vRMS dRMS

kM H1 H2 H1 H2 H1 H2 H1 H2 H1 H2 H1 H2 H1 H2 H1 H2 H1 H2

1 6.70 62.80 1.61 1.62 0.027 0.027 19.85 19.90 32.67 32.90 0.21 0.17 0.25 0.15 3.16 2.60 0.015 0.013 0.25 0.242 6.70 51.24 2.67 2.00 0.031 0.033 19.60 19.37 30.80 30.71 0.22 0.16 0.25 0.14 2.64 1.96 0.012 0.006 0.19 0.093 6.70 58.11 2.24 1.80 0.029 0.031 19.65 19.41 35.79 35.81 0.18 0.16 0.19 0.15 2.42 2.32 0.010 0.022 0.18 0.454 6.70 32.50 4.17 4.75 0.064 0.069 19.61 21.98 36.04 36.05 0.28 0.45 0.49 1.22 4.08 5.95 0.008 0.013 0.13 0.265 6.70 39.43 3.57 3.07 0.071 0.077 19.76 19.84 34.20 34.27 0.35 0.34 0.69 0.66 4.96 5.06 0.042 0.040 0.80 0.68

Variation of PGA with distance

Comments: -

1.

PGA, PGV, AI, aRMSwill attenuate with distance from hypocentre for an earthquake

2.

Strong motion duration is almost same in both horizontal directions

3.

TTri_Brais always greater than TBracketfor the event considered

4.

Ratio of PGAs in both horizontal directions is almost constant

0

1

2

3

4

5

0 20 40 60 80

PGA(

g)

Distance (kM)


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Q4

PGA PGV TBracket TTri_Bra aRMS AI CAV vRMS dRMS

PGA 1 0.84 0.62 0.49 0.89 0.88 0.84 0.17 0.18

PGV 1 0.42 0.44 0.89 0.84 0.92 0.60 0.58TBracket 1 0.36 0.75 0.83 0.70 -0.04 -0.01TTri_Bra 1 0.41 0.46 0.46 0.18 0.23aRMS 1 0.99 0.98 0.44 0.43

AI 1 0.96 0.36 0.36CAV 1 0.53 0.52vRMS 1 0.99dRMS 1

Comments:

1. All the parameters in both directions were considered in the calculation of

correlation.

2.

dRMSand vRMSare well correlated.

3. PGA is correlated well with all the parameters considered except dRMSand vRMS

4. PGV is correlated well with all the parameters

5. aRMSis correlated well with AI, CAV

6.

AI is correlated well with CAV

Q5

A SDoF with damping 5% of the critical damping is assumed for the analysis. Geometric and

material properties used for modelling were described below.

Mass, m = 2 kg;

b = d = 2 cm; I = 1.33 cm4;

E = 200 GPa;

L = 1.5 m;

So k = 3EI/L3

fn= (1/2)(k/m) = 5.48 Hz

This configuration will give the natural frequency of 5.48 Hz.

A sinusoidal loading of frequency 1 Hz, amplitude 500 is applied for 1 second and then it

was allowed to vibrate freely with initial conditions obtained at the end of 1 sec.

Displacement of SDoF was observed till 2 seconds. Comparison of displacements obtained

from the OPENSEES analysis and the exact solution has been shown in Figure 1;


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Figure 1: Comparison of displacements obtained from the OPENSEES analysis and the exact

solution

Q6:-

SDoF described in Q5 has been considered for calculation of Pseudo spectral

acceleration, but the length of the system has been varied to get the desired natural time

period

T(sec) GM1 GM2 GM3 GM4 GM5 GM6 GM7 GM8 GM9 GM10

0.01 3.396 3.640 4.861 3.025 4.792 3.556 4.210 5.936 6.679 8.1290.05 7.854 5.659 3.634 2.625 2.189 1.091 9.127 22.064 6.729 4.859

0.1 0.946 0.734 4.594 5.568 1.158 0.424 10.728 7.234 2.032 2.3030.3 0.286 0.388 0.708 1.209 0.300 0.436 0.879 0.727 0.565 0.5240.5 0.172 0.271 0.176 0.343 0.107 0.230 0.240 0.394 0.497 0.345

1 0.100 0.097 0.126 0.148 0.079 0.111 0.085 0.213 0.157 0.2572 0.026 0.056 0.026 0.037 0.045 0.028 0.030 0.028 0.125 0.1023 0.019 0.034 0.011 0.020 0.025 0.018 0.024 0.020 0.058 0.0625 0.015 0.017 0.012 0.016 0.016 0.018 0.018 0.017 0.050 0.053

Comments:

1.

Pseudo spectral acceleration (PSA) is initially increasing till certain time periods andthen it is decreasing

2.

PSA is almost zero for time periods more than 3 seconds.

3.

PSA at 0.01 seconds is proportional to the PGA

4. Peak value of PSA is also proportional to the PGA in most of the earthquakes.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0 0.5 1 1.5 2

Displacemen

t(m)

Time(seconds)

Opensees Exact solution

ground motion characteristics

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