Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...
Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ... Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...
-5 -4 -3 -2 -1 0.01 0.05 0.10 0.50 1.00 5.00 10.00 Period (sec) Figure 31: Variation of parameter c1 with spectral period. Number of Usable Data 400 600 800 1000 0.01 0.05 0.10 0.50 1.00 5.00 10.00 Period (sec) 0.8 1.1 1.6 Figure 32: Variation of number of usable recordings as a function of spectral period. C&Y2006 Page 43 4 8
Slope -1.5 -1.0 -0.5 0.0 0.5 1.0 0.01 0.05 0.10 0.50 1.00 5.00 10.00 Period (sec) Figure 33: Variation of the derivative of parameter c1 with respect to spectral period. FINAL MODEL FORMULATION The final model formulation is given by the relationships: ln ( SA ) = c + c F + c F + c ( Z − 4) ln 1130ij + c + c + 1 ( ) 2 3 cn ( cM −M i ) ( M − 6) + ln 1+ e ( R + c cosh( c ( M − c , 0) ) ) ( c − c ) ⎪⎧ + ⎨c ⎪⎩ + c 2 4 9 ln 4a γ 1 + τ ⋅ z i 1a i ⋅ cos RVi RUPij 4 ln⎜ ⎝ + cosh ( SA ) = ln( SA ) ij 2 1130ij 1b c 5 ⎛ 2 R RUPij + γ 2 ( M − c , 0) ) i n NMi − c c c γ 3 ⎛ R δ i ⋅ tanh ⎜ ⎝ 2 6 RUPij 7 c i 2 RB max ⎞ ⎟ tan ⎠ TORi ⎟⎞ ⎠ C&Y2006 Page 44 HM ⎪⎫ ⎬ ⋅ R ⎪⎭ −1 RUPij 0.8 max 1.1 1.6 ⎛ Wi cosδ i ⎜ ⎝ 2 TORi ( Z + 1) 4 ⎞ 1 ⎪⎧ ⎟ ⎨1 − ⎠ π / 2 ⎪⎩ R ⎛ ⎛V S 30ij ⎞ ⎞ + φ ⎜ ⎟ ⎜ ⎜ ⎟ 1 ⋅ ln , 0 ⎟ ⎝ ⎝ 1130 ⎠ ⎠ min φ ( ( V ) ) ( ) ⎛ SA S ij − ij + φ ⎞ 3 30 , 1130 360 φ − 1130 4 min 3 1130 360 + φ ⋅ { e − e } ⋅ ⎜ ⎟ 2 ln ⎝ φ4 ⎠ + σ ⋅ z ij The predictor variables for this model are: 8 RUPij RJBij ⎪⎫ ⎬ + 0. 001⎪⎭ (21a) (21b)
- Page 1 and 2: Chiou and Youngs PEER-NGA Empirical
- Page 3 and 4: data are consistent with strong mot
- Page 5 and 6: Figure 1: Magnitude-distance-region
- Page 7 and 8: Figure 2: Empirical ground motion d
- Page 9 and 10: EQID Earthquake M Table 3: Inferred
- Page 11 and 12: Site Average Shear Wave Velocity: A
- Page 13 and 14: Figure 6: Relationship between VS30
- Page 15 and 16: 1 ) ∝ C2 × M + ( C2 − C ) × l
- Page 17 and 18: Figure 9: Peak acceleration data fr
- Page 19 and 20: C4+C5M slowly and the value of the
- Page 21 and 22: allows the interpretation of the co
- Page 23 and 24: Figure 13: Coefficients resulting f
- Page 25 and 26: the top of rupture located at x = 0
- Page 27 and 28: Figure 18: Intra-event residuals fo
- Page 29 and 30: Figure 21: Variation of HW* with ma
- Page 31 and 32: The interpretation of the parameter
- Page 33 and 34: to the PEER-NGA pga data selected f
- Page 35 and 36: EFFECT OF DATA TRUNCATION The initi
- Page 37 and 38: term [ 1 Φ( y ( θ ) + τ ⋅ z ,
- Page 39 and 40: Table 4: Estimate of Anelastic Atte
- Page 41 and 42: data truncated at a maximum distanc
- Page 43: faulting earthquakes at long period
- Page 47 and 48: C&Y2006 Page 46 Table 5: Coefficien
- Page 49 and 50: c1 of T0.010S c1 of T1.000S MODEL R
- Page 51 and 52: esid 1 0 -1 -2 resid resid 1 0 -1 -
- Page 53 and 54: esid resid resid 1 0 -1 -2 1 0 -1 -
- Page 55 and 56: esid 2 1 0 -1 -2 SCEC Version 2 0 2
- Page 57 and 58: Amplification w.r.t. Vs30 = 1130 m/
- Page 59 and 60: Sa(g) Sa(g) 10 1 0.1 0.01 10 1 0.1
- Page 61 and 62: Sa (g) Sa (g) 1 0.1 0.01 0.001 0.00
- Page 63 and 64: Sa (g) Sa (g) 1 0.1 0.01 0.001 1 0.
- Page 65 and 66: EXAMPLE CALCULATIONS FORTRAN routin
- Page 67 and 68: Table 6: Example Calculations Perio
- Page 69 and 70: REFERENCES Abrahamson, N.A., and Si
- Page 71 and 72: Frankel, A., A. McGarr, J. Bicknell
- Page 73 and 74: Appendix A Recordings from PEER-NGA
- Page 75 and 76: RSN EQID Earthquake M Station No, S
- Page 77 and 78: RSN EQID Earthquake M Station No, S
- Page 79 and 80: RSN EQID Earthquake M Station No, S
- Page 81 and 82: RSN EQID Earthquake M Station No, S
- Page 83 and 84: RSN EQID Earthquake M Station No, S
- Page 85 and 86: RSN EQID Earthquake M Station No, S
- Page 87 and 88: RSN EQID Earthquake M Station No, S
- Page 89 and 90: RSN EQID Earthquake M Station No, S
- Page 91 and 92: RSN EQID Earthquake M Station No, S
- Page 93 and 94: RSN EQID Earthquake M Station No, S
Slope<br />
-1.5 -1.0 -0.5 0.0 0.5 1.0<br />
0.01 0.05 0.10 0.50 1.00 5.00 10.00<br />
Period (sec)<br />
Figure 33: Variation of the derivative of parameter c1 with respect to spectral period.<br />
FINAL MODEL FORMULATION<br />
The final model <strong>for</strong>mulation is given by the relationships:<br />
ln<br />
( SA ) = c + c F + c F + c ( Z − 4)<br />
ln<br />
1130ij<br />
+ c<br />
+ c<br />
+<br />
1<br />
( )<br />
2 3<br />
cn<br />
( cM<br />
−M<br />
i )<br />
( M − 6)<br />
+ ln 1+<br />
e<br />
( R + c cosh(<br />
c ( M − c , 0)<br />
) )<br />
( c − c )<br />
⎪⎧<br />
+ ⎨c<br />
⎪⎩<br />
+ c<br />
2<br />
4<br />
9<br />
ln<br />
4a<br />
γ 1<br />
+ τ ⋅ z<br />
i<br />
1a<br />
i<br />
⋅ cos<br />
RVi<br />
RUPij<br />
4<br />
ln⎜<br />
⎝<br />
+<br />
cosh<br />
( SA ) = ln(<br />
SA )<br />
ij<br />
2<br />
1130ij<br />
1b<br />
c<br />
5<br />
⎛ 2<br />
R RUPij +<br />
γ 2<br />
( M − c , 0)<br />
)<br />
i<br />
n<br />
NMi<br />
− c<br />
c<br />
c<br />
γ 3<br />
⎛ R<br />
δ i ⋅ tanh<br />
⎜<br />
⎝ 2<br />
6<br />
RUPij<br />
7<br />
c<br />
i<br />
2<br />
RB<br />
max<br />
⎞<br />
⎟ tan<br />
⎠<br />
TORi<br />
⎟⎞<br />
⎠<br />
C&Y2006 Page 44<br />
HM<br />
⎪⎫<br />
⎬ ⋅ R<br />
⎪⎭<br />
−1<br />
RUPij<br />
0.8<br />
max<br />
1.1 1.6<br />
⎛ Wi<br />
cosδ<br />
i<br />
⎜<br />
⎝ 2 TORi<br />
( Z + 1)<br />
4<br />
⎞ 1 ⎪⎧<br />
⎟ ⎨1<br />
−<br />
⎠ π / 2 ⎪⎩ R<br />
⎛ ⎛V<br />
S 30ij<br />
⎞ ⎞<br />
+ φ ⎜ ⎟<br />
⎜ ⎜<br />
⎟<br />
1 ⋅ ln , 0<br />
⎟<br />
⎝ ⎝ 1130 ⎠ ⎠ min<br />
φ ( ( V ) ) ( ) ⎛ SA<br />
S ij −<br />
ij + φ ⎞<br />
3 30 , 1130 360 φ −<br />
1130 4<br />
min<br />
3 1130 360<br />
+ φ ⋅ { e<br />
− e } ⋅<br />
⎜<br />
⎟<br />
2<br />
ln<br />
⎝ φ4<br />
⎠<br />
+ σ ⋅ z<br />
ij<br />
The predictor variables <strong>for</strong> this model are:<br />
8<br />
RUPij<br />
RJBij<br />
⎪⎫<br />
⎬<br />
+ 0.<br />
001⎪⎭<br />
(21a)<br />
(21b)
Change language