4.13 Stewart et al. (2005)

1) Reference

Jonathan P. Stewart, Yoojoong Choi, and Robert W. Graves, 2005, Empirical Characterization of Site Conditions on Strong Ground Motion, Pacific Earthquake Engineering Research Center.

2) Used strong motion data

- Area: Worldwide

- Type of earthquake: shallow crustal earthquakes

- Period: 1940-1999

- Number of events: 51

- Number of records: 1032

- Magnitude: M4.4-7.4

3) Formula for estimation

Empirical relationships are developed to predict amplification factors for 5% damped response spectral acceleration as a function of site condition. Amplification factor are evaluated as residuals between ground motion recordings and predictions from modified rock attenuation relationships. Both shallow and deep characteristics of site condition are considered to identify those parameters that are most effective from the standpoint of bias and dispersion reduction. The parameterization of shallow site condition is based on (1) surface geology, (2) NEHRP classification, (3) geotechnical site categories, (4) average shear wave velocity in upper 30 m of site (V_s-30), and (5) deep sedimentary structure at many pf the strong motion sites.

[Ground motion amplification factors for various classification schemes]

F_ij: amplification factor for ground motion j within site category i

S_ij: geometric mean of 5% damped acceleration response spectra for the two

horizontal components of shaking

(S_r)_ij: reference ground motion for the site

G_ij: PHA_r

ε_ij: error,

[Standard Deviation]

ε_i: mean residual

σ_i: standard deviation of the residual

N_i: number of data points in category i

df_i: number of degrees of freedom in the regression equation for category i

Table 4.13-1 Site categories in NEHRP provisions (Martin, 1994; Dobry et al., 2000)

Table 4.13-2 Geotechnical site categories proposed by Rodriguez-Marek et al. (2001)

Table 4.13-3 Criteria for surface geology classifications (ans no. of sites)

Table 4.13-4 Surface geology categories (smoothed)

Table 4.13-5 NEHRP and geotechnical categories (smoothed)

[Ground motion amplification factors within V_s-30 categories]

E: V_s-30<180 m/s + soft clay

D_lv: 180<V_s-30<310 m/s

CD: 310<V_s-30<520 m/s

C_hv: 520<V_s-30<760 m/s

B: 760< V_s-30<1500 m/s

Table 4.13-6 Regression coefficients for Sa amplification factors

[Nonlinear site amplification as function of V_{s-30 ]}

F_ij: amplification factor for ground motion j within site category i

PHA_r: expected in unit of g

b: function of parameter as given in,

Category E

(m/s)

(m/s)

(m/s)

(m/s)

η_i: random effect term for earthquake event i (standard deviation is denoted τ)

ε_ij: intra-event model residual for motion j in event i (standard deviation is denoted σ)

the models and corresponding site conditions used to evaluate S_r values are as follows:

Model A1. Abrahamson and Silva, (1997): rock

Model A2. Sadigh et al., (1997): rock

Model A3. Campbell and Bozorgnia, (2003): generic rock

[Standard Deviation]

Table 4.13-7 Regression coefficients for Model A1 (smoothed)

Table 4.13-8 Regression coefficients for Model A2 and Model A3 (smoothed)

[Ground motion amplification as function of basin geometry for Southern California Basins]

AF: amplification factor

(S_a)_{3D_sim}, (S_a)_{1D_rock_sim}: geometric means of the horizontal spectral acceleration

3D_sim: 3D basin geometry in the analysis of Green’s functions

1D_rock_sim: 1D layered rock model

Z_1.5i: depth in meters to the 1500 m/s shear wave isosurface for data point i

ε_i: residual between data point i and fit line

Figure 4.13-1 Schematic illustration of coincident and distinct site-source basin locations (CRL and DBL, respectively)

Table 4.13-9 Bilinear regression results