Attenuation relationships are presented for peak acceleration and response spectral accelerations from shallow crustal earthquakes. The relationships are based on strong motion data primarily from California earthquakes. Relationships are presented for strike-slip and reverse-faulting earthquakes, rock and deep firm soil deposits, earthquakes of moment magnitude M4 to 8+, and distances up to 100 km.
A numerical analysis parametric study was conducted to determine the stress and strain states within an idealized soil specimen enclosed by a wire-reinforced rubber membrane and tested in the Norwegian Geotechnical Institute (NGI) simple shear apparatus. The computations were performed utilizing a finite-element program applicable to three-dimensional elastic analysis of nonaxisymmetrically loaded axisymmetric solids. Orthotropic membrane elements were incorporated in the program to simulate the action of the wire-reinforced rubber membrane. A total of 14 cases was analyzed using different combinations of material properties, membrane stiffness, specimen geometry, and boundary displacements. In general, for the values of the parameters studied, the uniformity of shear strain distribution improves as (1) the specimen height-to-diameter ratio is decreased, (2) the percent of wire-reinforcement is increased, (3) the elastic modulus of the soil decreases, (4) the Poisson's ratio of the soil decreases, and (5) the applied horizontal displacement is increased.
We examine the variability of peak horizontal and vertical accelerations of the large California strong-motion data set for the time period 1957 to 1991 and find a statistically significant dependence of the standard error on earthquake magnitude. Specifically, the standard error decreases with increasing magnitude. The analysis was conducted using a rigorous methodology that examines both earthquake to earthquake (inter-event) variability and within earthquake (intra-event) variability. The magnitude dependence is stronger for inter-event variability than intra-event variability, and stronger for horizontal peak acceleration than for vertical peak acceleration. The data from the recent Landers, Big Bear, and Northridge earthquakes are consistent with these results.
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