This series includes technical reports prepared by faculty, students and staff who are associated with the John A. Blume Earthquake Engineering Center at Stanford University. While the primary focus of Blume Center is earthquake engineering, many of the reports in this series encompass broader topics in structural engineering and materials, computational mechanics, geomechanics, structural health monitoring, and engineering life-cycle risk assessment. Each report includes acknowledgments of the specific sponsors for the report and underlying research. In addition to providing research support, the Blume Center provides administrative support for maintaining and disseminating the technical reports. For more information about the Blume Center and its activities, see https://blume.stanford.edu.
The main objective of this research is to develop procedures that will permit an explicit incorporation of the effects of deterioration of structural properties and site surface geology on the seismic demands imposed on structures by strong ground motions. This implies consideration of the influence of stiffness degradation and strength deterioration of structures and of the effects of source-site distance and site soil conditions on those demand parameters that can be used directly for design of structures. Thus, the research combines ground motion and structure response issues, with an emphasis on response parameters that incorporate both relevant ground motion as well as structural response characteristics.
During severe earthquakes the performance of structures depends upon the characteristics of ground motions (frequency content, duration etc.) and the restoring force (hysteretic) characteristics of structural system. The first part of this study focuses on the effects of negative strain hardening (P-delta) and strength deterioration on the demand imposed by ground motions on the strength of inelastic SDOF systems. Strength demand is defined here as the strength that needs to be provided in order to limit the ductility of the SDOFsystem to predefined target value.
P-delta effect may cause a negative lateral stiffness in a structure once a mechanism has formed, This negative "hardening" will increase the drift (displacement) of the system and may lead to incremental collapse if the structure has insufficient strength. Thus, if a predefined target ductility ratio is to be maintained, more strength must be provided for the structural system. The strength reduction factor (ratio of required elastic strength to required strength of the inelastic system), which is the most relevant parameter for strength design, is used here for a quantitative assessment of P-delta effects. The required strength (strength demand) for target ductility ratios from 2 to 8 is evaluated statistically for bilinear and stiffness degrading SDOF systems with a period ranging from 0.10 to 4.0 seconds. The ratio of "hardening" stiffness to elastic stiffness is varied from +0.10 to -0.20. The study shows that the strain hardening/softening has a significant effect on seismic response. Bilinear hysteresis systems with a negative hardening stiffness drift significantly and their strength, compared to hardening systems, needs to be increased considerably in order to limit the inelastic deformations to the same ductility ratio. This is reflected in a rapid decrease of the R-factor for systems with negative stiffness. Stiffness degrading systems behave similar to bilinear systems for positive hardening stiffness but are clearly superior once stain softening occurs. The effect of strain hardening/softening on the Rfactor is presented in terms of the ratio of Rjactors of the system with positive or negative strain hardening to the system with zero strain hardening. This ratio reaches a maximum of 1.4 for positive strain hardening and may be as low as 0.40 for systems with negative strain hardening, depending on the strain hardening ratio, ductility ratio, and period of the SDOF system.
This study is also concerned with the effect of strength and stiffness deterioration on inelastic strength and displacement demands. Since deterioration is a history dependent problem, a general hysteresis model with energy based deterioration is developed. The hysteretic energy dissipation in each excursion is used to update a deterioration parameter. This parameter is utilized to incorporate the effect of deterioration into the bilinear hysteresis model. The effects of stiffness and strength deterioration are evaluated statistically for SDOF systems with periods of 0.50 and 1.0 second. The results are presented in terms of the ratios of seismic demands of deteriorated systems over undeteriorated systems. The study shows that strength deterioration may greatly affect the response of SDOF systems if the hysteretic energy demand approaches the hysteretic energy capacity of the structural system. The response is sensitive to the deterioration parameter that identifies the rate at which strength deterioration occurs. Stiffness degradation is a problem of much less consequence than strength deterioration. In fact, stiffness degradation by itself is not an issue unless is occurs at an accelerated rate that prevents recovery of the structure strength within the displacement range associated with the response to the ground motion.
The research related to the study of soft soil effects on seismic demands is carried out in two parts. In the first part advantage is taken of the extensive set of ground motions recorded during the Loma Prieta earthquake and the availability of data on local soil conditions at recording stations. These data sets are utilized to improve the basic understanding of the phenomena involved, identify the most relevant parameters, develop analytical models, and calibrate these models. In the second part of the study simplified models of soil columns are employed for an extensive parameter study on the effects of site soil conditions on seismic demands. The properties of the soil columns are varied to cover soil periods ranging from 0.5 to 4.0 seconds. A comprehensive set of recorded and generated soft soil ground motions are utilized to obtain phenomenological as well as statistical information on the effects of site soil conditions on PGA, PGD, and elastic and inelastic displacement and strength demands spectra. In order to generate soft soil motions, a total 25 rock records are used as input for linear and nonlinear ground response analyses of soil columns of different period. In the nonlinear ground response analysis the top layer of the soil is modeled as a nonlinear medium represented by a bilinear hysteresis model. The severity of the rock motions is increased in successive analyses to obtain soft soil motions that are affected more and more by the limited shear strength and nonlinearity in the top soil layer.
The motions obtained at the top of the soil columns are used to derive strength and displacement demand spectra for elastic and inelastic SDOF structural systems. The so derived spectra as well as the soft soil PGA and PGD values are evaluated in the context of seismic design, and a methodology is suggested that permits a more realistic incorporation of soft soil effects in the seismic design process. The study shows the effects of soft soil on elastic and inelastic strength demands can be represented in a consistent manner through soil modification functions expressing the ratio of strength demands of soft soil motions to rock motions versus the ratio of structure period to soil column period. The elastic and inelastic displacement demand spectra for structures located on soft soils can be derived directly from the strength demands of the motions in the rock underlying the soft soil and the soil modification function, which is a function of soil period and structure ductility. The amplification of strength demands and PGA decreases as the level of ground shaking increase, whereas the PGD amplification remains almost constant as the level of input motion increases.
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