Maximal Integral Forces under the Base: Different Estimates of Shear Stability and Potential Uplift

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Rubric:     Theoretical and experimental studies   
Annotation:
The authors discuss different estimates of shear stability andpotential uplift during seismic events. They compare the results obtained with 6D time-histories of integral seismic forces under the base to the approximate estimates obtained with maximal integral forces only. The goal is to estimate the applicability of extended Newmark rule (sometimes called 100-40-40 rule). In fact, this rule is based on two assumptions. First, when each of several statistically independent components reaches its’ maximal absolute value, the other components reach about 40% of their maximal absolute values. Second, absolute maximum of the target function of these components may be estimated after comparing target functions in specific time points mentioned above, when one component reaches its maximum, and all other components reach 40% of their maximums. In the paper twelve cases were studied (four different seismic excitations and three soil profiles for each of them). For base shear the target function is ratio of the absolute value of the shear force vector to the compression force consisting of dead weight and vertical seismic force. It turned out that the approximate approach described above gave good results for this target function. For the potential uplift estimates the target function is an area where vertical stresses due to the seismic base rocking turned to be tensile. Here the same 100-40-40 approach gave non-conservative results. It turned out, that the first assumption mentioned above was more or less applicable, but the second assumption was not valid. Maximal target function was actually reached in the time point different from each of the time points with single maximal components, and maximal target function was considerably greater than each of the target functions in these specific “partial” time points. To restore the conservatism of the approximate estimate one has to apply Newmark rule only to the rocking moments, and seismic vertical force has to be considered in full.