Effect of foundation rocking on the seismic response of shear walls

Abstract

Some designers have long known that elastically responding shear-wall or core-wall type high-rise structures will not overturn if the footing size is smaller than that required to resist the elastic forces. Most shear walls are designed and built with a yield hinge mechanism at the base using a relatively high value of the force reduction factor R, and the foundation should be stronger than the yield hinge strength if the wall is to perform as designed. Many walls, however, built with R = 2 are stronger than they need to be because of reasons such as architectural sizing and minimum reinforcement requirements. If for these cases the foundation is to be stronger than the wall, then it will in effect be designed for forces corresponding to an R value of <2. This study looks at the effect on the displacement of a shear-wall type structure if the footing is allowed to rock. The structure is kept elastic and the footing is sized to correspond to R values ranging from 1.0 to 3.5. The analysis uses gap elements to model the foundation soil response so that the footing can lift off the soil. Soil stiffness and strength are modelled for a rock and a firm clay site. The response of 7-, 15-, and 30-storey structures to 11 different acceleration records, modified to match a spectrum given in the 1995 National Building Code of Canada (NBCC) for Vancouver, is determined for the different footing dimensions. The results indicate that a footing sized for an R value of 2 does not result in a significant increase in displacement when compared with the fixed base elastic case. In the next version of the NBCC it is suggested that footings need not be designed for forces corresponding to R < 2.Key words: seismic shear walls, overturning, liftoff, rocking footings.