may result in permanent deformations that also cause damage to the building. Seven series ... 1 shows the moment-rotation and settlement-rotation relationships ...
PHYSICAL AND ANALYTICAL MODELING OF CYCLIC LOAD-DEFORMATION BEHAVIOR OF SHALLOW FOUNDATIONS Sivapalan Gajan1, Jeremy M Thomas2 and Bruce L Kutter3 1,2 Graduate student researcher and 3Professor Department of Civil and Environmental Engineering University of California at Davis Davis, CA 95616, USA Abstract Soil-foundation interaction associated with heavily loaded shear walls during large seismic events may produce highly nonlinear behavior. Geotechnical components of the foundation are known to have a significant effect on the building response to seismic shaking. The nonlinearity of the soil and the interaction between the soil and foundation are shown to cause the building's stiffness and period to change to varying degrees. One of the major changes in the traditional seismic design procedures adopted in the 1997 Building Retrofit NEHRP Guidelines, was that by allowing mobilization of the ultimate capacity and rocking behavior of shallow foundations, the ductility demands on structures could be reduced, particularly for shear walls. Available results of this research indicate that moment-rotation hysteresis curves display excellent ductility. The nonlinearity of the soil may act as an energy dissipation mechanism, potentially reducing shaking demands exerted on the building. This nonlinearity, however, may result in permanent deformations that also cause damage to the building. Seven series of tests on a large centrifuge, including about 60 models of shear wall-footings, were performed to study the nonlinear load-deformation characteristics of shallow foundations during cyclic and earthquake loading. Footing dimensions, depth of embedment, wall weight, initial static vertical factor of safety, soil density, and soil type (dry sand and saturated clay) were systematically varied. Static vertical loading, slow cyclic horizontal loading at different heights of the wall and dynamic earthquake shaking events were applied to the models to study cyclic and permanent deformation behavior of soilfooting interface at prototype stress levels over a typical range of moment to shear ratio and shear to axial load ratio. The behavior of the footing-soil system is analyzed in terms of the resultant of the vertical, horizontal, and moment load (V-H-M) acting at the center of the base of the footing and the corresponding displacements (settlement, sliding and rotation). Fig. 1 shows the moment-rotation and settlement-rotation relationships for a slow cyclic horizontal push test on sand. The moment-rotation relationship is highly nonlinear and encloses a large area in hysteresis loops indicating a considerable amount of energy is dissipated at the footing-soil interface. Rocking of the footing progressively rounds the foundation soil, and this rounding causes a reduction in contact area between the footing and soil (uplift) thereby causing a nonlinearity and stiffness reduction on the moment-rotation relationship. The formation of a gap and uplift of the footing on one side of the footing, evidence from the settlement-rotation relationship, causes yielding of the soil on the other side of the footing and vise versa. Permanent deformations beneath footing continue to accumulate with the number of cycles of loading, though the rate of accumulation of settlement decreases as the footing embeds itself. Normalized settlement per cycle of loading is shown to increase as axial to shear load ratio increases and as moment to shear load ratio decreases. The observed failure points and the interaction between forces in V-H-M space compare well with previously published analytical failure envelopes and interaction diagrams in V-H-M space. Analytical modeling was carried out to model the coupled load-displacement behavior of footing-soil interface during cyclic loading. The rigid footing and the soil beneath the footing are considered as a single element (contact element). The moment-rotation behavior is modeled by using the opening and closing gaps behind and in front of the footing contact area that moves based on the geometry of the
footing and the shape of the rounded soil-foundation interface. Footing and the soil surface beneath the footing are modeled with finite number of nodes inside the contact element and each node has a history of following internal variables: footing location, current soil surface location, maximum past settlement experienced by the soil, current bearing pressure distribution and the maximum bearing pressure experienced by the soil. The ultimate bearing capacity, vertical stiffness of the soil along with the vertical and moment equilibrium of footing-soil interface are used to obtain moment-rotation and settlement rotation relationships. The coupling between vertical and shear force and moment and shear force and the corresponding displacements were incorporated using interaction diagrams and failure envelopes in V-HM loading space. Shear force-sliding relationship is modeled using a bounding surface plasticity approach with the failure envelope being the bounding surface. Fig. 1 shows the comparison of contact element model simulations with experimental results for a slow cyclic lateral push test. At the beginning of loading, for small rotations, the contact length is closer to L (the length of the footing), the curvature of the soil surface is small and the rate of increase in eccentricity with rotation (de/dθ) is large, hence, the moment rotation plot shows higher stiffness. As the rotation goes to higher values, progressive rounding of the soil surface increases the curvature and decreases the contact length and hence rotational stiffness degradation is observed. The ultimate moment obtained in both experiment and simulation is very close to the theoretical ultimate value. The dependence of the relationships between settlement, uplift and rotation on the geometry of the soil surface and the contact location of footing is clearly visible in the settlement-rotation relationship of contact model simulation. Settlement to rotation ratio (ds/dθ) at various magnitudes of rotations and the permanent settlement from the simulation are close enough to the experimental results. In general, the computationally efficient contact element model, with only three major soil parameters (friction angle and initial vertical and horizontal stiffness of soil), captures the essential features of the relationships and coupled behavior between the three dimensional forces and displacements that act on a plane (vertical load – settlement, shear force – sliding and moment – rotation).
Fig. 1 Comparison of contact element model simulations with experimental results for a slow cyclic lateral push test: Dr = 80% sand; geometry of the footing: L = 2.84 m, B = 0.65 m, D = 0.0 m; FS = 6.0; M/H = 5.0 m
