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A three-steel-shim elastomeric bearing with a durometer hardness of 56 has been designed for the bridge. The bearing is 55.9 cm in width (in the transverse direction), 22.9 cm in length (in the longitudinal direction), and has four layers of 12.7-mm-thick elastomer. The thickness of the steel shim is 2.5 mm.Astiff elastomeric bearing (behaving as a fixed bearing) is installed at the south pier, whereas regular bearings (behaving as expansion bearings) have been installed at other piers and abutments. These bearings are not designed for uplifts, and the weight of the superstructure holds down the bearings.
It has been observed from experimental results that the yielding of the steel shims or delamination of steel/elastomer interfaces mainly cause the failure modes of elastomeric bearings. Hence, these two materials have been modeled separately in the finite-element model of the bearings to identify failure modes related to bearings during blast load events. In the FEM model of elastomeric bearings, elastomeric layers are modeled by solid elements and steel shims by shell elements. They are connected together at shared nodes. Thesteel/elastomer interface is not modeled separately in the FEM model because the peel strength of the steel/elastomer interface is almost the same as the tensile strength of the elastomer (Ash et al. 2002). Hence, eroding elastomer elements in this FEM simulation implies either tensile failure of the elastomer or the delamination of the steel/elastomer interface. Fig. 13(a) shows the finite-element model of elastomeric bearings where every layer of the elastomer has been modeled by several layers of solid elements. Fig. 13(b) shows the deformed shape of the bearing under uniform pressure on top of the bearing. It is observed from Fig. 13(b) that elastomer elements along the edge that are not connected to steel shims deform significantly, resulting in failure of the bearing at the load well below the experimental failure strength. To simulate confinement of elastomers between steel shims/plates and friction between the elastomer and steel shims/plates, a coarser mesh, where only one layer of solid elements models every elastomer layer, was developed and calibrated with experimental data. Fig. 13(c) shows this model of bearings.
Fig. 13. Finite-element model of bearings: (a) fine mesh at time 5 0 s; (b) fine mesh at time 5 0.5 s; (c) coarse mesh
Material Properties and Constitutive Models
Table 4 shows several existing concrete constitutive models to simulate blast load effects in LS-DYNA. Among these models, the JHC material model has been selected to simulate blast load effects. The JHC model is a computational constitutive model for concrete members subjected to large strains, high strain rates, and high pressures, and is well-suited for both Lagrangian and Eulerian codes. The model is similar to a smeared crack model but is expanded to include material damage, strain rate effects, and permanent crushing as a function of the pressure and air void ratio (Holmquist et al. 1993).
Table 4. Constitutive Model for Concrete in LS-DYNA
Fig. 14 illustrates an example of the behavior of the JHC concrete model by simulating a quasi-static, uniaxial strain compression test. In Fig. 14, concrete behaves essentially elastic from point 1 to point 2, although a small amount of plastic volumetric strain is seen to occur. At point 2, the yield surface is reached and an equivalent plastic strain begins to accumulate. From point 2 to point 3, an increase in the equivalent plastic strain causes the material to damage, which in turn causes a gradual loss of cohesive strength. At point 3, the maximum strength is reached and the material continues to flow plastically and accumulate damage until the loading is reversed at point 4. From point 4 to point 5, the unloading is elastic. The yield surface is again encountered at point 5, and the material continues to flow plastically until the load is removed at point 6. Of special interest is the elastic unloading response between points 4 and 5. The unloading path is different than the elastic loading that occurs between points 1 and 2 due to the crushing of the material. Strain rate-dependent behavior of the JHC model can be observed from the equation for the equivalent stress, s, in Fig. 15.