Simulating the Response of Free-Standing Rocking Rigid Blocks using Abaqus/Standard

Abstract

This work presents detailed finite element models developed in Abaqus/Standard to study the rocking response of free-standing rigid blocks, which is characterised by the alternation of impacts between the block and the foundation that suddenly change the contact point between the two members. Nonlinear dynamic analysis with implicit time integration is carried out to study rocking initiation (uplift) and rocking attenuation (at impact) of free-standing rigid blocks with different slenderness under pulse-type motions. The attenuation effects are further studied by allowing the block to rock freely on the foundation. Solid homogenous sections are analysed with fully integrated 4-node plane stress quadrilateral elements (CPS4) for the block and the equivalent reduced integration elements (CPS4R) for the foundation. Rigid body constraints are used to refer the motion of each body to the respective centre of gravity. Contact is treated using the small-sliding formulation and the resulting system of equations of dynamics is solved by means of the Abaqus/Standard HHT algorithm, with the value of alpha that provides the maximum numerical dissipation. A sensitivity analysis is conducted for the time incrementation and mesh element size. Large time steps lead to higher attenuation of rocking movement due to the increment of the contact constraint discontinuity work (ALLCCDW), an energy component which highly influences rocking movement. However, smaller values of the step time yield very accurate results in comparison with the analytical solution. The element size sensitivity analysis revealed that the rocking initiation is generally well captured, but the coarse mesh results in inaccurate capture of the instant at which impact occurs and unrealistic attenuation of the rocking response. On the contrary, the fine mesh (defined as 1% of the corresponding contact surface) seems to capture well the rigid rocking response. These suggest that the selection of the analysis parameters is crucial to capture the desired response of free-standing rigid blocks