Recognizing the beneficial effect of nonlinear soil-foundation response has led to a novel design concept, termed 'rocking isolation'. The analysis and design of such rocking structures require nonlinear dynamic time history analyses. Analyzing the entire soil-foundation-structure system is computationally demanding, impeding the application of rocking isolation in practice. Therefore, there is an urgent need to develop efficient simplified analysis methods. This paper assesses the robustness of two simplified analysis methods, using (i) a nonlinear and (ii) a bilinear rocking stiffness combined with linear viscous damping. The robustness of the simplified methods is assessed by (i) one-toone comparison with a benchmark finite element (FE) analysis using a selection of ground motions and (ii) statistical comparison of probability distributions of response quantities, which characterize the time history response of rocking systems. A bridge pier (assumed rigid) supported on a square foundation, lying on a stiff clay stratum, is used as an illustrative example. Nonlinear dynamic FE time history analysis serves as a benchmark. Both methods yield reasonably accurate predictions of the maximum rotation θ max. Their stochastic comparison with respect to the empirical cumulative distribution function of θ max reveals that the nonlinear and the bilinear methods are not biased. Thus, both can be used to estimate probabilities of exceeding a certain threshold value of θ. Developed in this paper, the bilinear method is much easier to calibrate than the nonlinear, offering similar performance.

Problems for which it is impossible to make a precise causal prediction are commonly tackled with statistical analysis. Although fairly simple, the problem of a rocking block on a rigid base subjected to seismic excitation exhibits a fascinating, complex response, making it extremely difficult to validate numerical models against experimental results, thus calling for a statistical approach. In this context, this paper statistically studies the rocking behaviour of rigid blocks, excited by synthetic far‐field ground motions. A total of 50 million analyses are performed, considering rocking blocks of height ranging from 1 to 20 m and slenderness angle ranging from 0.1 to 0.35 rad. The results are used to explore the performance of different ground motion intensity measures (IMs), in terms of their ability to predict the maximum rocking rotation. By comparing the efficiency, sufficiency and proficiency of the IMs, it is found that the peak ground velocity (PGV) performs optimally. Then, fragility curves are constructed using different IMs, concluding again that the PGV is the most efficient IM. Impressively, the fragility curves for different block sizes collapse to a single curve, if a non‐dimensional IM that involves PGV and the block geometry is used. Finally, the results produced on the basis of far‐field synthetic motions are compared to results based on recorded ground motions.

The simplest 3D extension of Housner's planar rocking model is a rocking (wobbling) cylinder allowed to uplift and roll on its circumference, but constrained not to roll out of its initial position. The model is useful for the description of bridges that use rocking as a seismic isolation technique, in an effort to save material by reducing the design moment and the size of the foundations. This paper shows that describing wobbling motion in terms of displacements rather than rotations is more useful. It unveils that a remarkable property of planar rocking bodies extends to 3D motion: A small and a large wobbling cylinder of the same slenderness will sustain roughly equal top displacement, as long as they are not close to overturning. This allows for using the response of an infinitely large wobbling cylinder of slenderness α as a proxy to compute the response of all cylinders having the same slenderness, irrespectively of their size. Thus, the dimensionality of the problem is reduced by one. Moreover, this paper shows that the median wobbling response to sets of ground motions can be described as an approximate function of only two non-dimensional parameters, namely (𝑔 tan 𝛼∕𝑃𝐺𝐴, 𝑢∕𝑃𝐺𝐷)or (𝑔 tan 𝛼∕𝑃𝐺𝐴, 𝑢𝑃𝐺𝐴∕𝑃𝐺𝑉 2 ) where u is the top displacement of the wobbling body.

SummaryThe paper studies the performance of a typical overpass bridge, with continuous deck and monolithic pier‐deck connections, subjected to strike‐slip faulting. A three‐dimensional (3D) finite element (FE) model of the entire bridge–foundation–abutment–soil system is developed, accounting for soil, structure and geometric nonlinearities. Soil behaviour is simulated with a thoroughly validated strain softening constitutive model. The concrete damaged plasticity (CDP) model is implemented for piers, accounting for the interaction between axial force N, bending moment M, shear force Q and torsion T (NMQT); the model is validated against experimental results from the literature. The location of the fault rupture is parametrically investigated, confirming the vulnerability of indeterminate structural systems to large tectonic deformation. The deck is shown to sustain both in‐plane and out‐of‐plane bending moments, as well as torsion; the piers are subjected to biaxial bending, shear and torsion. The response is highly dependent on the location of the fault rupture, emphasizing the need to develop cost‐effective modelling techniques. Four such techniques are developed (with and without decoupling) and comparatively assessed using the detailed 3D FE model as benchmark. The best prediction is achieved by a coupled model, which includes the bridge superstructure, detailed 3D modelling of the soil‐foundation system only for the pier directly affected by the fault, and nonlinear springs representing the foundations of all other piers. The proposed technique offers a computationally efficient means to parametrically analyse long multispan bridges subjected to faulting, for which full 3D FE modelling is impractical.

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