Rocking isolation of frames on isolated footings:Design insights and limitations

To date, a significant research effort has been devoted attempting to introduce novel seismic protection schemes, taking advantage of mobilization of inelastic foundation response. According to such an emerging seismic design concept, termed rocking isolation, instead of over-designing the footings of a frame (as in conventional capacity design), they are intentionally under-designed to promote uplifting and respond to strong seismic shaking through rocking, thus bounding the inertia forces transmitted to the superstructure. Recent research has demonstrated the potential effectiveness of rocking isolation for the seismic protection of frame structures, using a simple 1-bay frame as an illustrative example. This article: (a) sheds light in the possible limitations of rocking isolation, especially in view of the unavoidable uncertainties regarding the estimation of soil properties; (b) investigates the potential detrimental effects of ground motion characteristics; and (c) assesses the effectiveness of rocking isolation to more complex structures. It is shown that the concept may be generalized to 2-bay frames, and that even when foundation rocking is limited, the positive effect of foundation under-design remains, especially when it comes to very strong seismic shaking. In contrast, its effectiveness may be limited when the frame is subjected to combined horizontal and synchronous vertical acceleration components a possible scenario on the surface of alluvial basins

Hybrid Method for Analysis and Design of Slope Stabilizing Piles

Piles are extensively used as a means of slope stabilization. Despite the rapid advances in computing and software power, the design of such piles may still include a high degree of conservatism, stemming from the use of simplified, easy-to-apply methodologies. This paper develops a hybrid method for designing slope-stabilizing piles, combining the accuracy of rigorous three-dimensional (3D) finiteelement (FE) simulation with the simplicity of widely accepted analytical techniques. It consists of two steps: (1) evaluation of the lateral resisting force (RF) needed to increase the safety factor of the precarious slope to the desired value, and (2) estimation of the optimum pile configuration that offers the required RF for a prescribed deformation level. The first step utilizes the results of conventional slope-stability analysis. A novel approach is proposed for the second step. This consists of decoupling the slope geometry from the computation of pile lateral capacity, which allows numerical simulation of only a limited region of soil around the piles. A comprehensive validation is presented against published experimental, field, and theoretical results from fully coupled 3D nonlinear FE analyses. The proposed method provides a useful, computationally efficient tool for parametric analyses and design of slope-stabilizing piles

Rocking isolation of low-rise frame structures founded on isolated footings

This paper explores the effectiveness of a new approach to foundation seismic design. Instead of the present practice of over-design, the foundations are intentionally under-dimensioned so as to uplift and mobilize the strength of the supporting (stiff) soil, in the hope that they will thus act as a rocking-isolation mechanism, limiting the inertia transmitted to the superstructure, and guiding plastic 'hinging' into soil and the foundation-soil interface. An idealized simple but realistic one-bay two-story reinforced concrete moment resisting frame serves as an example to compare the two alternatives. The problem is analyzed employing the finite element method, taking account of material (soil and superstructure) and geometric (uplifting and P-? effects) nonlinearities. The response is first investigated through static pushover analysis. It is shown that the axial forces N acting on the footings and the moment to shear (M/Q) ratio fluctuate substantially during shaking, leading to significant changes in footing moment-rotation response. The seismic performance is explored through dynamic time history analyses, using a wide range of unscaled seismic records as excitation. It is shown that although the performance of both alternatives is acceptable for moderate seismic shaking, for very strong seismic shaking exceeding the design, the performance of the rocking-isolated system is advantageous: it survives with no damage to the columns, sustaining non-negligible but repairable damage to its beams and non-structural elements (infill walls, etc.)

Dimensional analysis of SDOF systems rocking on inelastic soil

Aiming to derive results of generalized applicability and provide a generalization framework for future research on the subject, this article performs a dimensional analysis of SDOF systems rocking on compliant soil, taking account of soil inelasticity, foundation uplifting, and P-?effects. The effectiveness of the proposed formulation, under static and dynamic conditions, is verified through numerical analyses of self-similar equivalent systems. Then, a parametric study is conducted to gain further insights on the key factors affecting the performance, with emphasis on metaplastic ductility and toppling rotation. It is shown that P-?effects may lead to a substantial reduction of (monotonic) moment capacity, especially in the case of slender and heavily loaded structures. Interestingly, this reduction in moment capacity is compensated (to some extent) by an overstrength that develops during cyclic loading. Asymmetric (near-field) seismic excitations tend to produce larger maximum and permanent rotation, compared to symmetric multi-cycle (far-field) excitations, which are critical in terms of settlement. The dimensionless toppling rotation ult /c (where c is the toppling rotation of the equivalent rigid block) is shown to be a function of the factor of safety against vertical loads FS v and the slenderness ratio h/B. In the case of lightly loaded systems (FS v ), soil plastification is limited and the metaplastic response approaches that of the equivalent rigid block: ult /c 1. The toppling rotation ult /c is shown to decrease with FS v : ult /c 0 for FS v 1. The role of the h/B becomes increasingly important when the response is governed by soil nonlinearity (FS v 1). Finally, an approximate simplified empirical equation is proposed, correlating ult /c with h/B and FS v

Interaction of foundation-structure systems with seismically precarious slopes:Numerical analysis with strain softening constitutive model

This paper studies the combined effects of earthquake-triggered landslides and ground shaking on foundation-structure systems founded near slope crests. Plane-strain nonlinear finite element dynamic analyses are performed. The soil constitutive model is calibrated against published data to simulate the (post-peak) softening behavior of soil during a seismic event and under the action of gravitational forces. The plastic shear zones and the yield accelerations obtained from our dynamic analyses are shown to be consistent with the slip surfaces and the seismic coefficients obtained by classical pseudostatic limiting equilibrium and limit analysis methods. The foundation and frame columns and beams are modeled as flexural beam elements, while the possibility of sliding and detachment (separation) between the foundation and the underlying soil is considered through the use of special frictional gap elements. The effects of foundation type (isolated footings versus a rigid raft) on the position of the sliding surface, on the foundation total and differential displacements, and on the distress of the foundation slab and superstructure columns, are explored parametrically. It is shown that a frame structure founded on a properly designed raft could survive the combined effects of slope failure and ground shaking, even if the latter is the result of a strong base excitation amplified by the soil layer and slope topography

Rocking-isolated frame structures:Margins of safety against toppling collapse and simplified design approach

This paper aims to explore the limitations associated with the design of "rocking-isolated" frame structures. According to this emerging seismic design concept, instead of over-designing the isolated footings of a frame (as entrenched in current capacity-design principles), the latter are under-designed with the intention to limit the seismic loads transmitted to the superstructure. An idealized 2-storey frame is utilized as an illustrative example, to investigate the key factors affecting foundation design. Nonlinear FE analysis is employed to study the seismic performance of the rocking-isolated frame. After investigating the margins of safety against toppling collapse, a simplified procedure is developed to estimate the minimum acceptable footing width B, without recourse to sophisticated (and time consuming) numerical analyses. It is shown that adequate margins of safety against toppling collapse may be achieved, if the toppling displacement capacity of the frame d (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand d. With respect to the capacity, the use of an appropriate "equivalent" rigid-body is suggested, and shown to yield a conservative estimate of d. The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SD is proposed as a conservative measure of d. The validity and limitations of such approximation are investigated for a rigid-block on rigid-base, utilizing rigorous analytical solutions from the bibliography; and for the frame structure on nonlinear soil, by conducting comprehensive nonlinear dynamic time history analyses. In all cases examined, the simplified SD approach is shown to yield reasonably conservative estimates

Simplified constitutive model for simulation of cyclic response of shallow foundations:Validation against laboratory tests

The nonlinear response of shallow foundations has been studied experimentally and analytically. However, the engineering community is not yet convinced of the applicability of such concepts in practice. A key prerequisite is the ability to realistically model such effects. Although several sophisticated constitutive models are readily available in the literature, their use in practice is limited, because (1) they typically require extensive soil testing for calibration; (2) as they are implemented in highly specialized numerical codes, they are usually restricted to simple superstructures; and (3) in most cases, they can only be applied by numerical analysis specialists. Attempting to overcome some of these difficulties, this paper develops a simplified but fairly comprehensive constitutive model for analysis of the cyclic response of shallow foundations. On the basis of a kinematic hardening constitutive model with Von Mises failure criterion (readily available in commercial finite element codes), the model is made pressure sensitive and capable of reproducing both the low-strain stiffness and the ultimate resistance of clays and sands. Encoded in ABAQUS through a simple user subroutine, the model is validated against (a) centrifuge tests of shallow footings on clay under cyclic loading and (b) large-scale tests of a square footing on dense and loose sand under cyclic loading, conducted in the European Laboratory for Structural Analysis for the TRISEE project. The performance of the model is shown to be quite satisfactory, and discrepancies between theory and experiment are discussed and potential culprits are identified. Requiring calibration of only two parameters and being easily implemented in commercial FE codes, the model is believed to provide an easily applicable engineering solution