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Multistory Building Frames and Shear Walls Founded on “Rocking” Spread Footings
Abstract
The seismic performance of a two-story 2D frame and a five-story 3D frame–shear-wall structure founded on spread (isolated) footings is investigated. In addition to footings conventionally designed in accordance with “capacity-design” principles, substantially under-designed footings are also used. Such unconventional (“rocking”) footings may undergo severe cyclic uplifting while inducing large plastic deformations in the supporting soil during seismic shaking. It is shown that thanks to precisely such behaviour they help the structure survive with little damage, while experiencing controllable foundation deformations in the event of a really catastrophic seismic excitation. Potential exceptions are also mentioned along with methods of improvement.
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This paper presents the results of a series of shake table tests of two 460-mm-diameter columns supported on 1.5-meter-square shallow rocking foundations. The tests were conducted using the Large Outdoor High-Performance Shake Table of the Network for Earthquake Engineering Simulation at the University of California at San Diego. The first specimen was aligned with the uniaxial direction of shaking, and the second was positioned in a skew configuration. The specimens were placed inside a soil-confining box 10.1 m long and 4.6 m wide with a 3.4-m height of clean sand compacted at 90% relative density. Three series of tests were performed; each had different groundwater and backfill conditions. The test protocols included up to six historical ground motions and resulted in peak drift ratios up to 13.8%. For peak drift ratios up to 6.9%, the rocking foundations performed very well, with residual drift ratios between 0.5 and 0.9% depending on the backfill conditions and with minimal settlements and no structural damage.
The uplifting and rocking of slender, free-standing structures when subjected to ground shaking may limit appreciably the seismic moments and shears that develop at their base. This high-performance seismic behavior is inherent in the design of ancient temples with emblematic peristyles that consist of slender, free-standing columns which support freely heavy epistyles together with the even heavier frieze atop. While the ample seismic performance of rocking isolation has been documented with the through-the-centuries survival of several free-standing ancient temples; and careful post-earthquake observations in Japan during the 1940's suggested that the increasing size of slender free-standing tombstones enhances their seismic stability; it was George Housner who 50 years ago elucidated a size-frequency scale effect that explained the "counter intuitive" seismic stability of tall, slender rocking structures. Housner's 1963 seminal paper marks the beginning of a series of systematic studies on the dynamic response and stability of rocking structures which gradually led to the development of rocking isolation-an attractive practical alternative for the seismic protection of tall, slender structures. This paper builds upon selected contributions published during this last half-century in an effort to bring forward the major advances together with the unique advantages of rocking isolation. The paper concludes that the concept of rocking isolation by intentionally designing a hinging mechanism that its seismic resistance originates primarily from the mobilization of the rotational inertia of its members is a unique seismic protection strategy for large, slender structures not just at the limit-state but also at the operational state.
A new seismic design philosophy is illuminated, taking advantage of soil "failure" to protect the superstructure. Instead of over-designing the foundation to ensure that the loading stemming from the structural inertia can be "safely" transmitted onto the soil (as with conventional capacity design), and then reinforce the superstructure to avoid collapse, why not do exactly the opposite by intentionally under-designing the foundation to act as a "safety valve" ? The need for this "reversal" stems from the uncertainty in predicting the actual earthquake motion, and the necessity of developing new more rational and economically efficient earthquake protection solutions. A simple but realistic bridge structure is used as an example to illustrate the effectiveness of the new approach. Two alternatives are compared : one complying with conventional capacity design, with over-designed foundation so that plastic "hinging" develops in the superstructure; the other following the new design philosophy, with under-designed foundation, "inviting" the plastic "hinge" into the soil. Static "pushover" analyses reveal that the ductility capacity of the new design concept is an order of magnitude larger than of the conventional design: the advantage of "utilising" progressive soil failure. The seismic performance of the two alternatives is investigated through nonlinear dynamic time history analyses, using an ensemble of 29 real accelerograms. It is shown that the performance of both alternatives is totally acceptable for moderate intensity earthquakes, not exceeding the design limits. For large intensity earthquakes, exceeding the design limits, the performance of the new design scheme is proven advantageous, not only avoiding collapse but hardly suffering any inelastic structural deformation. It may however experience increased residual settlement and rotation: a price to pay that must be properly assessed in design.
ASCE 41-13 supports three methods of modeling the soil-structure interaction for rocking footings as components of a foundation-building system. Method 1 uses uncoupled moment, shear, and axial springs; Method 2 uses a nonlinear gapping bed of springs; and, Method 3 is used for structural footings that are flexible relative to the underlying soil. New component action tables in ASCE 41-13 provide modeling parameters and acceptance criteria for nonlinear and linear analysis of shallow foundation components. The values in the component action tables for nonlinear procedures were largely based upon analysis of foundation performance in model tests on rocking foundations. The primary measure to assess foundation performance is residual settlement or uplift. The acceptance criteria for linear analysis procedures (m-factors) were derived from the allowable rotations for nonlinear procedures. A design example is presented in an appendix to illustrate differences between the current and previous versions of ASCE 41 and ASCE31.
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 Bmin, 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 δtopl (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand δdem. With respect to the capacity, the use of an appropriate “equivalent” rigid-body is suggested, and shown to yield a conservative estimate of δtopl. The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SDmax is proposed as a conservative measure of δdem. 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 SDmax approach is shown to yield reasonably conservative estimates.
In good soil conditions, spread footings for bridges are less expensive than deep foundations. Furthermore, rocking shallow foundations have some performance advantages over conventional fixed-base foundations; they can absorb some of the ductility demand that would typically be absorbed by the columns, and they have better recentering characteristics than conventional reinforced-concrete (RC) columns. Foundations designed for elastic behavior do not have these benefits of nonlinear soil-structure interaction. One potential disadvantage of rocking systems is that they can produce significant settlement in poor soil conditions. Centrifuge model tests were performed to account for the interaction between soil, footing, column, deck and abutments systems. Bridge systems with rocking foundations on good soil conditions are shown to perform well and settlements are small. An improved method for quantification of settlements is presented. The model tests are described in some detail. One of the important factors limiting the use of rocking foundations is the perception that they might tip over; experiments show that tipping instability is unlikely if the foundations are properly sized. In one experiment, a column for a system with large fixed-base foundation collapsed while the systems with smaller rocking foundations did not collapse. DOI: 10.1061/(ASCE)GT.1943-5606.0000605. (C) 2012 American Society of Civil Engineers.
Rocking isolation is a relatively new design paradigm advocating the intense rocking response of the superstructure as a whole, instead of flexural column deformation. This is accomplished through intentionally underdesigning the foundation to guide plastic hinging below the ground surface rather than in the columns. A 2-story, 2-bay asymmetric frame is used to explore the effectiveness of this novel design approach. Finite-element dynamic analyses are performed using as seismic excitation idealized pulses and 20 real accelerograms, taking into account material (soil and superstructure) and geometric (uplifting and P- effects) nonlinearities. A conventionally, Eurocode-designed frame and its foundation are compared to a design featuring the same frame but with substantially underdesigned (unconventional) footings. It is found that the performance of the unconventional system is advantageous, as not only does it escape collapse but it also suffers reparable damage. Despite their reduced width, the residual settlements of the underdesigned footings are comparable to those of the conventional ones. However, the analyses also reveal that residual rotation and differential settlement of the underdesigned footings may be unavoidable and must be critically evaluateda need exaggerated by the asymmetry of the examined frame. Three possible ways of improvement at the foundation level are studied: (1) a single conventional tie beam, monolithically connected to the footings; (2) two separate tie beams hinged at each footing (allowing rotation, but resisting axial deformation); and (3) a hybrid system, comprising a single continuous tie beam connecting the three footings but externally hinged to each of them. The first solution hardly offers improvement, as it hinders rocking, and the second fails to reduce differential settlements. The hybrid solution provides encouraging results in terms of residual rotation and differential settlement, while it does not hinder the development of beneficial rocking isolation mechanisms and fully restrains horizontal differential movements.
Although modern seismic codes have undoubtedly led to safer structures, the seismic vulnerability of metropolitan areas is unavoidably governed by that of older buildings, which constitute the vast majority of the current building stock. Quite alarmingly, even relatively moderate intensity earthquakes have been proven capable of challenging their structural integrity, leading to severe damage or collapse. Therefore, there is an urgent need to assess the vulnerability of existing structures and to evaluate the efficiency of novel retrofit techniques. This paper studies experimentally the seismic performance of an existing three-storey building, retrofitted through addition of shear walls. Emphasis is placed on the foundation of the shear walls, and two design alternatives are comparatively assessed: (a) conventional design according to current seismic codes and (b) ‘rocking isolation’ by reducing the size of the foundation. A series of reduced-scale shaking table tests are conducted at the Laboratory of Soil Mechanics of the National Technical University of Athens. The physical model encompasses the structural system, along with the foundations, and the soil. The nonlinearity of structural members is simulated through specially designed and carefully calibrated artificial plastic hinges. The vulnerability of the original structure is confirmed, as it is found to collapse with a soft-storey mechanism when subjected to moderate intensity shaking. The conventionally retrofitted structure is proven capable of sustaining larger intensity shaking, and the rocking-isolated structure is shown to offer increased safety margins. Thanks to its inherent self-centering mechanism, the rocking system is characterized by reduced permanent drifts. Copyright © 2014 John Wiley & Sons, Ltd.
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.
Shallow foundations supporting building structures might be loaded well into their nonlinear range during intense earthquake loading. 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. Five series of tests on a large centrifuge, including 40 models of shear wall footings, were performed to study the nonlinear load-deformation characteristics 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. The moment capacity was not observed to degrade with cycling, but due to the deformed shape of the footing–soil interface and uplift associated with large rotations, stiffness degradation was observed. Permanent deformations beneath the footing continue to accumulate with the number of cycles of loading, though the rate of accumulation of settlement decreases as the footing embeds itself.
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