Drift Limits Research Articles

Method of Reliability-Based Seismic Design. II: Calibration of Code Parameters

This is the second part of a two-part investigation on the method of a reliability-based seismic design. To account for large uncertainties in structural design under seismic load, a method of calibration of the design parameters in seismic codes is proposed based on the consideration of satisfactory performance under future earthquakes in terms of reliability. The calibration is carried out by a minimization of the difference between target and actual reliabilities against serviceability and ultimate limit states over a given period of time. The response surface method (RSM) in conjunction with a central composite design is used to expedite the minimization solution process. To reduce the computational effort required for reliability evaluation under seismic loads, the equivalent nonlinear system (ENS) developed in part I is used for dynamic-response analysis of multi–degree-of-freedom (MDOF) inelastic structures. Numerical examples on the calibration of the earthquake load factor and drift limit for selected target limit-state probabilities are given. Parametric studies are also carried out to examine the dependence of these parameters on the target reliability levels against both serviceability and ultimate limit states.

Drift control and damage in tall buildings

The interstorey drift limitations in earthquake codes of various countries around the world, have been reviewed. It is emphasized that, the aseismic safety of a tall building as well as its susceptibility to nonstructural damage are primarily indexed to its ability to restrict the relative storey displacements, in addition to its adequate strength, ductility and toughness. A moment resisting frame building satisfying all requirements of strength and ductility may still be subject to severe nonstructural damage, if the interstorey drifts are not restricted properly by means of shear walls. Several stringent deflection criteria as well as a damage control index are introduced to be conscientiously determined and checked during the design calculations for the purpose of controlling damage especially to nonstructural elements.

Interpretation of significant ground-response and structure strong motions recorded during the 1994 Northridge earthquake

Abstract Some of the largest accelerations and velocities ever recorded at ground-response and structural sites occurred during the Northridge earthquake. These motions are greater than most existing attenuation models would have predicted. Although the motions are large, the correspondence between measured acceleration and damage requires further study, since some sites with high acceleration experienced only moderate damage. Also, some peak vertical accelerations were larger than the horizontal, but in general, they are smaller and fit the pattern observed in previous earthquakes. Strong-motion records processed to date show significant differences in acceleration and velocity waveforms and amplitudes across the San Fernando Valley. Analysis of processed data from several buildings in the San Fernando Valley indicates that short-period buildings such as shear-wall buildings experienced large forces and relatively low inter-story drift during the Northridge earthquake. However, long-period (1 to 5 sec) steel or concrete moment-frame buildings experienced large inter-story drift. For this earthquake, accelerations did not always amplify from base to roof for flexible structures like the moment-frame buildings, but the displacements were always larger at the roof. The drifts at many of the moment-frame buildings were larger than the drift limit for working stress design in the building code. The records from a base-isolated building indicate that high-frequency motion was reduced significantly by the isolators. The isolators deformed about 3.5 cm, which is much less than the design displacement. The records from a parking structure show important features of the seismic response of this class of structure.

Dual-level designs of buildings under seismic loads

Three methods of dual-level seismic design for buildings are proposed based on consideration of reliability against the serviceability and ultimate limit states. The first is a method of calibration of design parameters according to the two target reliability levels within the context of current code procedures. The method is demonstrated by calibration of seismic load factor and drift limit. The second is an extension of the design earthquake approach to allow consideration of two levels of design earthquake. The performance is assured by linear and nonlinear equivalent static (pushover) analyses. It produces designs which come closer to the design objectives of most current codes. The third is an alternative to the current design procedures. It uses uniform hazard response spectra and a pushover analysis-based equivalent single-degree-of-freedom system to explicitly account for variability and uncertainty in the seismic loads and inelastic response behavior of the structures. This avoids the use of the controversial response reduction factor. Uncertainties in the soil amplification and structural system modeling are accounted for by corresponding design factors similar in concept to the LRFD method. It ensures that the structure meets local (interstory) drift and global ductility requirements with specified probabilities.

Low-Rise Shear Wall Ultimate Drift Limits

Drift limits for low aspect ratio reinforced concrete shear walls are investigated by reviewing the open literature for appropriate experimental data. Based on the geometry of structures designed for protective purposes and concerns regarding their response during seismic loading, data are obtained from pertinent references for which the wall aspect ratio is less than or equal to approximately 1, and for which loading is cyclic in nature (typically displacement controlled). In particular, lateral deflections at ultimate load, and at points in the softening region beyond ultimate for which the load has dropped to 90, 80, 70, 60, and 50 percent of its ultimate value, are obtained and converted to drift information. The statistical nature of the data is also investigated. For example, at ultimate load the median drift limit is 0.72 percent, and it increases to 1.84 percent when the load drops to 50 percent of its ultimate value. These data are shown to be lognormally distributed, and an analysis of variance is performed. The use of these statistics to estimate probability of failure for a shear wall structure is illustrated. Finally, a brief comparison of drift limit results with existing seismic design code requirements is presented.

Scale invariance in biased diffusion.

We have studied hopping transport on a one-dimensional disordered chain in which the hopping rates are characterized by scale-invariant distributions. As a model for dispersive transport, the distribution contains a large weight of small hopping rates. Emphasis has been placed on the range dependence of the diffusion coefficient D(L)\ensuremath{\sim}${\mathit{L}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\theta}}}$ and the frequency dependence of the electrical conductivity \ensuremath{\sigma}(\ensuremath{\omega})\ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathit{x}}$, with x=\ensuremath{\theta}/(2+\ensuremath{\theta}), so that comparison with conductivity experiments can be made. In the presence of a biased electric field, the frequency dependence of the conductivity \ensuremath{\sigma}(\ensuremath{\omega}) is found to cross over from ${\mathrm{\ensuremath{\omega}}}^{\mathit{x}}$ (diffusive limit) to ${\mathrm{\ensuremath{\omega}}}^{\mathit{y}}$ with y=\ensuremath{\theta}/(1+\ensuremath{\theta}) (drift limit). The transport exponents are calculated explicitly in terms of the parameters of the distribution. Numerical simulations have also been carried out to confirm the above scaling results. Excellent agreement is found.

UBC Seismic Serviceability Regulations: Critical Review

This paper discusses the widely accepted seismic design limit state philosophy and the serviceability limit state requirements for stress and drift controls in the 1988 \IUBC\N. The limit state philosophy implemented in the \IUBC\N is compared with that in the Japanese code. Although the service (or moderate) designa earthquake is explicitly specified in the Japanese code, this design earthquake is indirectly assumed in the \IUBC\N by specifying a drift limit that is inversely proportional to the \IR\dw\N factor. The study shows that \IUBC\N cannot control the level of stress in steel building structures for service design earthquakes; the allowable seismic stress implied by \IUBC\N was found to be too high for ductile structures and too low for structures of limited ductility. The \IUBC\N story drift limit of 0.04/\IR\dw\N (or 0.03/\IR\dw\N) may be too high, and the drift limit of 0.005 (or 0.004) is too conservative for buildings with low \IR\dw\N values.

Establishing R (or Rw) and Cd Factors for Building Seismic Provisions

This paper derives the basic formulas for establishing the response modification factor R and the displacement amplification factor Cd used in the National Earthquake Hazards Reduction Program (NEHRP) recommended provisions. An extension of the approach is used to derive the system modification factor Rw used in the 1988 Uniform Building Code. These terms are primarily functions of both the structural overstrength and structural ductility factors. Because of the empirical nature of the NEHRP recommended values for these factors, it is difficult to justify the relative values between R and Cd factors for most of the building systems. The structural overstrength factor, which can be determined from analytical studies, depends on structural redundancy, story drift limitations, multiple load combinations, strain hardening, participation of nonstructural elements, and other parameters. Although the ductility factor of an individual structural member can be determined experimentally, there is no general agreeme...

Assessment of Seismic Structural Damage

Most existing structural seismic damage measures are based either implicitly or explicitly on some measure of the maximum ductility attained or desired, or on peak acceleration. In this paper, two completely new damage measures are described, one based on the concept of equivalent hysteretic cycles of deformation and the second on concepts derived from low‐cycle fatigue theory. When combined, these techniques permit one to evaluate damage based not only on ductility principles, but also on the repetitive cyclic nature of the deformation response. Examples of the applicability of the damage measures are presented herein through comparisons with published experimental data, in which the recorded responses include hysteretic behavior. Two other types of possible applications also are demonstrated; namely, construction of response spectra for representing nonlinear effects, and a tentative new approach to building code drift limits. Other applications are obvious, such as evaluating remaining margins of strength. It is believed that the simplicity of the approaches, when adapted to specific applications, will make them especially attractive in the future for applications in practice as well as for research purposes.

Late Quaternary Ice-Surface Fluctuations of Hatherton Glacier, Transantarctic Mountains

AbstractFormer longitudinal profiles of Hatherton Glacier, an outlet through the Transantarctic Mountains, constrain nearby polar plateau elevations and ice-shelf grounding in the southwestern Ross Embayment. Four gravel drift sheets of late Quaternary age beside Hatherton Glacier are, from youngest to oldest, Hatherton, Britannia I, Britannia II, and Danum. The Hatherton drift limit is uniformly 20 to 70 m above the present ice surface. The Britannia II drift limit is within 100 m of the present surface of uppermost Hatherton Glacier but is 450 m above middle Hatherton Glacier. Extrapolation of this profile downglacier indicates a surface elevation 1100 m above the present Ross Ice Shelf. The Britannia I drift limit is parallel to, but 50–100 m below, Britannia II drift. The Danum drift limit is parallel to, but 50–100 m above, the Britannia II profile. From correlation with drifts near McMurdo Sound and from local 14C dates, we assign an early Holocene age to Hatherton drift, a late Wisconsin age to Britannia drifts, and an age of marine isotope Stage 6 to Danum drift. By our age model, the upper reaches of Hatherton Glacier (and presumably the adjacent polar plateau) have not exceeded their current elevations by more than 100–150 m during the last two complete global glacial-interglacial cycles, whereas the middle and lower reaches of Hatherton Glacier have thickened considerably during the last two global glaciations (late Wisconsin and marine isotope Stage 6). The effect of ice-shelf grounding probably was the major control of these changes of Hatherton Glacier. Holocene ice-surface lowering probably represents the last pulse of grounding-line recession in the southwestern Ross Embayment.

Linear theory of drift-tearing and -interchange modes

A drift dispersion relation, as applied to a resistive incompressible plasma in cylindrical geometry, is derived. This dispersion relation incorporates both drift-tearing and drift-interchange modes and is valid throughout the collisional regime by including kinetic theory factors. The dispersion relation reduces to the drift-tearing dispersion relation in the zero pressure gradient limit, and to the classical resistive dispersion relation in the zero drift limit. The electron temperature-gradient instability is still present. Now, however, the introduction of the drift-interchange instability increases the growth rate further above the drift-tearing case.

Ice-sheet Moraines in southern Skye

Early research on the glacial history of Skye indicated that at the last ice sheet maximum, ice moving westwards from the Scottish mainland overran the Kyleakin Hills but was deflected around an independent ice cap centred on the Cuillins and Red Hills, and that during a subsequent readvance locally-nourished glaciers radiated outwards from these mountain areas ([Harker 1901][1]; [Clough and Harker 1904][2]; [Peach et al. 1910][3]). Recent geomorphological mapping of southern Skye has revealed abundant evidence for a single readvance of locally-nourished glaciers during the Loch Lomond Stadial of c. 11–10 ka BP ([Ballantyne 1988; Walker et al. 1988][4]; Fig. 1). During the mapping programme evidence was also found for two former ice limits that relate to the earlier encroachment of mainland ice across southern Skye. This communication describes this evidence and discusses its significance. The first former ice limit occurs c. 1 km W of Strollamus ([NG 591271]; Fig. 1), where a clear double lateral moraine up to 2 m high and composed largely of erratic granite boulders descends in a NW direction from 150 m OD to 70 m OD over a distance of 300 m. Conspicuous drift limits marking the south-westwards extent of abundant granite and gabbro erratics (derived respectively from the Eastern Red Hills Centre and the Broadford Gabbro to the SE) continue this former ice margin to both the SE and NW. The northern extent of the drift limit is truncated by a lateral moraine that marks the former margin of a glacier that . . . [1]: #ref-4 [2]: #ref-3 [3]: #ref-5 [4]: #ref-1

The last glaciers (Loch Lomond Advance) in Snowdonia, N. Wales

AbstractEvidence for 35 former cwm glaciers has been mapped in Snowdonia, N. Wales. Glacial limits are based on end moraines, boulder and drift limits, and the down‐valley extent of hummocky moraine. Protalus ramparts indicate that at least 16 semi‐permanent snow beds down to altitudes of 150 m also existed. Radiocarbon dates and pollen stratigraphy indicate that the glaciers and snow beds belong to the Loch Lomond (Younger Dryas) Stadial. The existence of a large number of ‘Older Series Moraines’ is questionned. Glacier reconstruction and contouring allows calculation of fan line altitudes, and trend surface analysis indicates that they rise from 450 m in the southwest to 700 m in the northeast. It is inferred that mean July temperature at sea‐level was around 8·5°C. Two differences between north and south Britain are recognized. Firstly in Snowdonia, as in the Lake District and Southern Uplands, the dominance of southerly air streams appears less than in the Scottish Highlands. Secondly, whereas in the Scottish Highlands, the glaciers appear to have stagnated in situ following initial active retreat, some of those farther south were active during much of the time their margins retreated.

A Multiple-Frequency Phase Comparison Technique for the Determination of Remote Layer Thickness

A continuous-wave phase comparison technique which provides at least an order of magnitude improvement in accuracy over modulated carrier systems which operate in the same spectrum is described in this paper for the remote determination of the thickness of layered targets consisting of a known number of dielectric layers, each of a known maximum thickness. This system uses rationally related frequencies such as the fundamental and its harmonics to establish a multifrequency coherence relationship whereby a phase reference between frequencies can be conserved and information extracted from just the received and not the transmitted signals. Consequently, Doppler effects due to motion between the target layer and the apparatus, as well as local oscillator stability and drift limitations are avoided. Thus this system can measure the parameters of remote layered targets by interferometric techniques without the distance being a constraint.

Design of an Eccentrically Braced Steel Frame

In the design of earthquake resistant structures, two basic requirements must be met. First, the structure must remain serviceable during the ordinary, frequently occurring load applications. This is usually accomplished by designing the structure so that it remains elastic and provides adequate stiffness to limit deflections. The second requirement is to preclude a disaster during a major earthquake. For such an extreme event, considerable inelastic deformation is usually allowed. Thus, structures must possess sufficient ductility and inelastic stability to withstand these extreme excitations. Recent studies have shown that eccentrically braced frames offer considerable potential as seismic resistant structures. They are very stiff and can easily satisfy story drift limitations, and they can be designed to provide excellent inelastic behavior and energy dissipation characteristics. Therefore, such structures are likely to remain serviceable during the smaller, more frequently occurring earthquakes, and prevent collapse during severe, infrequent earthquakes. Eccentrically braced steel frames also appear to be very economical structures, indicating savings for some framing arrangements on the order of 30% in weight of steel over unbraced frames. This unique structural system offers several design advantages, but it also employs several unusual design requirements. The purpose of this paper is to summarize these special design requirements and to show a simple example illustrating their application.

A Late-Glacial Ice Cap in the Central Grampians, Scotland

Using evidence provided by hummocky moraines, end moraines, till sheets, drift limits, erratics, meltwater channels, outwash deposits, ice-contact fluvioglacial forms and major periglacial forms, an ice cap (with associated outlet glaciers) that developed in the central Grampians in Late-glacial times is reconstructed using a three-dimensional approach. The former ice surface is contoured at 50 m intervals. The ice mass had an area of nearly 3oo km2, a volume of 32 km3 and an average thickness of about 10 m. Former firn lines are determined and inferences made about contemporary temperatures and the distribution of precipitation. THE area investigated lies in the centre of the Grampian Highlands astride the major east-west watershed (for location see inset, Fig. 2). It is bounded in the west by the Pass of Drumochter glacial breach (D. L. Linton, I951) and in the east by the straight, fault-guided Glen Tilt trench. Part of the area is known as Gaick Forest, but for brevity the whole will be referred to as the Gaick area. The main relief feature is a plateau at 700-930 m that is limited almost everywhere by a sharp 200-450 m descent to lower ground (Fig. I). The plateau is especially well developed in the western half of the area, although it is here cut clean across by a major glacial breach 400 m deep (Loch an Duin breach). The bounding slopes of the plateau are broken by numerous valleys that trend perpendicular to its edge and thus collectively form a radial system. Unrelated to this radial pattern, on the northern edge of the area, is the Glen Feshie glacial breach (Linton, 1949), immediately beyond which are the Cairngorms. Apart from Linton's contributions on glacial breaching and a brief account by J. K. Charlesworth (I955), the only published work on the glaciation of the Gaick area is by G. Barrow et al. (1913). These authors concluded that glacier ice that accumulated in the Gaick area was subsequently largely surrounded and partly overwhelmed by an ice sheet centred in the western Grampians. Local ice later became important again in parts of the area as the exotic ice became less powerful. The limits of local ice were not specified and a readvance was not proposed. BASIC FIELD EVIDENCE

Pingos of Cardiganshire and the Latest Ice Limit

THE first attempt1 to define the extent of the most recent glaciation in South-West Wales, the “Newer Drift limit”, has been disputed by authors2–4 who place it further north, leaving Cardiganshire almost or quite ice-free. More recently, since the availability of radiocarbon dating, a latest glacial advance almost to the shore of the Bristol Channel has been postulated5. The distribution of pingos in Cardiganshire (Fig. 1) may contribute to a resolution of this disagreement.

THE TERTIARY HISTORY OF EAST YORKSHIRE

Since the discovery of the so-called Bridlington Crag in 1835 (2) the possible existence of Tertiary rocks in Yorkshire has been a matter of speculation but Phillips’ conclusion that Tertiary strata did not occur in Yorkshire has been accepted by most Yorkshire geologists. In 1904, Stather (13) reported the presence of scattered pebbles of quartzite over the Wolds even above the drift limit and concluded that they represented either the relics of an early glaciation or even of a Tertiary stratum. There exists in the Hull Museum a map produced by R. Mortimer, never officially published, showing a distribution of masses of sand and gravel covering the Chalk of the Wolds and allocated by him to the Eocene, Miocene and Pliocene periods. There is now no indication of such sand being exposed so far as the writer has been able to discover but the late Mr. Stather gave the author a sample of sand collected some thirty or forty years ago from Thixendale, one of the localities marked by Mortimer. The analysis of this sand is given later in this paper. Others of Mortimer’s areas seem to be simply the ordinary chalk gravel of glacial date. Among the many tumuli which are scattered on the Yorkshire Wolds and were excavated by J. R. Mortimer (10) there are some, 12 in all, which are described as having been dug, not in Chalk, but in sand which existed as a pipe in the Chalk. All these tumuli are found above the drift ...