Wave propagation in a seven-story reinforced concrete building: I. Theoretical models

For transient, high frequency, and pulse like excitation of structures in the near field of strong earthquakes, the classical design approach based on relative response spectrum and mode superposition may not be conservative. For such excitations, it is more natural to use wave propagation methods. In this paper (Part I), we review several two-dimensional wave propagation models of buildings and show results for theoretical dispersion curves computed for these models. We also estimate the parameters of these models that would correspond to a seven-story reinforced concrete building in Van Nuys, California. Ambient vibration tests data for this building imply vertical shear wave velocity β_z=112 m/s and anisotropy factor β_x/β_z=0.55 for NS vibrations, and β_z=88 m/s and β_x/β_z=1 for EW vibrations. The velocity of shear waves propagating through the slabs is estimated to be about 2000 m/s. In the companion paper (Part II), we estimate phase velocities of vertically and horizontally propagating waves between seven pairs of recording points in the building using recorded response to four earthquakes.     

Evidence of nonlinear site response in HVSR from SMART1 (Taiwan) data

Deamplification of strong motion and the increase of the effective period of soil deposits are typical nonlinear effects; we seek them in SMART1-array data by applying the horizontal-to-vertical spectral ratio (HVSR) technique. The recordings, from four soil and one rock stations, represent 23 earthquakes (M_L 4.9–7.0); PGA varies between 20–260 cm/s². For each station, mean HVSR curves are calculated for two PGA ranges: <75 cm/s² and >100 cm/s² (weak and strong motion). At the soil stations, the “weak” (linear) and “strong” (nonlinear) responses are significantly different. Below 1–1.8 Hz, the nonlinear response exceeds the linear one. Above 2 Hz, the nonlinear response drops below the linear one and above 4–6 Hz below unity (deamplification). From 10 to 16 Hz, the two responses converge. One soil site shows significant negative correlation between resonance frequency and ground acceleration. Such behaviour agrees with other empirical studies and theoretical predictions. Our results imply that the HVSR technique is sensitive to ground-motion intensity and can be used to detect and study nonlinear site response.     

Seismic response evaluation of the linked column frame system

The linked column frame (LCF) system is proposed as a seismic load resisting system that uses conventional components to limit seismic damage to relatively easily replaced elements. The LCF features a primary lateral system, denoted the linked column, which is made up of dual columns connected with replaceable links, and a secondary flexible moment frame system with beams having fully restrained connections at one end and simple connections at the other. The linked columns are designed to limit seismic forces and provide energy dissipation via link yielding, while preventing damage to the moment frame under certain earthquake hazard levels. A design procedure is proposed that ensures plastic hinges develop in the links of the linked columns at a significantly lower story drift than when plastic hinges develop in the moment frame beams. The large drift difference helps enable design of this system for two distinct performance states: rapid return to occupancy, where only link damage occurs and relatively simple link replacement is possible, and collapse prevention, where both the links and the beams of the moment frame may be damaged. A series of 3‐story, 6‐story, and 9‐story prototype LCF buildings were designed using the proposed design approach. Nonlinear models were developed for the designs with the link models validated using recent experimental results. The seismic response of these systems was investigated for ground motions representing various seismic hazard levels. Results show that the LCF system not only provides collapse prevention, but also has the capability of limiting economic loss by reducing structural damage and allowing for rapid return to occupancy following earthquakes with shorter return periods. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental evidence for flexibility of a building foundation supported by concrete friction piles

This article explores the possibility to measure deformations of building foundations from measurements of ambient noise and strong motion recordings. The case under study is a seven-storey hotel building in Van Nuys, California. It has been instrumented by strong motion accelerographs, and has recorded several earthquakes, including the 1971 San Fernando (M_L=6.6, R=22 km), 1987 Whittier–Narrows (M_L=5.9, R=41 km), 1992 Landers (M_L=7.5, R=186 km), 1992 Big Bear (M_L=6.5, R=149 km), and 1994 Northridge (M_L=6.4, R=1.5 km) earthquake and its aftershocks (20 March: M_L=5.2, R=1.2 km; 6 December, 1994: M_L=4.3, R=11 km). It suffered minor structural damage in 1971 earthquake and extensive damage in 1994. Two detailed ambient vibration tests were performed following the Northridge earthquake, one before and the other one after the 20 March aftershock. These included measurements at a grid of points on the ground floor and in the parking lot surrounding the building, presented and analyzed in this article. The analysis shows that the foundation system, consisting of grade beams on friction piles, does not act as a “rigid body” but deforms during the passage of microtremor and therefore earthquake waves. For this geometrically and by design essentially symmetric building, the center of stiffness of the foundation system appears to have large eccentricity (this is seen both from the microtremor measurements and from the earthquake recordings). This eccentricity may have contributed to strong coupling of transverse and torsional responses, and to larger than expected torsional response, contributing to damage during the 1994 Northridge, earthquake.     

Earthquake-induced variations in the composition of the water in the geothermal reservoir at Vulcano Island, Italy

During 1979–1989, variations were observed in the oxygen composition of the water contained in the geothermal reservoir at Vulcano Island, Italy.The reservoir water, that has a magmatic origin, showed an oxygen composition of +1.0±0.5‰ δ¹⁸O during periods without local tectonic earthquakes, and an oxygen composition of +3.4±0.5‰ δ¹⁸O after the highest-energy seismic activity that occurred recently near the island. A slight increase of the δ¹⁸O value in the reservoir water was also observed after a low-energy sequence of tectonic earthquakes that occurred at very shallow depth just beneath Vulcano Island. These ¹⁸O variations in the reservoir water are consistent with earthquake-induced increases in the contribution from high-temperature δ¹⁸O-rich magmatic condensate to the geothermal reservoir, and with subsequent decreases in the δ¹⁸O value due to ¹⁸O exchanges at the temporarily increased reservoir temperature during reactions between the highly reactive magmatic condensate and the local rocks.Only minor changes in the deuterium composition of the reservoir water occurred with time, as the δD value in the magmatic condensate released from the magma after major local earthquakes quickly approached the δD value of the water contained in the geothermal reservoir.Also the chloride concentration in the reservoir water appears to be linked to the contribution from the magmatic fluid. This chloride content seems not to have undergone major changes with time, as it may be buffered by temporary increases in the reservoir temperature up to values >300°C induced by major local earthquakes. This mechanism may possibly occur also in other magmatic–hydrothermal systems.     

Volcanic earthquakes, and their relationship to eruptions at Ruapehu and Ngauruhoe volcanoes

Crustal earthquakes near Ruapehu and Ngauruhoe fall into two classes, each of which can be subdivided. On the one hand, there are high-frequency events ( 3 Hz) with sharp, well-defined phases, mainly concentrated beneath Ruapehu Crater Lake. Low-frequency events (< 2 Hz), on the other hand, are common at shallower depths under both volcanoes. These are usually emergent multiple events, and are often closely associated with eruptions.The low-frequency events resemble Minakami's B-type and explosion earthquakes, but sometimes occur where no vent exists and rather deeper than his formal definition (< 1 km) permits. More importantly, they lack reliable criteria (wave-form or magnitude differences) to distinguish between his two groups. Whether or not they accompany an eruption (Minakami's definition of explosion earthquake) appears to depend on whether the volcanoes are in a “closed-” or “open-vent” condition. The high-frequency earthquakes are similar in wave-form to Minakami's A-type. However, many at Ruapehu (here designated “roof-rock” earthquakes) originate at shallower depths than the B-type earthquakes, which is contrary to Minakami's definition.Difficulty in applying Minakami's classification rigorously, and the fact that low frequencies may be due to abnormal attenuation of higher frequencies along the path, rather than to their suppression or absence at the source, has led to reclassification of earthquakes near the volcanoes into two broad groups, tectonic and volcanic. The former includes all high-frequency earthquakes, and those discrete events in which dominant low frequencies are due to path effects. The latter includes multiple and emergent events which show evidence of prolonged or repetitive source mechanism. Dominant low frequencies are ascribed to occurrence in heat-weakened material, and high frequencies to instantaneous source mechanisms operating in competent rock. The term volcano-tectonic describes tectonic earthquakes within some arbitrary distance of a volcano.At Ngauruhoe and Ruapehu, volcanic earthquakes accompany explosive, vent-clearing eruptions. Subsequent “open-vent” degassing and ash emission, however, although often powerful and prolonged, usually occurs without earthquakes. Such activity is, however, frequently accompanied by volcanic tremor. At Ruapehu, under “closed-vent” conditions, when lake temperature is low, low-frequency earthquakes up to magnitude M_L = 3.4 have occurred without any eruption.Five types of phreatic eruptions are identified at Ruapehu, each having a distinctive seismic pattern. The three most explosive types appear to be generated by a chain reaction process, and all involve flashing of water to steam; the first by failure of the roof, with little precursory seismicity, after a “closed-vent” period, during which lake temperature decreases; the second, after prolonged heating of the lake and much preliminary volcanic tremor, interpreted as due to rising magma; and the third, under “open-vent” conditions in the wake of one of the two preceding types. A fourth probably occurs in wet sediments near the base of the lake, as a result of upward migration of hot gas, and a fifth, aseismic, or accompanied by very weak volcanic tremor, is associated with convective overturn within Crater Lake.     

A note on differences in tsunami source parameters for submarine slides and earthquakes

The nature of tsunami sources is reviewed, including source duration, displacement amplitudes, and areas and volumes of selected past earthquakes, slumps and slides that have or may have generated a tsunami. This review shows that the velocity of spreading of submarine slides and slumps (1–100 m/s) can be comparable to the long wavelength tsunami velocity (30–140 m/s for water depth 100<h<2000 m). In contrast, typical velocities of spreading dislocations during most earthquakes are one order of magnitude larger (2–3 km/s). Other significant differences between earthquake and slide and slump sources are that the balance of the total uplifted material in the case of slides is essentially zero, while for earthquakes it can be considerable, and that the vertical displacements for slides and slumps, per unit area of their horizontal projection, can be orders of magnitude larger than during earthquakes. This can result in high concentrations of the total change in the potential energy of fluid, above the source, over much smaller areas than during earthquakes.     

A note on strength-reduction factors for design of structures near earthquake faults

Strength-reduction factors are analyzed for simplified near-fault, fault-normal and fault-parallel strong-motion displacements. It is shown that the common design rules for selection of the strength-reduction factors are conservative and properly describe the reduction amplitudes near faults of strong earthquakes, for fault-normal pulses. However, for fault-parallel displacements, the same reduction factors are not conservative and should be changed. It is recommended that for design close to active faults, the strength-reduction factors for all components of motion should be constant for all periods and equal to (2μ−1)^1/2, where μ is ductility.     

Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 John Wiley & Sons, Ltd.     

Unified modeling of flow liquefaction and cyclic mobility

Flow liquefaction and cyclic mobility are two different phenomena that are encountered during strong earthquakes. Flow liquefaction is associated with the contractive behavior of loose granular materials and cyclic mobility is associated with the dilative response of both loose and dense granular materials at low confining stresses. These two types of response pertain to the same material and therefore should be modeled in a consistent manner. Whether a soil in a given state exhibits contractive or dilative behavior is dependent on its dilatancy, d=d_v^p/d_q^p. A form of the dilatancy d=d(η,ψ,C) is proposed, where η=q/p is the stress ratio, and ψ and C denote the internal state variables and the intrinsic properties, respectively. It has been shown that such a state-dependent dilatancy is effective in describing both the contractive and dilative behavior. This allows the soil behavior associated with flow liquefaction and cyclic mobility during earthquakes to be modeled in a unified way.     

Visualisation of resonant basin response at the Parkway array, New Zealand

Seismograms recorded by a temporary dense seismometer array at Parkway, New Zealand, are displayed in various frequency bands, as moving pictures of the ground motion due to earthquakes, thus improving our understanding of the amplified response of a small alluvial basin. Transverse waves, longitudinal waves and a “cellular mode of resonant response” are seen. The separately available movies are essential for the paper to be appreciated properly.     

Using postglacial sea level, crustal velocities and gravity-rate-of-change to constrain the influence of thermal effects on mantle lateral heterogeneities

Lateral heterogeneities in the mantle can be caused by thermal, chemical and non-isotropic pre-stress effects. Here, we investigate the possibility of using observations of the glacial isostatic adjustment (GIA) process to constrain the thermal contribution to lateral variations in mantle viscosity. In particular, global historic relative sea level, GPS in Laurentide and Fennoscandia, altimetry together with tide-gauge data in the Great Lakes area, and GRACE data in Laurentide are used. The lateral viscosity perturbations are inferred from the seismic tomography model S20A by inserting the scaling factor β to determine the contribution of thermal effects versus compositional heterogeneity and non-isotropic pre-stress effects on lateral heterogeneity in mantle viscosity. When β = 1, lateral velocity variations are caused by thermal effects alone. With β < 1, the contribution of thermal effect decreases, so that for β = 0, there is no lateral viscosity variation and the Earth is laterally homogeneous. These lateral viscosity variations are superposed on four different reference models which differ significantly in the lower mantle viscosity. The Coupled Laplace Finite Element method is used to predict the GIA response on a spherical, self-gravitating, compressible, viscoelastic Earth with self-gravitating oceans, induced by the ICE-4G deglaciation model.Results show that the effect of β on uplift rates and gravity rate-of-change is not simple and involves the trade-off between the contribution of lateral viscosity variations in the transition zone and in the lower mantle. Models with small viscosity contrast in the lower mantle cannot explain the observed uplift rates in Laurentide and Fennoscandia. However, the RF3S20 model with a reference viscosity profile simplified from Peltier's VM2 with the value of β around 0.2–0.4 is found to explain most of the global RSL data, the uplift rates in Laurentide and Fennoscandia and the BIFROST horizontal velocity data. In addition, the changes in GIA signals caused by changes in the value of β are large enough to be detected by the data, although uncertainty in other parameters in the GIA models still exists. This may encourage us to further utilize GIA observations to constrain the thermal effect on mantle lateral heterogeneity as geodetic and satellite gravity measurements are improved.     

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σ 10³dyne/cm²), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σ = 10⁴ dyne/cm², if the flow rate is greater than 10⁵ g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.     

TRANSFER FUNCTIONS FOR RIGID RECTANGULAR FOUNDATIONS

Closed-form expressions and comprehensive numerical solutions are presented for the transfer functions of surface-supported, rigid, rectangular foundations excited by horizontally polarized, incoherent shear waves for which the motions are parallel to one of the foundation sides. The free-field ground motion is specified stochastically in terms of a local power spectral density function and an orthotropic incoherence function which decays exponentially with the square of the excitation frequency and the separation distance. The response quantities examined include the lateral and torsional components of the foundation motion. Displayed graphically, the results elucidate the effects and relative importance of the numerous parameters involved. For vertically incident incoherent wave fields, the lateral transfer function of a rectangular foundation is related to that of a judiciously selected square foundation, and the interrelationship of the results is examined. © 1997 by John Wiley & Sons, Ltd.     

Spectral parameters of ground motion in different regions: comparison of empirical models

Fourier-amplitude spectrum is one of the most important parameters describing earthquake ground motion, and it is widely used for strong ground motion prediction and seismic hazard estimation. The relationships between Fourier-acceleration spectra, earthquake magnitude and distance were analysed for different seismic regions (the Caucasus and Taiwan island) on the basis of ground motion recordings of small to moderate (3.5≤M_L≤6.5) earthquakes. It has been found that the acceleration spectra of the most significant part of the records, starting from S-wave arrival, can be modelled accurately by the Brune's “ω-squared” point-source model. Parameters of the model are found to be region-dependent. Peak ground accelerations and response spectra for condition of rock sites were calculated using stochastic simulation technique and obtained models of source spectra. The modelled ground-motion parameters are compared with those predicted by recent empirical attenuation relationship for California.     

AN ANALYSIS OF THE SEISMIC CHARACTERISTICS OF STEEL-JACKETED CIRCULAR BRIDGE COLUMNS

The current approach for seismic retrofit of deficient bridge columns in California involves extensive use of steel jacketing. In this paper, the influence of steel jacketing on the lateral response of circular bridge columns is studied; particularly, the enhancement of the ultimate compressive strain of concrete, the increase in curvature ductility capacity and the increase in lateral stiffness are investigated. The current steel jacket thickness used in California is shown to enhance the ultimate compressive strain of concrete by 4–9 times the spalling strain of unconfined concrete. For larger steel jacket thickness, the ultimate limit state of steel-jacketed columns may be governed by the low-cycle fatigue fracture of the longitudinal reinforcement instead of the ultimate compressive strain of concrete. Steel jacketing is also expected to increase significantly the lateral stiffness of columns if full-height steel jackets are used. The increase in lateral stiffness of flexural columns (3⩽L/D⩽9) is estimated to be 35–60 per cent using current jacket thickness. Inelastic dynamic analyses of steel-jacketed columns using ground motions recorded during the 1989 Loma Prieta earthquake indicated that the current steel jacket thickness provides adequate protection against the damage potential of the ground motions with comparable spectral acceleration as that specified in current design spectra, and the damage sustained by the steel-jacketed column is likely to be repairable.     

A note on computed magnitude ML from strong motion records

It is shown that a new definition of M_L^SM (Trifunac¹⁴), which is computed from recorded strong motion earthquake accelerograms, leads to stable and unbiased estimates of the local earthquake magnitude M_L (Richter⁸) for epicentral distance R < 100 km and for 3 M_nL < 6.5. Tables of the uniform estimates using this new M_L^SM are presented for all earthquakes contributing to the current data base of free field strong motion accelerograms in EQINFOS files (Lee and Trifunac⁶).     

Evidence of nonlinear site response in horizontal-to-vertical spectral ratio from near-field earthquakes

The issue is addressed as to whether the horizontal-to-vertical spectral ratio (HVSR) method is sensitive to the amplitude of ground motion from near-field earthquakes. Twenty-one three-component accelerograms from two closely located similar soil sites in the town of Lefkas are used. The recordings represent 17 earthquakes covering a wide range of magnitudes, epicentral distances and azimuths. Peak horizontal accelerations (PGA) and velocities (PGV) lie in the ranges 20–540 cm/s² and 1.4–55.2 cm/s. For each HVS ratio, the site's fundamental-resonance frequency, f_res, is determined visually. Linear correlation analysis shows that f_res is strongly (negatively) correlated to PGA and PGV (r between −0.7 and −0.8); no correlation is found with resonance amplitude or epicentral distance. We show that the observed correlation is attributable to soil nonlinearity and indicate how weak-motion estimates of f_res can be corrected for use in assessing site response during strong shaking.     

Depth distribution of stresses in the Hokkaido Wadati-Benioff zone as deduced by inversion of earthquake focal mechanisms

This study is based on the detailed geometry of the Hokkaido Wadati-Benioff zone and the paleosubduction zone as delineated by Hanus and Vanek (1984). The used data includes 217 CMT Harvard solutions for earthquakes, which belong to the Wadati-Benioff zone and 13 for the paleosubduction zone. The inverse technique by Gephart and Forsyth (1984) was incorporated for determining the best fit principal stress directions σ₁, σ₂, σ₃ and the ratio (R=σ₂−σ₁/σ₃−σ₁) for 20 km depth intervals in the Wadati-Benioff zone and for the paleosubduction zone considered as a single body. In almost all the considered depth layers, the maximum compressive stress σ₁ is normal to the strike of the slab and dips less than 25°, indicating the NW-SE convergence between the Pacific and Eurasian lithospheric plates. Exceptions are in the depth layer 81–120 km, the paleosubduction zone with steeply dipping along-strike σ₁, and the lower part of the subduction zone (161–220 km) where σ₁ is almost horizontal and of E trend. The minimum compressive stress σ₃ is mostly along-strike and of a different dip with the exception of the 21–60 km layer wher they are down-dipping. The results obtained for the depth ranges 0–20 km, 81–100 km, 121–160 km, and the paleosubduction zone indicate heterogeneous stress fields. These results show that the slab pull and the mantle resistance, acting on the slab edge, are not the main forces which control the contemporary plate tectonics in the Hokkaido region. Along-strike compression at depths 81–120 km and along-strike extension at 0–20 and 61–220 km are involved in the slab dynamics. These can be related to horizontal bending of the subducting Pacific plate.     

Earthquakes in the Himalayan region

Summary Himalayan earthquakes have been studied following the method of Benioff and then a comparative study of energy relased by the Himalayan and the world shallow earthquakes is made. Frequency-magnitude analysis of these earthquakes gives the frequency-magnitude relation of the form logN =a –b M wherea=8.46±0.07 andb=1±0.8.