Numerical simulations of deformation and movement of blocks within North China in response to 1976 Tangshan earthquake

Using methods of discontinuous deformation analysis and finite element (DDA+FEM), this paper simulates dynamic processes of the Tangshan earthquake of 1976, which occurred in the northern North China where its internal blocks apparently interacted. Studies focus upon both the movement and deformation of the blocks, in particular, the Ordos block, and variations of stress states on the boundary faults. The Tangshan earthquake was composed of three events: slipping motions of NNE-striking major fault, NE-striking fault near the northeastern end of the NNE-striking fault, and NW-striking fault on the southeastern side of the NNE-striking fault. Compared with previous studies, our model yields a result that is more agreeable with the configuration of aftershock distributions. A number of data are presented, such as the principle stress field during the earthquake, contours of the maximum shear stress, the strike-slip deformation between blocks near the earthquake focus, time-dependent variations of slips of earthquake-triggered faulting, the maximum slip distance, and stress drops. These results are in accord with the earthquake source mechanism, basic parameters from earthquake wave study, macro-isoseismic line, observed horizontal displacement vectors, etc. The Tangshan earthquake exerted different influences on the adjacent blocks and boundary faults between them, thus resulting in differential movement and deformation. The Ordos block seems to have experienced the small-scale counterclockwise rotation and deformation, but its northeast part, bounded on the east by the Taihangshan and on the north by the Yanshan and Yinshan belts, underwent relatively stronger deformation. The Tangshan earthquake also changed the stress state of boundary faults of the North China, leading to an increase in shear stress and a decrease in normal stress in the NW-trending Zhangjiakou-Penglai fault through Tangshan City and the northern border faults of the Ordos block, and therefore raises the potential risk of earthquake occurrence. This result is supported by the facts that a series of Ms ≥ 6 earthquakes took place at the northern margin of the Ordos block after the Tangshan earthquake.     

Active blocks and strong seismic activity in North China region

The active North China block consists of three second-order blocks: Ordos, North China Plain, and East Shandong-Huanghai Sea blocks. Two active tectonic zones, the Anyang-Heze-Linyi and Tangshan-Cixian zones, exist in the active North China Plain block and have separated the active block into 3 third-order active blocks, Taihangshan, Hebei-Shandong, and Henan-Huai blocks. The 3 third-order active blocks are characterized by their entire motion and are clearly different in their Cenozoic structures and deep structures. The active boundary tectonic zones between the third-order active blocks are less than those between the first- and second-order active blocks in their movement strength, extent, and seismic activity. The density of M· ·6 earthquakes in the boundary zones between active blocks is higher than that within the blocks by 9–22 times in the North China region, up to one order of magnitude on average. M· · 7 earthquakes occurred basically in the boundary zones between active blocks. The difference is not occasional, but reflects the nature of intraplate movement and the characteristics of strong seismic activity and is the powerful evidence for hypothesis of active blocks.     

Fine structure of Pn velocity beneath Sichuan-Yunnan region

We use 23298 Pn arrival-time data from Chinese national and provincial earthquake bulletins to invert fine structure of Pn velocity and anisotropy at the top of the mantle beneath the Sichuan-Yunnan and its adjacent region. The results suggest that the Pn velocity in this region shows significant lateral variation; the Pn velocity varies from 7.7 to 8.3 km/s. The Pn-velocity variation correlates well with the tectonic activity and heat flow of the region. Low Pn velocity is observed in southwest Yunnan, Tengchong volcano area, and the Panxi tectonic area. These areas have very active seismicity and tectonic activity with high surface heat flow. On the other hand, high Pn velocity is observed in some stable regions, such as the central region of the Yangtze Platform; the most pronounced high velocity area is located in the Sichuan Basin, south of Chengdu. Pn anisotropy shows a complex pattern of regional deformation. The Pn fast direction shows a prominent clockwise rotation pattern from east of the Tibetan block to the Sichuan-Yunnan diamond block to southwest Yunnan, which may be related to southeastward escape of the Tibetan Plateau material due to the collision of the Indian Plate to the Eurasia Plate. Thus there appears to be strong correlation between the crustal deformation and the upper mantle structure in the region. The delay times of events and stations show that the crust thickness decreases from the Tibetan Plateau to eastern China, which is consistent with the results from deep seismic sounding.     

Optimum multiple tuned mass dampers for structures under the ground acceleration based on the uniform distribution of system parameters

The five MTMD models, with natural frequencies being uniformly distributed around their mean frequency, have been recently presented by the first author. They are shown to have the near‐zero optimum average damping ratio (more precisely, for a given mass ratio there is an upper limit on the total number, beyond which the near‐zero optimum average damping ratio occurs). In this paper, the eight new MTMD models (i.e. the UM‐MTMD1～UM‐MTMD3, US‐MTMD1～US‐MTMD3, UD‐MTMD1 and UD‐MTMD2), with the system parameters (mass, stiffness and damping coefficient) being, respectively, uniformly distributed around their average values, have been, for the first time here, proposed to seek for the MTMD models without the near‐zero optimum average damping ratio. The structure is represented by the mode‐generalized system corresponding to the specific vibration mode that needs to be controlled. Through minimization of the minimum values of the maximum dynamic magnification factors (DMF) of the structure with the eight MTMD models (i.e. through the implementation of Min.Min.Max.DMF), the optimum parameters and values of Min.Min.Max.DMF for these eight MTMD models are investigated to evaluate and compare their control performance. The optimum parameters include the optimum mass spacing, stiffness spacing, damping coefficient spacing, frequency spacing, average damping ratio and tuning frequency ratio. The six MTMD models without the near‐zero optimum average damping ratio (i.e. the UM‐MTMD1～UM‐MTMD3, US‐MTMD1, US‐MTMD2 and UD‐MTMD2) are found through extensive numerical analyses. Likewise, the optimum UM‐MTMD3 offers the higher effectiveness and robustness and requires the smaller damping with respect to the rest of the MTMD models in reducing the responses of structures subjected to earthquakes. Additionally, it is interesting to note, by comparing the optimum UM‐MTMD3 with the optimum MTMD‐1 recently investigated by the first author, that the effectiveness and robustness for the optimum UM‐MTMD3 is almost identical to that for the optimum MTMD‐1 (without inclusion of the optimum MTMD‐1 with the near‐zero optimum average damping ratio). Recognizing these performance benefits, it is preferable to employ the optimum UM‐MTMD3 or the optimum MTMD‐1 without the near‐zero optimum average damping ratio, when installing the MTMD for the suppression of undesirable oscillations of structures under earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

An experimental study of nominally symmetric and asymmetric structures isolated with the FPS

This experimental investigation deals with the earthquake behaviour of a nominally symmetric and a mass‐asymmetric three‐storey structural model isolated with the frictional pendulum system (FPS). Both accidental and natural torsion are evaluated in the structure by using recorded accelerations in all building floors and measured deformations at the isolation level. A 3D‐shaking table was used to subject the model to five different ground motions, including impulsive as well as far‐field subduction‐zone type earthquakes. Results show that the analytical predictions of the earthquake behaviour of the isolated structure, as obtained from a physical model of the FPS, are in close agreement with the true complex inelastic measured behaviour of the FPS. Besides, experimental results also validate previous observations about the importance of accounting for the variability of the normal loads in modelling the earthquake behaviour of FPS isolators. Measured torsional deformation amplifications at the base of the building vary, in the mean, from 2.5% to 6% for the symmetric and asymmetric structural configurations, respectively. In relation to the fixed base structure, the reduction factors for the base shear of the isolated structure are, in the mean, about 3.9 for both configurations. Finally, it is concluded that the FPS is capable of controlling the lateral–torsional motions of mass‐asymmetric structures quite effectively by aligning the centre of mass of the superstructure with the centre of pendular and frictional resistance of the isolation system. Copyright © 2003 John Wiley & Sons, Ltd.     

Physical model for dynamic analysis of structures with FPS isolators

This article presents a physical model for frictional pendulum isolators (FPS) that is ready to be implemented in most commercial software. The model is capable of accounting for effects such as large deformations, sticking, and uplift and impact by sensing the normal loads in the isolators through a gap element. Sticking has been incorporated into the model by extending the Park–Wen hysteretic model to the case of large deformations. The proposed model has been tested against a theoretically ‘exact’ formulation leading to essentially identical results. To facilitate its use, the physical FPS model has been cast into a typical non‐linear structural element format, i.e. with deformation as input and restoring force as output. Examples of a building and a bridge have been chosen to show the potential of the element and to provide further insight into the earthquake response of structures with FPS isolators; in particular, in aspects such as the orientation in placement of the isolator, sticking, P? Δ, and other large deformation effects. Copyright © 2003 John Wiley & Sons, Ltd.     

On the circulation in the East Frisian Wadden Sea: numerical modeling and data analysis

 In this paper we use a combination of numerical modeling and data analysis to gain a better understanding of the major characteristics of the circulation in the East Frisian Wadden Sea. In particular, we concentrate on the asymmetry of the tidal wave and its modulation in the coastal area, which results in a complex pattern of responses to the sea-level forcing from the North Sea. The numerical simulations are based on the 3-D primitive equation General Estuarine Transport Model (GETM) with a horizontal resolution of 200 m and terrain-following vertical coordinates. The model is forced at its open boundaries with sea-level data from an operational model for the German Bight (German Hydrographic Office). The validation data for our model simulations include time series of tidal gauge data and surface currents measured at a pile in the back-barrier basin of the Island Langeoog, as well as several ADCP transects in the Accumer Ee tidal inlet. Circulation and turbulence characteristics are investigated for typical situations driven by spring and neap tides, and the analysis is focused on dominating temporal and spatial patterns. By investigating the response of five back-barrier basins with rather different morphologies to external forcing, an attempt is made to elucidate the dominating physical balances controlling the circulation in the individual sub-basins. It is demonstrated that the friction at the seabed tends to slow down the tidal signal in the shallow water. This leads to the establishment of flood dominance in the shallow sea north of the barrier islands. South of the islands, where the water volume of the channels at low tide is smaller than the tidal prism, the asymmetry of the tidal signal is shifted towards ebb dominance, a feature which is particularly pronounced at spring tide. At the northern open boundary, the tidal wave propagating from west to east generates a sea-level difference of ∼1 m along the boundary, and thereby triggers vigorous alongshore currents. The frictional control in the model is located in the inlets, as well as along the northern boundary. The correlation between velocity and turbulent kinetic energy tends to the establishment of a net southward transport, giving theoretical support to the observed accumulation of sediments on the intertidal flats. Weak turbulence along the northern shores of the barrier islands and the small magnitude of the residual currents there promote accumulation of suspended matter in these areas, although wave action will generally counteract this effect. Received: 29 May 2002 / Accepted: 26 September 2002 Responsible Editor: Jean-Marie Beckers Acknowledgements We are indebted to S. Dick for providing the data from the operational model of BSH and to B. Flemming for the useful discussions. The topography data and Fig. 1 have been prepared in cooperation with F. Meyer. Figure 2 has been prepared by G. Brink-Spalink. We also thank for the comments from an anonymous reviewer which helped to improve our paper.     

Two and Half Dimensional Simulation of Ridge Effects on the Ground Motion Characteristics

— Seismic responses of weathered and non-weathered ridge models were simulated to study the ridge effects on the ground motion characteristics. The range of ridge slope from 19.98° to 45° was considered to produce a possible set of generalized results. 2.5-D modeling based on parsimonious staggered grid approximation of elastodynamic wave equations was adopted in simulations. Computed results reveal an increase of amplitude of incoming waves with both elevation and the slope of the ridge. Further, the characteristics of surface waves are highly ridge slope dependent. The analysis of responses of weathered and non-weathered ridge models reveals that ridge has caused a strong generation of surface waves near its top. The surface waves are not dominating on the top of the ridge but at some lower elevation. The increase of weathering of ridge further intensified the ridge effect. Analysis in frequency domain, based on spectral ratio method, does not indicate any pattern in the spectral amplification factor and is very much sensitive to slope, source focal mechanism and location. However, on an average there is a continuous decrease of amplification with slope in the vertical component and increase in the transverse component, and it is increasing in the radial component up to slope =38.0° and thereafter decreasing.     

Lateral tidal mixing in the Antarctic marginal seas

Tidal mixing plays an important role in the modification of dense water masses around the Antarctic continent. In addition to the vertical (diapycnal) mixing in the near-bottom layers, lateral mixing can also be of relevance in some areas. A numerical tide simulation shows that lateral tidal mixing is not uniformly distributed along the shelf break. In particular, strong mixing occurs all along the Ross Sea and Southern Weddell Sea shelf breaks, while other regions (e.g., the western Weddell Sea) are relatively quiet. The latter regions correspond surprisingly well to areas where indications for cross-shelf exchange of dense water masses have been found. The results suggest that lateral tidal mixing may account for the relatively small contribution of Ross Sea dense water masses to Antarctic Bottom Water.