A synthetic optimization analysis method on structures with viscoelastic dampers

The paper introduces a synthetic optimization analysis method of structures with viscoelastic (VE) dampers, namely the simplex method. The optimal parameters and location of VE dampers can be determined by this method. Numerical example and a shaking table test about reinforced concrete structures with VE dampers show that the seismic responses of structures will be reduced more effectively when the parameters and location of VE dampers are designed in accordance with the results calculated by the simplex method.     

Shear waves at a corrugated interface between anisotropic elastic and visco-elastic solid half-spaces

Rayleigh’s method of approximation is employed to find out the reflection and transmission coefficients due to an incident plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space and a laterally and vertically inhomogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities are described by the exponential variations of elastic parameters. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface, the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied analytically and numerically for a specific model containing a periodic interface. The results of earlier workers have been reduced as particular cases from the present formulation.     

On the motion around the centre of mass of a viscously elastic sphere in the restricted elliptic three-body problem

In the restricted three-body problem we consider the motion of a viscously elastic sphere (planet) with its centre of mass moving in a conditionally-periodic orbit. The approximate equations describing the rotational motion of the sphere in terms of the Andoyer variables are obtained by the method of the separation of motion and averaging; the evolution of the motion is also analysed.     

Semi-analytical solution to one-dimensional consolidation for viscoelastic unsaturated soils

This paper presents a semi-analytical solution to one-dimensional consolidation of viscoelastic unsaturated soils with a finite thickness under oedometric conditions and subjected to a sudden loading. The solution is obtained by using Lee’s correspondence principle based on the semi-analytical solution to one-dimensional consolidation of elastic unsaturated soils. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. A typical example is given to show the evolution of excess pore-air and pore-water pressures as well as the total degree of consolidation of the soil layer with time for different ratios of air–water permeability coefficient, elastic modulus and viscoelastic coefficient. The one-dimensional consolidation behavior of viscoelastic unsaturated soil is discussed according to the semi-analytical solution. These results contribute to a better understanding of the consolidation behavior of viscoelastic unsaturated soils.     

Response of a tunnel deeply embedded in a viscoelastic medium

This paper presents a three‐dimensional energy‐based solution for the time‐dependent response of a deeply embedded and unsupported semi‐infinite tunnel of circular cross‐section. The tunnel is taken to be excavated quasi‐instantaneously from an infinite rock body that initially exhibits an isotropic stress state and that is made up of a homogeneous, isotropic and viscoelastic material. The viscoelastic behaviour is modelled by means of Burger's model, and the rock is taken to behave volumetrically linear elastic and to exhibit exclusively deviatoric creep. This viscoelastic problem is transformed into the Laplace domain, where it represents a quasi‐elastic problem. The displacement fields in the new solution are taken to be the products of independent functions that vary in the radial and longitudinal directions. The differential equations governing the displacements of the system and appropriate boundary conditions are obtained using the principle of minimum potential energy. The solutions for these governing equations in the Laplace domain are then obtained analytically and numerically using a one‐dimensional finite difference technique. The results are then transformed back into the time domain using an efficient numerical scheme. The accuracy of the new solution is comparable with that of a finite element analysis but requires much less computation effort. Copyright © 2011 John Wiley & Sons, Ltd.     

Mechanism on Moho offset induced by aseismic slip of deeply buried faults

Recent high-resolution deep seismic reflection profile across the Kunlun fault in northeastern Tibet shows clearly that the Moho is cut off by a complex thrust fault system. Moho offset is a general phenomenon, but little is known about the dynamic mechanism. In this study, contact models with Maxwell materials are used to simulate the mechanical process of Moho offset induced by the aseismic slip of deeply buried faults. Based on the seismic reflection data, we project a single fault model and a complex fault system model with two faults intersecting. The deformations of the Moho, the aseismic slips, and contact stresses on faults in different models are discussed in detail. Results show that the Moho offset might be produced by aseismic slip of deeply buried faults, and the magnitude is influenced by the friction coefficient of faults and the viscosity of the lower crust. The maximum slip occurs near the Moho on the single fault or at the crossing point of two intersecting faults system. Stress concentrates mainly on the Moho, the deep end of faults, or the crossing point. This study will throw light on understanding the mechanism of Moho offset and aseismic slip of deeply buried faults. The results of complex fault system with two faults intersecting are also useful to understand the shallow intersecting faults that may cause earthquakes.     

巴颜喀拉块体周缘几次强震对甘肃地区地震形势的影响

以青藏高原为目标,采用黏弹性体本构关系建立3D有限元模型,模拟了在印度板块持续向北推进、挤压下,巴颜喀拉块体周缘强震对邻近地区的影响.通过降低强震发生位置处单元弹性模量的方法模拟了2001年昆仑山口西MS8.1、2008年汶川MS8.0、2010年玉树MS7.1地震,计算了发生这3次MS7.0以上强震后50年内每5年的黏弹性调整过程,讨论了3次强震对祁连地震带及甘东南地区地震形势的影响,尝试开展依据区域应力调整特征判定未来强震危险区的探索试验.     

昆仑山Ms 8.1级地震震后变形场数值模拟与成因机理探讨

2001年11月14日,在青海和新疆交界处发生了昆仑山M_s8.1级强烈地震,GPS后观测显示,此次地震震后形变不仅在断裂南北两侧存在很大的差异,而且在短时间调整后断裂南北两侧表现为同向运动.本文以观测的地震形变为约束,通过有限元数值模拟分析昆仑山地震震后形变的物理机制.建立有关的有限元虚功方程,通过有限元数值方法模拟震后形变,从理论上分析介质的非均匀性、黏滞性松弛、流体调整对震后形变的影响.采用网格搜索确定昆仑断裂南北两侧下地壳的黏滞系数分别为5.0×10¹⁷Pa·s, 9.0×10¹⁸Pa·s左右,正是这十余倍的差异引起了断裂两侧震后形变的非对称性和同向运动,这一差异既是长期地质作用的结果,又是现代地球动力学环境的决定因素之一.通过数值模拟定性讨论了断裂北侧地表形变在震后短期内的调整,对于靠近断裂附近的测点可能是黏弹性松弛和孔隙流体调整共同作用的结果,所以在分析短期震后形变时综合考虑黏弹松弛和孔隙流体调整是很有必要的.     

The Chi-Chi 1999 earthquake: Correlation between the spatio-temporal distribution of aftershocks and viscoelastic stress changes

The Chi-Chi 1999 (M_L = 7.3) earthquake generated a large number of aftershocks in the vicinity of the rupture plane. The spatial-temporal distribution of these aftershocks was recorded with high precision and thus provided a unique possibility to study whether the correlation between aftershocks and stress changes are primary due to coseismically induced stress changes (static), or whether stress relaxation processes (viscoelastic) in the lower crust contribute significantly to this correlation. From our analysis of a 3D finite element model simulating the viscoelastic stress changes due to the coseismic displacement and tectonic loading we found that the aftershocks are highly correlated with the stress variations (static and viscoelastic) caused by the main shock. Although we found that the correlation between seismicity rate changes and viscoelastic stress fluctuation is slightly better than that of the static stress changes, these differences can only be identified well in the lower crust. As a result, it is reasonable to conclude that static stress changes are the key mechanism for triggering early and shallow aftershocks in the upper crust. It is reasonable to infer that the viscoelastic relaxation in the lower crust does affect the occurrence of early aftershocks in the deep crust, but it does not significantly affect the shallow aftershocks. However, the stress changes induced from the lower crust gradually transfer to the upper crust and may influence the occurrence of aftershocks after a longer time period (>four Maxwell times).