Generation of SH-type waves due to shearing stress discontinuity in a sandy layer overlying an isotropic and inhomogeneous elastic half-space

The generation of SH-type waves due to sudden application of a stress discontinuity which moves after creation at the sandy layer of finite thickness overlying an isotropic and inhomogeneous elastic half-space is considered. The displacements are obtained in exact form by the method due to Cagniard modified by De Hoop. The numerical calculations are obtained. Two cases of shearing stress discontinuities are considered for different sandiness parameters. The graphs are drawn to show the effect of sandiness in the displacement components.     

Accidental torsion in buildings due to base rotational excitation

This investigation is concerned with accidental torsion in buildings resulting from rotational excitation (about a vertical axis) of the building foundations as a result of spatially non-uniform ground motions. Because of this accidental torsion, the displacements and deformations in the structural elements of the building are likely to increase. This increase in response is evaluated using actual base rotational excitations derived from ground motions recorded at the base of 30 buildings during recent California earthquakes. Accidental torsion has the effect of increasing the building displacements, in the mean, by less than 5 per cent for systems that are torsionally stiff or have lateral vibration periods longer than half a second. On the other hand, short period (less than half a second) and torsionally flexible systems may experience significant increases in response due to accidental torsion. Since the dependence between this increase in response and the system parameters is complex, two simplified methods are developed for conveniently estimating this effect of accidental torsion. They are the ‘accidental eccentricity’ and the ‘response spectrum’ method. The computed accidental eccentricities are much smaller than the typical code values, 0.05bb or 0.1b, except for buildings with very long plan dimensions (b ≥ 50 m). Alternatively, by using the response spectrum method the increase in response can be estimated by computing the peak response to each base motion independently and combining the peak values using the SRSS rule.     

Coulomb stress change due to 2005 Kashmir earthquake and implications for future seismic hazards

We calculate static stress change due to the 2005 Kashmir earthquake (M = 7.6). We suggest that the earthquake caused significant increase in stress in the Indo-Kohistan seismic zone (IKSZ) region, lying to the NW of the rupture and moderate increase in the adjacent Himalayan region, lying to the SE of rupture. Thus, these regions have been brought closer to the failure. On the other hand, the Salt Range region lies in the stress shadow of the earthquake, implying that future earthquakes in this region will be inhibited. We find that this earthquake may not be compared with typical Himalayan earthquake, and hence, rupture features of this earthquake may not be directly applicable to the earthquakes of the Himalayan region. This article has previously been published in issue 12/3, under .     

Coulomb stress change due to 2005 Kashmir earthquake and implications for future seismic hazards

We calculate static stress change due to the 2005 Kashmir earthquake (M = 7.6). We suggest that the earthquake caused significant increase in stress in the Indo-Kohistan seismic zone (IKSZ) region, lying to the NW of the rupture and moderate increase in the adjacent Himalayan region, lying to the SE of rupture. Thus, these regions have been brought closer to the failure. On the other hand, the Salt Range region lies in the stress shadow of the earthquake, implying that future earthquakes in this region will be inhibited. We find that this earthquake may not be compared with typical Himalayan earthquake, and hence, rupture features of this earthquake may not be directly applicable to the earthquakes of the Himalayan region.     

Stress Changes due to Recent Seismic Events in the Central Apennines (Italy)

The Central Apennines, Italy, are characterized by moderate seismic activity on normal faults, oriented in directions parallel to the Apenninic chain. The subject of this study is the Umbria-Marche Apennines, a segment approximately 200-km long, where three main seismic events occurred in the last three decades. The 1979 Norcia earthquake was a M_w = 5.8 event, taking place at the south end of the considered segment. The 1984 Gubbio earthquake was a M_w = 5.6 event which took place at the north end. The 1997-1998 Colfiorito sequence constituted 8 main shocks with magnitudes M_w between 5 and 6 and epicenters located between the Gubbio and the Norcia earthquake areas. A model made of an elastic half-space is considered, in which the seismic sources are represented by rectangular dislocations which have the appropriate values of source parameters, and in which the static stress field produced by each event is calculated. The analysis of the Coulomb stress change (ΔC) as a function of time shows that the coseismic stress transfer and fault interaction played an important role in the region during the past three decades: 7 earthquakes of the 9 considered took place where ΔC>0. Such an interaction has been confirmed by the analysis of the aftershocks in the Colfiorito zone post September 26, 1997: about the 61% of the aftershocks considered took place where ΔC>0. The comparison between the ΔC^s due to the coseismic stress transfer and the rate ΔĊ^t due to the tectonic stress allows us to quantify the time advance of the earthquakes. The ΔC^s pattern shows positive values in two areas that can be regarded as historical seismic gaps.     

Elastic radiation from buried sources in a semi-infinite heterogeneous medium

Summary The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated.     

Vibrations of the elastic half-space due to vertical surface loads

The displacements of the surface of the homogeneous elastic half-space subjected to a vertical concentrated load acting at the surface are calculated. The solution is shown to approach Lamb's simple formula for the far-field. The solution for the concentrated load can be used to calculate displacements due to distributed loads with high accuracy and economically. The results are applied to define the regions ‘near-field’ and ‘far-field’. Some near-field phenomena are described.     

On twisting of a non-homogeneous circular disk,due to a tangential traction of the boundary of a concentric circular hole

Summary In this note, the stresses and displacements due to tangential traction on the inner boundary of a nonhomogeneous annular circular disk, the outer boundary of the disk being kept fixed have been investigated. Some numerical results are given at the end.     

A possible change in stress field orientation due to the 1976 Tangshan earthquake

Two techniques are used to study the stress field in the Tangshan region. First, the mean directions of principal stress axes in three subregions of the Tangshan aftershock region are determined from 29 focal mechanism solutions. In doing so a slip-fitting technique is applied which determines the mean stress tensor by minimizing the angle between the observed slip direction on every fault plane and the calculated shear stress resolved onto the fault planes. Each of the two nodal planes of the focal mechanism solutions are alternately considered as a possible fault plane. Second, by making a grid search over all possible orientations of stress axes, the meanP,B andT axes in the Tangshan region, both before and after the Tangshan mainshock, are found on the basis of firstP-wave polarity readings from a number of small earthquakes. The results indicate that there is a possible azimuthal change of the principal stress axes in the focal region due to the occurrence of the mainshock.     

Response of soil media due to impulse loads and isolation using trenches

This paper examines the effectiveness of open and filled trenches for screening Rayleigh waves due to impulse loads for 3D problems. The effects of the geometric parameters of trench reducing ground displacements are studied in detail. The computational scheme involves the use of finite element method to discretize a large computational domain and the resulting integration dynamic equilibrium equations are integrated to get the response using Newmark's β method. Soil has been idealized as linear, isotropic continuum.     

Formation of cracks due to moving source over a thick crust

Summary In this paper the problem of a point source of stress moving over the surface of a thick aelotropic plate resting of a rigid foundation has been considered. Following the method ofAleksandrov & Vorovich (1960) the stress componentsZ _x andZ _z have been expanded in series of ascending powers of 1/h when the source velocity is less than (c ₄₄/)^1/2. When the velocity exceeds (c ₄₄/)^1/2 it has been shown that two cracks are produced in different directions and their successive reflections at the upper and lower surface are also obtained.     

2001年昆仑山口西MS8.1地震对周围断层的应力影响数值分析

大地震的发生往往会引起周围区域形变场和应力场变化,且对临近断层上的应力状态也有影响.2001年11月4日,昆仑山口西发生了半个世纪以来中国最大的M_S8.1级地震.本文基于已有的滑动模型,建立了三维含地形高程的横向不均匀性椭球型地球有限元模型,采用等效体力方法,分析了此次M_S8.1地震产生的全球同震位移和应力场变化.与解析方法相比,该模型考虑了地形、Moho面起伏和地球介质横向不均匀性;与一般的有限元数值模拟相比,该模型考虑了地球曲率和椭率,合理地规避了有限块体模型假定边界位移为零所引入的误差.计算得出同震位移与GPS观测数据可以很好地吻合.据库仑破裂应力准则和震源参数,计算得出昆仑山口西M_S8.1地震的发生造成了汶川、芦山、改则和当雄地震的发震断层上库仑应力增加,对这些地震的发生起促进作用;而造成玉树和德令哈地震发震断层上的库仑应力变化为负值,在一定程度上抑制了这些断层的地震活动性.此外,计算结果显示地球地形高程、介质非均匀性和椭率对昆仑山口西M_S8.1地震同震变化计算有一定的影响,其中地形和椭率造成的同震位移场相对误差约10%.     

Generation of rayleigh waves due to stress-discontinuity in a semi-infinite elastic medium

Summary In this paper, the displacements produced at the surface of a semi-infinite, clastic medium by the sudden creation and subsequent motion of discontinuities in the normal and tangential stresses have been obtained in the form of definite integrals byCagniard's method. Numerical values are given in a particular case.Published with the kind permission of the Director General, Geological Survey of India, Calcutta.     

Near‐fault effects on residual displacements of RC structures

Residual displacements of single‐degree‐of‐freedom systems due to ground motions with velocity pulses or fling step displacements are presented as a function of period T and of its ratio to the pulse period T_p. Four hysteretic behaviors are considered: bilinear elastoplastic, stiffness‐degrading with cycling, stiffness‐cum‐strength degrading, with or without pinching. When expressed in terms of T/T_p, peak inelastic and residual displacements due to motions with a pulse or fling appear similar to those due to far‐fault motions, if the response to far‐field records are expressed in terms of the ratio of T to the record's characteristic period. However, as the latter is usually much shorter than the pulse period of motions with fling, the range of periods of interest for common structures becomes a short‐period range under fling motions and exhibits very large amplification of residual and peak inelastic displacements. Similar, but less acute, are the effects of motions with a velocity pulse. Wavelets of different complexity are studied as approximations to near‐fault records. Simple two‐parameter wavelets for fling motions overestimate peak inelastic displacements; those for pulse‐type motions overestimate residual displacements. A more complex four‐parameter wavelet for motions with a velocity pulse predicts overall well residual and peak displacements due to either pulse‐ or fling‐type motions; a hard‐to‐identify parameter of the wavelet impacts little computed residual displacements; another significantly affects them and should be carefully estimated from the record. Even this most successful of wavelets overpredicts residual displacements for the periods of engineering interest. Copyright © 2016 John Wiley & Sons, Ltd.     

On the stresses produced by a moving stress discontinuity at the boundary between two transversely isotropic media

Summary This paper deals with the stresses produced by a moving stress discontinuity between two semi-infinite transversely isotropic media. The solutions for the stresses have been obtained in simple closed forms for certain types of moving stress discontinuity. Discontinuities in the normal stress as well as in the shear stress has been considered. The case in which one or both of the media are isotropic may be deduced as a special case from the results obtained here.     

Development of faults as zones of deformation bands and as slip surfaces in sandstone

Three forms of fault are recognized in Entrada and Navajo Sandstones in the San Rafael Desert, southeastern Utah; deformation bands, zones of deformation bands, and slip surfaces. Small faults occur asdeformation bands, about one millimeter thick, in which pores collapse and sand grains fracture, and along which there are shear displacements on the order of a few millimeters or centimeters. Two or more deformation bands adjacent to each other, which share the same average strike and dip, form azone of deformation bands. A zone becomes thicker by addition of new bands, side by side. Displacement across a zone is the sum of displacements on each individual band. The thickest zones are about 0.5 m and total displacement across a thick zone rarely exceeds 30 cm. Finally,slip surfaces, which are through-going surfaces of discontinuity in displacement, form at either edge of zones of highly concentrated deformation bands. In contrast with individual deformation bands and zones of deformation bands, slip surfaces accommodate large displacements, on the order of several meters in the San Rafael Desert.The sequence of development is from individual deformation bands, to zones, to slip surfaces, and each type of faulting apparently is controlled by somewhat different processes. The formation of zones apparently involves strain hardening, whereas the formation of slip surfaces probably involves strain softening of crushed sandstone.     

Coda wave analysis for distinguishing attenuation due to isotropic scattering from attenuation due to absorption

When the quality factorQ is taken into account in attenuation studies, it is necessary to know the relative losses of wave energy due to scattering and to anelastic absorption. The coda is the most important phenomenon now known which is related to elastic scattering of seismic waves. Utilizing coda, this study presents relationships which give theQ factors of the medium around the recording station and discriminate between attenuations arising from elastic scattering (under the assumption of isotropic scattering) and those arising from anelastic absorption. This work proposes a technique for separately determining the attenuation due to isotropic scattering and that due to absorption from the observed envelope of coda waves.     

Improvement in the Fault Boundary Conditions for a Staggered Grid Finite-difference Method

The staggered grid finite-difference method is a powerful tool in seismology and is commonly used to study earthquake source dynamics. In the staggered grid finite-difference method stress and particle velocity components are calculated at different grid points, and a faulting problem is a mixed boundary problem, therefore different implementations of fault boundary conditions have been proposed. Viriuex and Madariaga (1982) chose the shear stress grid as the fault surface, however, this method has several problems: (1) Fault slip leakage outside the fault, and (2) the stress bump beyond the crack tip caused by S waves is not well resolved. Madariaga et al. (1998) solved the latter problem via thick fault implementation, but the former problem remains and causes a new issue; displacement discontinuity across the slip is not well modeled because of the artificial thickness of the fault. In the present study we improve the implementation of the fault boundary conditions in the staggered grid finite-difference method by using a fictitious surface to satisfy the fault boundary conditions. In our implementation, velocity (or displacement) grids are set on the fault plane, stress grids are shifted half grid spacing from the fault and stress on the fictitious surface in the rupture zone is given such that the interpolated stress on the fault is equal to the frictional stress. Within the area which does not rupture, stress on the fictitious surface is given a condition of no discontinuity of the velocity (or displacement). Fault normal displacement (or velocity) is given such that the normal stress on the fault is continuous across the fault. Artificial viscous damping is introduced on the fault to avoid vibration caused by onset of the slip. Our implementation has five advantages over previous versions: (1) No leakage of the slip prior to rupture and (2) a zero thickness fault, (3) stress on the fault is reliably calculated, (4) our implementation is suitable for the study of fault constitutive laws, as slip is defined as the difference between displacement on the plane of z = + 0 and that of z = − 0, and (5) cessation of slip is achieved correctly.     

On the disturbances in an inhomogenous medium due to transient forces and twists on the surface of a burried spherical source

Summary In this paper the displacements and stresses are obtained due to two types of forces: (i) transient normal forces, (ii) transient twists on the surface of a burried spherical source. The material is assumed to be inhomogeneous and spherically aeolotropic. Laplace transform technique has been used here.     

断层错动引起的上覆土体破裂演化规律研究

断层引起的地面永久大变形是工程特别是生命线工程地震破坏的重要原因之一, 而研究断层错动下上覆土体变形和破裂的发展演化规律, 则是预测地面永久变形状态和分析断层危害性的基础． 本文采用有限元方法对垂直断层错动引起的上覆土体破裂演化规律进行了研究, 建立了垂直断层作用下上覆土体模拟的有限元模型, 对断层错动作用下上覆土体的破裂发展过程进行了模拟分析, 并分析了加载速率、 土体特性及断层倾角等参数对上覆土体的破裂演化发展过程的影响． 结果表明: ① 断层倾角越陡, 地表出现破裂时需要增加的垂直位移越大; ② 由于惯性力的影响, 断层加载速率对地表破裂所需施加位移和土层破裂角产生一定的影响; ③ 断层类型对土层地表破裂角与膨胀角、 摩擦角之间的关系有很大影响． 该分析结果可为新建工程的抗震设计和已建工程结构的抗震加固等工作提供依据．