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1.
Earlier solutions of deformations resulting from the movements of shear and tensile faults in a half space (Bull. Seismol. Soc. Amer. 1985; 75 :1135, 1992; 82 :1018) have been revised in view of cross‐anisotropic stress–strain relationships. The dislocation theory (Canad. J. Phys. 1958; 36 :192) is reviewed and the displacement field due to a concentrated force in an anisotropic half space is solved analytically for developing the current research. A fault is simulated as a point source of strain nuclei in applying the dislocation theory. Data (Terr. Atmos. Oceanic Sci. 2000; 11 (3):591, 631) that were used to study the Chi‐Chi earthquake (ML=7.3; 1999/9/21 AM 1:47) are introduced to compare the solution with the isotropic results. Results indicate that the anisotropy of stress–strain relationships does affect the results of predicted deformations. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

2.
This paper presents a simulation of three components of near-field ground shaking recorded during the main shock at three stations of the September 16, 1978, Tabas (M w = 7.4), Iran, earthquake, close to the causative fault. A hybrid method composed of a discrete wavenumber method developed by Bouchon (Bouchon in Bull Seismol Soc Am 71:959–971, 1981; Cotton and Coutant in Geophys J Int 128:676–688, 1997) and a stochastic finite-fault modeling based on a dynamic corner frequency proposed by Motazedian and Atkinson (Bull Seismol Soc Am 95:995–1010, 2005), modified by Assatourians and Atkinson (Bull Seismol Soc Am 97:935–1949, 2007), is used for generating the seismograms at low (0.1–1.0 Hz) and high frequencies (1.0–20.0 Hz), respectively. The results are validated by comparing the simulated peak acceleration, peak velocity, peak displacement, Arias intensity, the integral of velocity squared, Fourier spectrum and acceleration response spectrum on a frequency-by-frequency basis, the shape of the normalized integrals of acceleration and velocity squared, and the cross-correlation with the observed time-series data. Each characteristic is compared on a scale from 0 to 10, with 10 being perfect agreement. Also, the results are validated by comparing the simulated ground motions with the modified Mercalli intensity observations reported by reconnaissance teams and showed reasonable agreement. The results of the present study imply that the damage distribution pattern of the 1978 Tabas earthquake can be explained by the source directivity effect.  相似文献   

3.
A total of 163 free-field acceleration time histories recorded at epicentral distances of up to 200 km from 32 earthquakes with moment magnitudes ranging from M w 4.9 to 7.4 have been used to investigate the predictive capabilities of the local, regional, and next generation attenuation (NGA) ground-motion prediction equations and determine their applicability for northern Iran. Two different statistical approaches, namely the likelihood method (LH) of Scherbaum et al. (Bull Seismol Soc Am 94:341–348, 2004) and the average log-likelihood method (LLH) of Scherbaum et al. (Bull Seismol Soc Am 99:3234–3247, 2009), have been applied for evaluation of these models. The best-fitting models (considering both the LH and LLH results) over the entire frequency range of interest are those of Ghasemi et al. (Seismol 13:499–515, 2009a) and Soghrat et al. (Geophys J Int 188:645–679, 2012) among the local models, Abrahamson and Silva (Earthq Spectra 24:67–97, 2008) and Chiou and Youngs (Earthq Spectra 24:173–215, 2008) among the NGA models, and finally Akkar and Bommer (Seism Res Lett 81:195–206, 2010) among the regional models.  相似文献   

4.
The Sr isotopic composition of ‘seawater’, as measured on carbonate rocks, shows a composite pattern during geologic history. All known Archaean data are compatible with contemporaneous upper mantle 87Sr/86Sr values. This is followed by a strong increase in the radiogenic component during the 2.5–2.1 b.y. period, a less pronounced increase during the remaining portion of the Proterozoic and a decrease during the Phanerozoic. The trend closely resembles the K2O/Na2O secular variations in composition of igneous and sedimentary rocks (Engelet al, Bull. Geol. Soc. Amer. 85, 843–858, 1974) and probably reflects the fractionation state of the contemporary crust. The data are compatible with recent suggestions of three major tectonic regimes during geologic history: greenstone belts during the Archaean, mobile belts during the Proterozoic and plate tectonics during the Phanerozoic. They also indicate that continental crust during the Archaean contributed only subordinate Sr into the meteoric cycle.  相似文献   

5.
Hamdache  M.  Pel&#;ez  J. A.  Kijko  A.  Smit  A. 《Natural Hazards》2016,86(2):273-293

We estimate the energetic and spatial characteristics of seismicity in the Algeria–Morocco region using a variety of seismic and statistical parameters, as a first step in a detailed investigation of regional seismic hazard. We divide the region into five seismotectonic regions, comprising the most important tectonic domains in the studied area: the Moroccan Meseta, the Rif, the Tell, the High Plateau, and the Atlas. Characteristic seismic hazard parameters, including the Gutenberg–Richter b-value, mean seismic activity rate, and maximum possible earthquake magnitude, were computed using an extension of the Aki–Utsu procedure for incomplete earthquake catalogs for each domain, based on recent earthquake catalogs compiled for northern Morocco and northern Algeria. Gutenberg–Richter b-values for each zone were initially estimated using the approach of Weichert (Bull Seismol Soc Am 70:1337–1346, 1980): the estimated b-values are 1.04 ± 0.04, 0.93 ± 0.10, 0.72 ± 0.03, 0.87 ± 0.02, and 0.77 ± 0.02 for the Atlas, Meseta, High Plateau, Rif, and Tell seismogenic zones, respectively. The fractal dimension D 2 was also estimated for each zone. From the ratio D 2/b, it appears that the Tell and Rif zones, with ratios of 2.09 and 2.12, respectively, have the highest potential earthquake hazard in the region. The Gutenberg–Richter relationship analysis allows us to derive that in the Tell and Rif, the number of earthquake with magnitude above Mw 4.0, since 1925 normalized to decade and to square cell with 100-km sides is equal to 2.6 and 1.91, respectively. This study provides the first detailed information about the potential seismicity of these large domains, including maximum regional magnitudes, characteristics of spatial clustering, and distribution of seismic energy release.

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6.
Summary  This paper presents a simple graphical method for computing the displacement beneath/at the surface of a transversely isotropic half-space subjected to surface loads. The surface load can be distributed on an irregularly-shaped area. The planes of transverse isotropy are assumed to be parallel to the horizontal surface of the half-space. Based on the point load solutions presented by the authors, four influence charts are constructed for calculating the three displacements at any point in the interior of the half-space. Then, by setting z=0 of the derived solutions, another four influence charts for computing the surface displacements can also be proposed. These charts are composed of unit blocks. Each unit block is bounded by two adjacent radii and arcs, and contributes the same level of influence to the displacement. Following, a theoretical study was performed and the results showed that the charts for interior displacements are only suitable for transversely isotropic rocks with real roots of the characteristic equation; however, the charts for surface displacements are suitable for all transversely isotropic rocks. Finally, to demonstrate the use of the new graphical method, an illustrative example of a layered rock subjected to a uniform, normal circular-shaped load is given. The results from the new graphical method agree with those of analytical solutions as well. The new influence charts can be a practical alternative to the existing analytical or numerical solutions, and provide results with reasonable accuracy.  相似文献   

7.
This work presents analytical solutions for displacements caused by three‐dimensional point loads in a transversely isotropic full space, in which transversely isotropic planes are inclined with respect to the horizontal loading surface. In the derivation, the triple Fourier transforms are employed toyield integral expressions of Green's displacement; then, the triple inverse Fourier transforms and residue calculus are performed to integrate the contours. The solutions herein indicate that the displacements are governed by (1) the rotation of the transversely isotropic planes (?), (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′), (3) the geometric position (r, φ, ξ) and (4) the types of loading (Px, Py, Pz). The solutions are identical to those of Liao and Wang (Int. J. Numer. Anal. Methods Geomechanics 1998; 22 (6):425–447) if the full space is homogeneous and linearly elastic and the transversely isotropic planes are parallel to the horizontal surface. Additionally, a series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of the aforementioned factors on the displacements. The results demonstrate that the displacements in the infinite isotropic/transversely isotropic rocks, subjected to three‐dimensional point loads could be easily determined using the proposed solutions. Also, these solutions could realistically imitate the actual stratum of loading situations in numerous areas of engineering. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

8.
We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.  相似文献   

9.
Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

10.
The use of logic trees in probabilistic seismic hazard analyses often involves a large number of branches that reflect the uncertainty in the selection of different models and in the selection of the parameter values of each model. The sensitivity analysis, as proposed by Rabinowitz and Steinberg [Rabinowitz, N., Steinberg, D.M., 1991. Seismic hazard sensitivity analysis: a multi-parameter approach. Bull. Seismol. Soc. Am. 81, 796–817], is an efficient tool that allows the construction of logic trees focusing attention on the parameters that have greater impact on the hazard.In this paper the sensitivity analysis is performed in order to identify the parameters that have the largest influence on the Western Liguria (North Western Italy) seismic hazard. The analysis is conducted for six strategic sites following the multi-parameter approach developed by Rabinowitz and Steinberg [Rabinowitz, N., Steinberg, D.M., 1991. Seismic hazard sensitivity analysis: a multi-parameter approach. Bull. Seismol. Soc. Am. 81, 796–817] and accounts for both mean hazard values and hazard values corresponding to different percentiles (e.g., 16%-ile and 84%-ile). The results are assessed in terms of the expected PGA with a 10% probability of exceedance in 50 years for rock conditions and account for both the contribution from specific source zones using the Cornell approach [Cornell, C.A., 1968. Engineering seismic risk analysis. Bull. Seismol. Soc. Am. 58, 1583–1606] and the spatially smoothed seismicity [Frankel, A., 1995. Mapping seismic hazard in the Central and Eastern United States. Seismol. Res. Lett. 66, 8–21]. The influence of different procedures for calculating seismic hazard, seismic catalogues (epicentral parameters), source zone models, frequency–magnitude parameters, maximum earthquake magnitude values and attenuation relationships is considered. As a result, the sensitivity analysis allows us to identify the parameters with higher influence on the hazard. Only these parameters should be subjected to careful discussion or further research in order to reduce the uncertainty in the hazard while those with little or no effect can be excluded from subsequent logic-tree-based seismic hazard analyses.  相似文献   

11.
Multiple approaches are used to study the potential seismic hazard in the North China Craton (NCC, or North China Plain), where approximately 15 % of the Chinese population resides and under which active faults are located. In this study, we develop a new modified Mercalli intensity (MMI) attenuation relationship for the NCC using intensity data from 10 instrumentally recorded events. We then utilize this relationship to infer the magnitude and epicentral location of historic events based on the method proposed by Bakun and Wentworth (Bull Seismol Soc Am 87(6):1502–1521, 1997). In addition, a modified stochastic finite fault model is employed to simulate the strong ground motions caused by these historic events. The simulated peak ground accelerations and velocities are then converted into regional MMI distributions through empirical relationships, and these synthetic MMI maps are compared to field observations. The resultant MMI attenuation versus distance models of the 1976 M w 7.6 Tangshan event and the 1679 M 8.0 Sanhe-Pinggu event are consistent with the empirical attenuation relationships, and the location and size of the meizoseismal area (>VIII) are consistent with observations. The successful modeling of these historic events indicates that a stochastic finite fault model constrained by the regional MMI attenuation relationship can be used to evaluate a wide range of scenarios based on modern computational simulations. These findings may also provide useful information for the estimation and mitigation of potential seismic hazards in this region.  相似文献   

12.
In this paper, a single-region boundary element method (BEM) is presented for the analysis of transversely isotropic bi-material halfspaces with arbitrarily inclined planes of isotropy and material interfaces. The proposed BEM uses the fundamental solution of a transversely isotropic bi-material fullspace and five boundary element techniques. Infinite boundary elements are introduced to consider the far-fields of a transversely isotropic bi-material halfspace. The effective integration methods are proposed for dealing with various integrals in the discretized boundary integral equation. The stresses at internal points are obtained using the coordinate transformation of kernel functions, and the stresses on the boundary surface are calculated using an improved traction recovered method. Numerical verifications of displacements and stresses for a benchmark problem are conducted, and excellent agreement with previously published results is obtained. Numerical examples are presented to illustrate the influence of non-horizontal or horizontal planes of isotropy in bi-material halfspaces on the displacements and stresses induced by the tractions on the horizontal boundary surface. Results reveal that the elastic fields vary clearly with the dip angle of the isotropic plane and the stresses across the bi-material interface are closely related to the ratios of the elastic parameters of the bi-material.  相似文献   

13.
This paper presents the analytical layer element solutions for deformations of transversely isotropic elastic media subjected to nonaxisymmetric loading at an arbitrary depth. The state vectors for the nonaxisymmetric problem are deduced through the substitution of the Hu Hai‐chang solutions into the basic equations for the transversely isotropic elastic media. From the state vectors, the analytical layer element of a single layer is obtained in the Hankel transformed domain. The analytical layer element is an exact and symmetric stiffness matrix whose elements are without positive exponential functions, which can not only simplify the calculation but also improve the stability of computation. On the basis of the continuity conditions between adjacent layers, the global stiffness matrix is obtained by assembling the interrelated layer elements. The solutions for the multilayered elastic media in the transformed domain are obtained by solving the algebraic equation of the global stiffness matrix, which satisfies the boundary conditions. The actual solutions in the physical domain are further obtained by inverting the Hankel transform. Finally, some cases are analyzed to verify the solutions and evaluate the influences of the transversely isotropic character and stratified character of the media on the load–displacement responses. The numerical results show that the variations of the elastic properties between layers have a great effect on the displacements of the multilayered media. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

14.
The Munébrega Plio-Quaternary half-graben is a NW-SE trending neotectonic depression located in the central sector of the intraplate Iberian Range (NE Spain). The master fault of the half-graben offsets an Upper Pleistocene pediment deposit, forming an upslope-facing scarp. A trench dug across the fault scarp exposed a 25-m wide deformation zone consisting of graben and horst fault blocks with fissures in the upper part of the scarp, and a monoclinal flexure affected by normal and reverse faults in the lower part of the scarp. We infer a minimum of three faulting events over the past 72 ka, yielding an average (maximum) recurrence interval of 24 ka. The oldest event (72–41 ka) produced an antislope scarp on the relict pediment surface, confining deposition to the downthrown block. Cross-cutting faults affecting sedimentary units deposited in the sediment trap produced by the first event provide evidence for at least two younger events (33–19? ka). The measured cumulative vertical displacement (7.4 m) yield a minimum vertical slip rate of 0.10 ± 0.01 mm/year (2σ error) for the past 72 ka. If the paleoearthquakes ruptured the whole mappable length of the fault (ca. 20 km), they probably had moment magnitudes ca. 6.9 (Stirling et al. Bull Seismol Soc Am, 2002). Such earthquakes would have been more than a magnitude unit larger than the largest ones recorded historically in the Iberian Range. These results suggest that the official seismic hazard assessments, based solely on the historic and instrumental record, may underestimate the seismic hazard in the area.  相似文献   

15.
The classical equations relating the trace element concentrations of the liquid and solid phases coexisting in the simple fractional crystallization of a parental magma have been put in a simple graphical form, which allows rapid analysis of the possible genetic relationships in a given rock suite. The effects of an incomplete separation between the two phases are taken into account. The approach does not require the use of otherwise estimated partition coefficients. Trace element data concerning the minerals of cumulates, where available, may provide an independent estimation of the effective mineral-liquid partition coefficients. With reasonable assumptions, this approach may even be applied to plutonic rocks. Interpretation of the published rare earth element data from the Southern California Batholith by this procedure suggests that a tonalitic parental magma could generate a granodioritic liquid by crystallizing 40–50 wt % of a solid residue of gabbroic composition, in agreement with Larsen's (Mem. Geol. Soc. Amer. 29, 1948) calculations. The calculated mineral-liquid partition coefficients for the REE fall in the range of published phenocryst-groundmass values for acidic volcanic rocks.  相似文献   

16.
Two major traces of active thrust faults were identified in the Kashmir Basin (KB) using satellite images and by mapping active geomorphic features. The ~N130°E strike of the mapped thrust faults is consistent with the regional ~NE–SW convergence along the Indian–Eurasian collision zone. The ~NE dipping thrust faults have uplifted the young alluvial fan surfaces at the SW side of the KB. This created a major tectono-geomorphic boundary along the entire strike length of the KB that is characterised by (1) a low relief with sediment-filled sluggish streams to the SE and (2) an uplifted region, with actively flowing streams to the SW. The overall tectono-geomorphic expression suggests that recent activity along these faults has tilted the entire Kashmir valley towards NE. Further, the Mw 7.6 earthquake, which struck Northern Pakistan and Kashmir on 8 October 2005, also suggests a similar strike and NE dipping fault plane, which could indicate that the KB fault is continuous over a distance of ~210 km and connects on the west with the Balakot Bagh fault. However, the geomorphic and the structural evidences of such a structure are not very apparent on the north-west, which thus suggest that it is not a contiguous structure with the Balakot Bagh fault. Therefore, it is more likely that the KB fault is an independent thrust, a possible ramp on the Main Himalayan Thrust, which has uplifting the SW portion of the KB and drowning everything to the NE (e.g. Madden et al. 2011). Furthermore, it seems very likely that the KB fault could be a right stepping segment of the Balakot Bagh fault, similar to Riasi Thrust, as proposed by Thakur et al. (2010). The earthquake magnitude is measured by estimating the fault rupture parameters (e.g. Wells and Coppersmith in Bull Seismol Soc Am 84:974–1002, 1994). Therefore, the total strike length of the mapped KB fault is ~120 km and by assuming a dip of 29° (Avouac et al. in Earth Planet Sci Lett 249:514–528, 2006) and a down-dip limit of 20 km, a Mw of 7.6 is possible on this fault.  相似文献   

17.
In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (Ezz/Gxz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

18.
王俊林  祝彦知  张天航 《岩土力学》2007,28(7):1315-1322
在考虑横观各向同性含液饱和多孔介质固体骨架和流体可压缩性以及固体骨架的黏弹性特征下,基于横观各向同性含液饱和多孔介质u-w形式的三维动力控制方程,以固相位移u、液相相对位移w为基本未知量,综合运用Laplace变换、双重Fourier变换等方法,在直角坐标系下通过引入中间变量,将六元2阶动力控制方程组化为两组各含4个未知变量的常微分方程组,给出了直角坐标系下横观各向同性含液饱和多孔介质三维黏弹性动力反应的积分形式一般解;作为理论推导的验证,通过引入初始条件和边界条件,对横观各向同性含液饱和多孔介质半空间黏弹性瞬态反应问题进行了求解。解答的退化验证表明,所推导的理论解是正确的。  相似文献   

19.
The Biot linearized theory of fluid saturated porous materials is used to study the plane strain deformation of a two-phase medium consisting of a homogeneous, isotropic, poroelastic half-space in welded contact with a homogeneous, isotropic, perfectly elastic half-space caused by a two-dimensional source in the elastic half-space. The integral expressions for the displacements and stresses in the two half-spaces in welded contact are obtained from the corresponding expressions for an unbounded elastic medium by applying suitable boundary conditions at the interface. The case of a long dip-slip fault is discussed in detail. The integrals for this source are solved analytically for two limiting cases: (i) undrained conditions in the high frequency limit, and (ii) steady state drained conditions as the frequency approaches zero. It has been verified that the solution for the drained case (ω → 0) coincides with the known elastic solution. The drained and undrained displacements and stresses are compared graphically. Diffusion of the pore pressure with time is also studied.  相似文献   

20.
A transversely isotropic linear elastic half‐space, z?0, with the isotropy axis parallel to the z‐axis is considered. The purpose of the paper is to determine displacements and stresses fields in the interior of the half‐space when a rigid circular disk of radius a completely bonded to the surface of the half‐space is rotated through a constant angle θ0. The region of the surface lying out with the circle r?a, is free from stresses. This problem is a type of Reissner–Sagoci mixed boundary value problems. Using cylindrical co‐ordinate system and applying Hankel integral transform in the radial direction, the problem may be changed to a system of dual integral equations. The solution of the dual integral equations is obtained by an approach analogous to Sneddon's (J. Appl. Phys. 1947; 18 :130–132), so that the circumferential displacement and stress fields inside the medium are obtained analytically. The same problem has already been approached by Hanson and Puja (J. Appl. Mech. 1997; 64 :692–694) by the use of integrating the point force potential functions. It is analytically proved that the present solution, although of a quite different form, is equivalent to that given by Hanson and Puja. To illustrate the solution, a few plots are provided. The displacements and the stresses in a soil deposit due to a rotationally symmetric force or boundary displacement may be obtained using the results of this paper. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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