Modelling Rupture Dynamics of a Planar Fault in 3-D Half Space by Boundary Integral Equation Method: An Overview

In this article, we first reviewed the method of boundary integral equation (BIEM) for modelling rupture dynamics of a planar fault embedded in a 3-D elastic half space developed recently (ZHANG and CHEN, 2005a,b). By incorporating the half-space Green's function, we successfully extended the BIEM, which is a powerful tool to study earthquake rupture dynamics on complicated fault systems but limited to full-space model to date, to half-space model. In order to effectively compute the singular integrals in the kernels of the fundamental boundary integral equation, we proposed a regularization procedure consisting of the generalized Apsel-Luco correction and the Karami-Derakhshan algorithm to remove all the singularities, and developed an adaptive integration scheme to efficiently deal with those nonsingular while slowly convergent integrals. The new BIEM provides a powerful tool for investigating the physics of earthquake dynamics. We then applied the new BIEM to investigate the influences of geometrical and physical parameters, such as the dip angle (δ) and depth (h) of the fault, radius of the nucleation region (R_asp), slip-weakening distance (D_c), and stress inside (T_i) and outside (T_e) the nucleation region, on the dynamic rupture processes on the fault embedded in a 3-D half space, and found that (1) overall pattern of the rupture depends on whether the fault runs up to the free surface or not, especially for strike-slip, (2) although final slip distribution is influenced by the dip angle of the fault, the dip angle plays a less important role in the major feature of the rupture progress, (3) different value of h, δ, R_asp, T_e, T_i and D_c may influence the balance of energy and thus the acceleration time of the rupture, but the final rupture speed is not controlled by these parameters.     

Geodynamic studies of the April 20(21), 2006 Olyutorskii earthquake based on observations by the Kamchatka GPS network

This paper presents results from an analysis of GPS observations made by the Kamchatka regional GPS network (KAMNET) in relation to the Olyutorskii earthquake and plate interaction. The coseismic changes were interpreted for the Olyutorskii earthquake and its largest aftershock (May 22, 2006, M _W = 6.6) within the framework of a dislocation source in an elastic half-space.     

Factors affecting the measurement of the vertical hydraulic conductivity of a streambed sediment using standpipe tests

The vertical hydraulic conductivity (K_v) of a stream or lake sediment is often determined in the field using standpipe tests. Calculation of K_v is based on the assumption that the hydraulic head in the pipe is equal to that of the stream or lake stage. In this work, a modified equation for K_v is developed for the standpipe test which is applicable when this assumption is not valid. The equation involves not only the hydraulic head at different times but also the difference in the hydraulic head (a) between the groundwater level and river stage. The effects of certain factors on K_v, such as the ratio of the hydraulic head at different times (h₁/h₂), the difference a, and the initial water table height (h₀), are also discussed. The results show that when h₁/h₂ is constant, the relative error (E_r) in K_v increases with the ratio a/h₂. Furthermore, if a/h₂ < 0.05, then for any value of h₁/h₂, E_r is less than 5% using the modified equation. Also, if a/h₂ is large, hydraulic head readings with larger h₁/h₂ ratios must be used to avoid large E_r values. The results of a field test also indicate that the error in K_v decreases as the value of h₀ increases. Copyright © 2013 John Wiley & Sons, Ltd.     

Inelastic design spectra accounting for soil conditions

This paper is concerned with the effect of soil conditions on the response of single-degree-of-freedom inelastic systems subjected to earthquake motions. The ground motions considered are 72 horizontal components of motion, most of them recorded during the 3 March, 1985 Chile earthquake (M_s = 7·8) and two main aftershocks; among these records are some of the strongest and longer duration earthquake motions ever recorded. The recording station sites were classified in one of three soil types, which can be generically referred to as rock, firm ground, and medium stiffness soil. Response results for each group were analysed statistically to obtain factors for deriving inelastic design spectra of the Newmark-Hall type, as well as alternative simplified spectral shapes suitable for code formulation. Particular attention was given to the response modification factors (R) that are commonly used in seismic codes to reduce the ordinates of the elastic spectrum to account for the energy dissipation capacity of the structure. The response modification factors, known to be function of both the natural period of vibration and the ductility factor, are found to be dependent on soil conditions, particularly in the case of medium stiffness soils. It is also shown that the indirect procedure of applying R to the elastic design spectrum is less accurate than directly using functions that represent the inelastic design spectrum.     

Determination of ductility factor considering different hysteretic models

In current seismic design procedures, base shear is calculated by the elastic strength demand divided by the strength reduction factor. This factor is well known as the response modification factor, R, which accounts for ductility, overstrength, redundancy, and damping of a structural system. In this study, the R factor accounting for ductility is called the ‘ductility factor’, R_μ. The R_μ factor is defined as the ratio of elastic strength demand imposed on the SDOF system to inelastic strength demand for a given ductility ratio. The R_μ factor allows a system to behave inelastically within the target ductility ratio during the design level earthquake ground motion. The objective of this study is to determine the ductility factor considering different hysteretic models. It usually requires large computational efforts to determine the R_μ factor. In order to reduce the computational efforts, the R_μ factor is prepared as a functional form in this study. For this purpose, statistical studies are carried out using forty different earthquake ground motions recorded at a stiff soil site. The R_μ factor is assumed to be a function of the characteristic parameters of each hysteretic model, target ductility ratio and structural period. The effects of each hysteretic model to the R_μ factor are also discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Earthquake response spectra taking account of number of response cycles

Proposed is a new definition of earthquake response spectra, which takes account of the number of response cycles N. The Nth largest amplitude of absolute acceleration response of a linear oscilator with natural period T and damping ratio h, which is subjected to ground motion at its base, is defined as S_A(T, h, N). By defining a reduction factor η(T, h, N) as S_A(T, h, N)/S_A(T, h, 1), characteristics of η(T, h, N) were investigated based on 394 components of strong motion records obtained in Japan. Two practical empirical formulae to assess the reduction factor η(T, h, N) are proposed.     

Two-dimensional scattering of SH waves in a soil layer underlain with a sloping bedrock

A two-dimensional analysis is applied to examine the effect that a sloping bedrock half-space has on the amplification of an anti-plane shear wave. The direct boundary integral equation method is used for the two-dimensional analysis. The particular soil–rock configuration investigated includes a homogeneous soil layer underlain by a sloping rock half-space. The rock half-space dips for a horizontal distance L and then becomes horizontal so that the overlying soil layer has a thickness H that remains constant from this point to infinity. The materials in the soil–rock configuration are considered viscoelastic except in the rock half-space below soil layer thickness H, which is considered elastic. This limitation in damping is due to the correction used for the truncation of the half-space boundary. Four cases are used to study the relationship between rock slope and surface displacement, vertical, 1:2, 1:4, 1:8. Surface displacements are determined for each of these cases for half-space incidence angles of 90, 75, and 60°. To allow for applicability to a wide range of problems, results are determined as a function of dimensionless parameters. In addition, solutions from a one-dimensional analysis are compared with the results of the two-dimensional analysis to establish limits outside of which a one-dimensional analysis suffices.     

Anisotropy and depth‐related heterogeneity of hydraulic conductivity in a bog peat. I: laboratory measurements

Anisotropy and heterogeneity of hydraulic conductivity (K) are suspected of greatly affecting rates and patterns of ground‐water seepage in peats. A new laboratory method, termed here the modified cube method, was used to measure horizontal and vertical hydraulic conductivity (K_h and K_v) of 400 samples of bog peat. The new method avoids many of the problems associated with existing field and laboratory methods, and is shown to give relatively precise measurements of K. In the majority of samples tested, K_h was much greater than K_v, indicating that the bog peat was strongly anisotropic. Log₁₀K_h, log₁₀K_v, and log₁₀ (K_h/K_v) were found to vary significantly with depth, although none of the relationships was simple. We comment on the scale dependency of our measurements. Copyright © 2002 John Wiley & Sons, Ltd.     

Multifractal comparison of the outputs of two optical disdrometers

ABSTRACT

In this paper a universal multifractals comparison of the outputs of two types of collocated optical disdrometers installed on the roof of the Ecole des Ponts ParisTech is performed. A Campbell Scientific PWS100 which analyses the light scattered by the hydrometeors and an OTT Parsivel² which analyses the portion of occluded light are deployed. Both devices provide a binned distribution of drops according to their size and velocity. Various fields are studied across a range of scales: rain rate (R), liquid water content (ρ), polarimetric weather radar quantities such the horizontal reflectivity (Z_h) and the specific differential phase (K_dp), and drop size distribution (DSD) parameters such as the total drop concentration (N_t) and the mass-weighted diameter (D_m). For both devices, good scaling is retrieved on the whole range of available scales (2?h–30?s), except for the DSD parameters for which the scaling only holds down to few minutes. For R, the universal multifractal parameters are found to equal 1.5 and 0.2 for α and C₁, respectively. Results are interpreted with the help of the classical Z_h–R and R–K_dp radar relations.

Editor D. Koutsoyiannis; Associate editor E. Volpi     

Horizontal hydraulic conductivity of shallow streambed sediments and comparison with the grain‐size analysis results

Streambed horizontal hydraulic conductivity (K_h) has a substantial role in controlling exchanges between stream water and groundwater. We propose a new approach for determining K_h of the shallow streambed sediments. Undisturbed sediment samples were collected using tubes that were horizontally driven into streambeds. The sediment columns were analysed using a permeameter test (PT) on site. This new test approach minimizes uncertainties due to vertical flow in the vicinity of test tube and stream stage fluctuations in the computation of the K_h values. Ninety‐eight PTs using the new approach were conducted at eight sites in four tributaries of the Platte River, east‐central Nebraska, USA. The K_h values were compared with the nondirectional hydraulic conductivity values (K_g) determined from 12 empirical grain‐size analysis methods. The grain‐size analysis methods used the same sediment samples as K_h tests. Only two methods, the Terzaghi and Shepherd methods, yielded K_g values close to the K_h values. Although the Sauerbrei method produced a value relatively closer to K_h than other nine grain‐size analysis methods, the values from this method were not as reliable as the methods of Terzaghi and Shepherd due to the inconsistent fluctuation of the average estimates at each of the test sites. The Zunker, Zamarin, Hazen, Beyer, and Kozeny methods overestimated K_h, while the Slichter, US Bureau of Reclamation (USBR), Harleman, and Alyamani and Sen methods underestimated K_h. Any of these specific grain‐size methods might yield good estimates of streambed K_h at some sites, but give poor estimates at other sites, indicating that the relationship between K_g and K_h is significantly site dependent in our study. Copyright © 2011 John Wiley & Sons, Ltd.     

Features and physical process of the dynamic evolution pattern of ground resistivity precursor front

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The effect of travelling seismic waves on the dynamic response of earth dams

A theoretical investigation of the dynamic response of earth dams to the travelling seismic waves is presented. The earth dam is simplified as a truncated two-dimensional elastic wedge. The dam body consists of an isotropical linear viscoelastic material with homogeneous elastic modulus and density. The seismic waves travel along the longitudinal direction of the earth dam. The numerical calculations show the following. (i) For the longitudinal mode of vibration, the greater the ratio (H/L) of the height to the lenght of the complete wedge, the more the natural transverse period of vibrational of the two-dimensional wedge is less than that of the one-dimensional wedge. Especially for the first two natural transverse period, this influence is large. The decrease of the ratio of the natural transverse period for a two-dimensional wedge to that for a one-dimensional wedge with the ratio H/L is rapid for the higher than for the lower longitudinal modes. (ii) Comparing with the one-dimensional wedge, the natural transverse periods for the two-dimensional case in the complete wedge are lower, and they will increase as the coefficient of truncation, h/H increases. (iii) When the frequency of forced vibration is less than the natural transverse frequency for one-dimensional wedge, the amplification is less for a two-dimensional wedge than for a one-dimensional wedge. (iv) When the phase difference of ground motion at both ends of the dam equals π, the amplification for a two-dimensional wedge is less than that for a one-dimensional wedge, but when the phase difference equals nπ, (n > 1), the situation is reversed. (v) As the coefficient of truncation, h/H, increases, the displacement model partecipations decrease monotically. (vi) In general, the displacement caused by an earthquake is greater for a one-dimensional wedge than for a two-dimensional wedge when considering the seismic waves travelling, but the acceleration response of a two-dimensional wedge with long length of dam to travelling seismic waves with long dominant period is greater than that of a one-dimensional wedge. When the length of the dam is short enough, the response of a two-dimensional wedge without considering the influence of travelling seismic waves always gives the greatest value.     

Upward infiltration–evaporation method to estimate soil hydraulic properties

Determination of saturated hydraulic conductivity, K_s, and the van Genuchten water retention curve θ(h) parameters is crucial in evaluating unsaturated soil water flow. The aim of this work is to present a method to estimate K_s, α and n from numerical analysis of an upward infiltration process at saturation (Cap0), with (Cap0 + h) and without (Cap0) an overpressure step (h) at the end of the wetting phase, followed by an evaporation process (Evap). The HYDRUS model as well as a brute-force search method were used for theoretical loam soil parameter estimation. The uniqueness and the accuracy of solutions from the response surfaces, K_s–n, α–n and K_s–α, were evaluated for different scenarios. Numerical experiments showed that only the Cap0 + Evap and Cap0 + h + Evap scenarios were univocally able to estimate the hydraulic properties. The method gave reliable results in sand, loam and clay-loam soils.     

Start‐Up Study on Biohydrogen from Palm Oil Mill Effluent in a Pilot‐Scale Reactor

A start‐up study for biohydrogen production from palm oil mill effluent (POME) is carried out in a pilot‐scale up‐flow anaerobic sludge blanket fixed‐film reactor (UASFF). A substrate with a chemical oxygen demand (COD) of 30 g L^?1 is used, starting with molasses solution for 30 days and followed by a 10% v/v increment of POME/molasses ratio. At 100% POME, a hydrogen content of 80%, hydrogen production rate of 36 L H₂ per day, and maximum COD removal of 48.7% are achieved. Bio‐kinetic coefficients of Monod, first‐order, Grau second‐order, and Stover‐Kincannon kinetic models are calculated to describe the performance of the system. The steady‐state data with 100% POME shows that Monod and Stover‐Kincannon models with bio‐kinetic coefficients of half‐velocity constant (K_s) of 6000 mg COD L^?1, microbial decay rate (K_d) of 0.0015 per day, growth yield constant (Y) of 0.786 mg volatile suspended solids (VSS)/mg COD, specific biomass growth rate (μ_max) of 0.568 per day, and substrate consumption rate of (U_max) 3.98 g/L day could be considered as superior models with correlation coefficients (R²) of 0.918 and 0.989, respectively, compared to first‐order and Grau's second‐order models with coefficients of K₁ 1.08 per day, R² 0.739, and K_2s 1.69 per day, a = 7.0 per day, b = 0.847.     

Introductory notes on shock remanent magnetization and shock demagnetization of igneous rocks

Summary Effects of mechanical shocks of about 0.5 msec in duration on the remanent magnetization of igneous rocks are experimentally studied. The remanent magnetization acquired by applying a shock (S) in the presence of a magnetic field (H), which is symbolically expressed asJ _R (H₊S H_o), is very large compared with the ordinary isothermal remanent magnetization (IRM) acquired in the same magnetic field.J _R (H₊S H_o) is proportional to the piezo-remanent magnetization,J _R (H₊P₊P_o H_o).The effect of applyingS in advance of an acquisition of IRM is represented symbolically byJ _R (S H₊ H_o).J _R (S H₊ H_o) can become much larger than the ordinary IRM, and is proportional to the advance effect of pressure on IRM,J _R(P₊ P₀ H₊ H₀).The effect of shockS applied on IRM in non-magnetic space is represented by the shock-demagnetization effect,J _R(H₊ H₀ S), which also is proportional toJ _R(H₊ H₀ P₊ P₀).Because, the duration of a shock is very short, a single shock effect cannot achieve the final steady state. The effect ofn-time repeated shocks, is represented byJ ₀+J ^*(n), whereJ ₀ means the immediate effect and J ^*(n) represent the resultant effect of repeating, which is of mathematical expression proportional to [1–exp {–(n–1)}].

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Zusammenfassung Die Effekte des mechanischen Stosses mit der Dauer von etwa 0.5 ms auf der remanenten Magnetisierung wurden experimentell nachgesucht. Das erworbene Remanenz der Magnetisierung nach dem Stoss (S) unter dem magnetischen Feld (H), das hier symbolisch alsJ _R(H₊ SH₀) bezechnet wird, ist sehr stark im Vergleich mit der normalen isothermischen remanenten Magnetisierung (IRM) unter demselben magnetischen Feld.J _R(H₊ S H₀) ist im Verhältnis zur piezoremanenten Magnetisierung,J _R(H₊ P₊ P₀ H₀).Der Effekt vom Stoss vor der Erwerbung von IRM wird symbolisch alsJ _R(S H₊ H₀) bezeichnet.J _R(S H₊ H₀) kann viel stärker als die normale IRM werden, im verhältnis zum Effekt des vorausgegebenen Drucks auf IRMJ _R(P₊ P₀ H₊ H₀).Der Effekt des Stosses auf IRM im Raum ohne magnetisches Feld wird mit dem Stossentmagnetisierungseffekt dargestellt,J _R(H₊ H₀ S), der auch proportional zuJ _R(H₊ H₀ P₊ P₀) ist.Da die Dauer einzelnen Stosses sehr kurz ist, kann der Effekt des einmaligen Stosses den endgültigen stabilen Zustand nicht erreichen. Der Effekt nachn-maligen wiederholten Stossen wird alsJ ₀+J ^*(n) bezeichnet, wobeiJ ₀ den unverzüglichen Effekt bedeutet, und J ^*(n) beschreibt den resultanten Effekt der Stosswiederholung, dessen mathematische Darstellung proporational zu [1–exp {–(n–1)}] ist.

     

Peak and integral seismic parameters of L��Aquila 2009 ground motions: observed versus code provision values

The M _w 6.3 L’Aquila earthquake of April 6, 2009 hit a wide area of the Abruzzo region (Central Italy). The epicentre of the main shock was very close to the urban centre of L’Aquila, the regional capital, with an epicentral distance less than 10 km. It was the strongest earthquake ever recorded in Italy which has provided ground motion recordings from accelerometric stations located in close proximity to the epicentre. Because of this, several remarkable results can be achieved by analysing the strong motion recorded signals in terms of peak (PGA, PGV and PGD) and integral (Housner Intensity, I _H) seismic parameters. Additionally, an alternative time-domain representation of recorded signals has been used to furnish a rapid comparison of traces recorded at different stations and along different directions. Some comparisons between the response spectra derived from the recordings and the elastic demand spectra provided in the new seismic Italian code have also been performed. PGA recorded values are very high and generally higher than code values for seismic actions with return period T _R = 475 years. In some cases, this also happens for seismic actions with T _R up to 2,475 years. With regard to I _H, recorded values are generally higher for T _R = 475 years, whilst they are remarkably lower for T _R = 2,475 years. Accurate analyses have been carried out in the article to better understand the above differences and their significance and implications.     

Variation of lunar and solar geomagnetic tides with sunspot and geomagnetic activity

Summary Solar and lunar geomagnetic tides inH at Alibag have been determined by spectral analysis of discrete Fourier transforms following the method of Black and the well-known Chapman-Miller method. The seasonal variation inL ₂(H) is opposite to that inL ₂(D) with maximum in thed season and minimum in thej season. In bothH andD the enhancement due to sunspot activity is larger in lunar tide than in solar tide. Surprisingly, the enhancement due to magnetic activity is greater inL ₂(H) than inS ₁(H), while the contrary is true for declination. It is inferred that there is a local time component of the storm time variation contrary to the view expressed by Green and Malin. The enhancements in amplitudesL ₂ andS ₁ inH andD, due to sunspot activity and due to magnetic activity, have been separated. The results show that the amplitude at zero sunspot number increases with magnetic activity in all the four parameters, while the enhancement due to sunspot activity at different levels of magnetic activity decreases with increase ofK _p. But if bothK _p andR are increasing, whenK _p increases enhancement due toR decreases and whenR increases enhancement due toK _p decreases.     

Oscillations with planetary wave periods in variations in the ionospheric parameters over Eastern Siberia

The results of a periodogramanalysis of the variations in the ionospheric parameters, measured using the vertical radio sounding method at midlatitude Irkutsk observatory (Eastern Siberia), are presented. The 1984–1986 period of observations was used. It has been indicated that the statistically significant oscillations with periods typical of planetary waves are present in the variations in f ₀E_s, f _bE_s, h′E_s, f _min, f ₀F2, and h′F.

     

InSAR数据约束的2022年1月8日青海门源MS6.9地震发震构造研究

利用Sentinel-1A卫星升降轨道数据和D-InSAR技术获得青海门源2022年1月8日M_S6.9地震的同震形变场,并基于弹性半空间位错模型反演其震源参数,利用分布滑动模型确定断层面上的滑动分布。结果表明,2022年1月8日青海门源地震的同震形变场沿NWW-SEE方向分布;断裂带南缘升轨影像和降轨影像最大视距分别为61 cm和62 cm,断裂带北缘升轨影像和降轨影像最大视距地表形变量分别为43 cm和56 cm。InSAR同震形变场断裂尺度模型断层长30 km,宽18 km,最大滑移量3.5 m;断层滑动分布模型表明该地震为左旋走滑地震。结合冷龙岭断裂的运动特征和几何特征,初步确定此次M_S6.9地震的发震断裂为冷龙岭断裂     

Quantification of fundamental frequency drop for unreinforced masonry buildings from dynamic tests

The knowledge of fundamental frequency and damping ratio of structures is of uppermost importance in earthquake engineering, especially to estimate the seismic demand. However, elastic and plastic frequency drops and damping variations make their estimation complex. This study quantifies and models the relative frequency drop affecting low‐rise modern masonry buildings and discusses the damping variations based on two experimental data sets: Pseudo‐dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL. The relative structural frequency drop is shown to depend mainly on shaking amplitude, whereas the damping ratio variations could not be explained by the shaking amplitude only. Therefore, the absolute frequency value depends mostly on the frequency at low amplitude level, the amplitude of shaking and the construction material. The decrease in shape does not vary significantly with increasing damage. Hence, this study makes a link between structural dynamic properties, either under ambient vibrations or under strong motions, for low‐rise modern masonry buildings. A value of 2/3 of the ambient vibration frequency is found to be relevant for the earthquake engineering assessment for this building type. However, the effect of soil–structure interaction that is shown to also affect these parameters has to be taken into account. Therefore, an analytical methodology is proposed to derive first the fixed‐base frequency before using these results. Copyright © 2010 John Wiley & Sons, Ltd.