Rotation and strain seismology

Asymmetric continuum theory points to the equal roles of the rotation motions and those related directly to shear or confining strains. The strain motions could be quite independent or mutually related with the eventual phase shifts, while the displacements have only a mathematical sense; a real displacement may appear along the fracture slip only. Formally, any deformation could be presented as related to the displacements; however, its origin in a fracture source should be considered either as belonging to an individual process or to complex correlated events; in these cases, the confining, shear and rotation strains can be related mathematically to the different displacement fields. Some of these related deformations could be emitted from a source with a phase shift, while the observed displacements (deduced from records) result as a sum of these independent displacements. An important influence on a source process and on the premonitory micro-events has the material defects, their distribution, and mobility. The defect arrays lead to a concentration of stresses and their local reorganization. Thus, in this paper, we consider the induced stresses and strains related to defect content and to its modification and redistribution. Moreover, an important role in understanding the complex correlated events in a source plays the release?Crebound mechanism. The release?Crebound mechanism in an earthquake source processes leads to a possible direct or phase-shifted correlations between the emitted motions; in this aspect, a propagation of the coupled strain and rotation waves is discussed. In particular, we consider the point fracture events as related either to a confining load or/and to the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. In some important seismic regions, we have the recording system which permits to record the strains and rotations. However, we should point that the wordwide seismological network is not adequate to record the complex strain deformations released in the fracture processes and remains quite insufficient to understand the global stress changes and related strain waves of a very low period. Consideration on a recording mechanism of the long displacement waves indicates the insufficiencies of the present global recording system and points that recording of the global strain and rotation waves is an important and urgent task.     

Molecular transport in fracture processes

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mechanism. In particular, we consider the point fracture events as associated with a confining load or/and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. It is to be pointed out that such molecular motions are too small to be observed by the existing seismological networks.     

Plasticity model for sand under small and large cyclic strains: a multiaxial formulation

This paper presents the multiaxial formulation of a plasticity model for sand under cyclic shearing. The model adopts a kinematic hardening circular cone as the yield surface and three non-circular conical surfaces corresponding to the deviatoric stress ratios at phase transformation, peak strength and critical state. The shape of the non-circular surfaces is formulated in accordance with the experimentally established failure criteria, while their size is related to the value of the state parameter ψ. To simulate cyclic response under small and large shear strain amplitudes without a change in model parameters, it was found necessary to introduce: (a) a non-linear hysteretic (Ramberg–Osgood type) formulation for the strain rate of elastic states and (b) an empirical index of the effect of fabric evolution during shearing which scales the plastic modulus. This index is estimated in terms of a macroscopic second-order fabric tensor, which develops as a function of the plastic volumetric strain increment and the loading direction in the deviatoric plane. Comparison of simulations to pertinent data from 27 resonant column, cyclic triaxial and cyclic direct simple shear tests provide a measure for the overall accuracy of the model.     

漳州台深井应变不变量同震响应分析

在解决钻孔应变观测加衬模型的待定常数的基础上,巧妙地利用不变量与坐标系选择无关的性质,推导出了5组观测组合计算不变量的简洁表达式,并以玉树地震为例,选取漳州台深井观测系统的探头上、下端面8分量应变观测单元的观测资料,采用加衬模型分别根据探头上下端面的5组观测组合公式计算了地震当天的最大主应变、最小主应变、最大主应变相应...     

YRY-4型钻孔应变仪观测的P波剪应变

传统地震仪观测的是一个点的位移随时间的变化, 而应变仪观测的是位移的空间导数随时间的变化。 在四川姑咱台用YRY-4型四分量钻孔应变仪进行的每秒100次采样观测实验, 记录到三次地方震。 在这样高的采样率下, YRY-4型四分量应变仪观测数据保持了令人满意的自洽和足够高的信度。 观测表明, P波的应变不仅有面应变成分, 而且有剪应变成分。 这为澄清P波的性质, 给出了直接的观测证据。 根据弹性波理论, P波无旋转, 可以有体应变和剪应变成分。     

The effect of a deviatoric stress on physical rock properties

Petrophysical measurements were carried out on dry specimens of mica-gneiss, amphibolite and serpentinite from KTB core samples and samples of surface outcrops in order to determine the effect that a deviatoric stress field, as observed at the KTB area, may have on the in-situ rock properties. Simulating the variation of the actual principal stresses and temperature with depth, seismic wave velocities, densities, linear and volumetric strain (porosity) have been measured, taking into account the overall spatial orientation of the foliation at the KTB area with respect to the principal stress axes. Comparison with respective data evaluated for lithostatic pressure conditions revealed that the stress-related (crack-related) effect on wave velocities respectively on velocity anisotropy is in the range 1–3%, due to microcracks which are selectively closed or kept open by the deviatoric stress. The effect of the deviatoric stress is particularly documented by shear wave splitting due to microfractures that are oriented normal to the minimum principal stress axis.     

A terrestrial shear pattern?

The concept of the strain ellipsoid is applied to indicate a possible regular shear pattern of earthquake distribution over the Earth's surface. A simple model of the Earth is assumed in the form of a rotating sphere with a plastic interior and a thin, fragile, crust. On this basis rotation of the Earth generates an internal radial pressure at the equator equivalent to 1/300g causing a proportionate distortion of the spherical shell. The system is in dynamic equilibrium with an increase in gravity at the equator. The ellipsoid representing the distortion, has orthogonal principal axes corresponding to the principal strains while radial directions at 54°44 from the poles are unchanged in length and are thus possible axes of shear generating the same distortion. The Alpide region of earthquakes extending from Lisbon to Tokyo and restriction of earthquakes mainly to the broad band between latitudes 55°N or S are in support of the proposed view.Four unique sets of orthogonal shear systems have been identified which form a regular pattern with a definite symmetry with respect to the plane of the ecliptic. This suggests that the hoop stress at the Equator associated with Earth rotation may be triggered off by tidal forces and that earthquake prediction may well be possible. Other implications of this new approach are also discussed.     

Characterization and utilization of noisy displacement signals from simple shear device using linear and kernel regression methods

Small strain testing of dynamic soil properties such as threshold strains, γ_tv, are often conducted using specialized devices such as dual-specimen simple-shear, as devices configured for large strain testing produce noisy signals in the small strain range. Working with a simple shear device originally developed for large-strain testing, we extend its low-strain capabilities by characterizing noisy signals and utilizing several statistical methods to extract meaningful responses in the small strain range. We utilize linear regression of a transformed variable to estimate the cyclic shear strain from a noisy signal and the confidence interval on its amplitude. We utilize Kernel regression with the Nadaraya–Watson estimator and a Gaussian kernel to evaluate vertical strain response. A practical utilization of these techniques is illustrated by evaluating threshold shear strains for volume change with a procedure that takes into account uncertainties in the measured shear and vertical strains.     

循环荷载下南京片状细砂的动应力——应变关系

以片状颗粒成分为主的片状结构砂与常用的圆形颗粒标准石英砂相比,在物理力学特性上有显著的差异。循环荷载作用下,饱和砂土振动孔压上升会导致土体刚度发生软化,当振动孔压累积达到一定水平时,会产生液化现象,从而引起土体结构发生破坏。采用英国WFI动三轴仪,研究了南京片状细砂在循环荷载作用下,静偏应力水平、循环应力比水平和循环次数对其动应力一应变关系的影响,考虑每一次循环过程中动应力—应变关系滞回曲线的卸载及再加载割线动剪切模量Gsec和最大割线模量Gmax的变化特性,建立了动剪模量软化的经验公式;静偏应力水平对动剪模量软化有显著影响,随着循环次数的增加,动应力—应变滞回圈逐渐向应变累积方向滑移和向应变轴方向倾斜,且彼此分离;考虑循环软化特性,采用修正的Masing准则,描述了循环荷载下南京片状细砂的动应力—应变关系。     

Undrained cyclic triaxial behavior of saturated clays under variable confining pressure

A laboratory study on the undrained dynamic behavior of saturated clays in cyclic triaxial tests with a variable confining pressure (VCP tests) is presented. Tests were performed on remolded clayey samples using a dynamic triaxial device where the deviatoric stress and confining pressure can be varied simultaneously. Various cyclic stress paths have been applied on the specimens through varying the ratios or phase differences between the cyclic deviatoric stress and cyclic confining pressure. Specifically, the stress paths used in the present study were designed to simulate the coupling effects of simultaneously varying shear and normal stresses in clays due to earthquakes and other vibration sources. Test results obtained from this study show that the undrained response of saturated clays is strongly influenced by the variation of confining pressure, in terms of pore water pressure, development speed of cyclic strain and magnitude of cyclic strength. It is found that when strong P-waves are propagating in soil layers, VCP tests are more appropriate for the simulation of in situ stress fields than the conventional cyclic triaxial tests with a constant confining pressure (CCP tests).     

A Review of the Calculation Formula for the Four-component Borehole Strainmeter and Application to Earthquake Cases

Based on the principle formula for the four-component strainmeters, we can directly obtain the specific plane strain, shear strain and azimuthal angle of the principal strain, and the maximum and minimum principal strains calculated afterwards are the indirect result. The problems of practicality of the sensitivity coefficients A and B of plane strain and shear strain are then discussed. Based on this idea, we analyzed the observation data of several four-component borehole strainmeters near the epicenter of the Yiliang M_S5.7 earthquake in 2012 and the Ludian M_S6.5 earthquake in 2014 in the Zhaotong area, Yunnan Province. The results show that the analysis based on the perspective of plane strain and shear strain has an obviously better effect than that based on the component readings, and can directly peel off the respective abnormality of the plane strain and shear strain. In addition, the correlation coefficient curves between measured data of two plane strains show significant anomalies which often occur several days before and during the earthquake.     

Three-dimensional seismic analysis of submarine slopes

Three-dimensional effects in seismic analysis of submarine slopes are assessed by comparing results of two- and three-dimensional (2D & 3D) analyses, in terms of predicted displacements, shear strains, and excess pore water pressure ratios. Limits of applicability of the 2D, plane strain analysis assumptions are quantitatively assessed. Some regression equations are also presented that express ratios of 3D vs. 2D predictions as a function of slope width/height ratio and earthquake peak acceleration. It is found that the results of 2D and 3D dynamic slope stability analysis are within a tolerance of about 15% for width/height ratios larger than 3–5, and 3D effects induced by lateral boundaries become insignificant for width/height ratios larger than 6–7. The results of the present dynamic, fully coupled, non-linear analyses are also compared with those of static slope stability analyses.     

Strain localisation in bimineralic rocks: Experimental deformation of synthetic calcite–anhydrite aggregates

Deformation of synthetic calcite–anhydrite aggregates to large shear strains (up to γ = 12.4 at 600 °C, 300 MPa confining pressure and a constant angular displacement rate corresponding to a shear strain rate of 10^− 3 s^− 1) resulted in the first experimental observation of strain localisation from initially homogeneous rocks. In contrast to experiments on pure calcite and anhydrite, which deformed homogeneously to large strains (γ ≥ 5), all experiments on calcite–anhydrite mixtures resulted in heterogeneous deformation at γ > 1 and the formation of narrow localised bands in the microstructures at γ > 4. In these bands, the amount of strain is at least twice as large as in the rest of the sample and individual grains of the same phase cluster and align, thereby forming microstructural layering similar to planar fabrics in natural mylonites. A switch in deformation mechanism in anhydrite from dislocation creep to diffusion creep and/or grain boundary sliding occurs simultaneously with strain localisation. It is concluded that deformation-induced heterogeneous phase distributions cause local strength differences initiating strain localisation in the calcite–anhydrite mixtures. The study suggests that the presence of two phases in combination with a change in deformation mechanism may be responsible for strain localisation in natural poly-mineralic mylonites.     

Simplified approximate method for analysis of rocking systems accounting for soil inelasticity and foundation uplifting

A simplified approximate method to analyze the rocking response of SDOF systems lying on compliant soil is introduced, accounting for soil inelasticity and foundation uplifting. The soil–foundation system is replaced by a nonlinear rotational spring, accompanied by a linear rotational dashpot, and linear horizontal and vertical springs and dashpots. Considering a square footing on clay under undrained conditions, the necessary moment–rotation (M–θ) relations are computed through monotonic pushover finite element (FE) analyses, employing a thoroughly-validated constitutive model. Cyclic pushover analyses are performed to compute the damping–rotation (C_R–θ) relations, necessary to calibrate the rotational dashpot, and the settlement–rotation (Δw–θ) relations, required to estimate the dynamic settlement. The effectiveness of the simplified method is verified through dynamic time history analyses, comparing its predictions with the results of 3D FE analyses. The simplified method is shown to capture the entire rotation time history θ(t) with adequate accuracy. The latter is used to compute the time history of dynamic settlement w(t), employing a simplified approximate procedure. The proposed simplified method should, by no means, be considered a substitute for more sophisticated analysis methods. However, despite its limitations, it may be utilized for (at least preliminary) design purposes.     

Seismic-frequency Laboratory Measurements of Shear Mode Viscoelasticity in Crustal Rocks II: Thermally Stressed Quartzite and Granite

—Forced torsional oscillation techniques have been used to explore the seismic-frequency shear mode viscoelasticity of specimens of two crustal rocks (Cape Sorell quartzite and Delegate aplite), cycled between room temperature and 700°C under conditions of moderate confining pressure. The anisotropy and intergranular inhomogeneity of thermal expansivity in these materials give rise to large deviatoric stresses, resulting in thermal cracking at temperatures above a pressure-dependent threshold temperature, associated with the onset of very pronounced temperature sensitivity of the shear modulus, in general accord with the predictions of fracture mechanics models. For Delegate aplite in particular, the shear modulus behaves reproducibly during multiple thermal cycles at different confining pressures, consistent with the notion that the thermal cracks are of low aspect ratio (minimum/maximum dimension), and are therefore readily closed by the prevailing confining pressure once the thermal stresses are removed. Marked frequency-dependent dissipation of shear strain energy is observed on heating each rock to temperatures ≥ 500°C, although the attenuation varies significantly with prior thermal history, probably as a result of progressive dehydration and relaxation of deviatoric stresses. Temperature and pressure dependent crack densities for Delegate aplite have been estimated by comparison of the observed shear moduli with those expected for a crack-free aggregate. In parallel with the forced oscillation tests, measurements have been made of the rate at which (argon) pore pressure equilibrium is re-established following a perturbation. Combination of these results, which provide a proxy for permeability, with the inferred crack densities indicates that the variation of permeability with crack density is well described by a percolation model with a threshold crack density of ～0.2.     

根据走滑大地震前后应力轴偏转和应力降求取偏应力量值的研究

运用走滑地震造成的地震前后应力方向偏转和地震应力降Δτ推导得到地震震源处偏应力量值τ的解析表达式为τ=［Δτcos2(φ′[KG-*2]P-E)］/sin2(φ′[KG-*2]P-φP)(其中,φ\-P和φ′[KG-*2]P分别为地震前后的统计P轴走向,E为地震断层走向.).当震前P轴与震后P轴与断层走向夹角为45°时,该公式失效.对偏应力值与应力降比值随应力场主压应力轴与断层走向夹角及应力场主压应力轴偏转的变化进行分析表明,相同应力降造成的应力轴偏转越大,地下偏应力越小; 断层走向越接近主压应力轴方向,地震应力降场对偏应力场的贡献越小.将该方法运用于Landers地震震源区,求得了该地震Homestead Valley段的偏应力量值为10MPa.     

Explicit finite‐element analysis for the in‐plane cyclic behavior of unreinforced masonry structures

A simple constitutive model is proposed for an in‐plane numerical analysis of unreinforced masonry structures, which are subject to cyclic loading, by using explicit dynamic procedures. The proposed model is implemented by using two‐dimensional plane‐stress finite elements. Three different constitutive relations that are based on the total strain in the global material system are used. Cracking and crushing are controlled through normal strains, whereas shear is controlled through shear strain. Separate hysteretic rules are adopted for each mode of damage. A numerical analysis of masonry walls that are subject to cyclic loading has demonstrated that the use of explicit procedures in conjunction with the proposed model results in an acceptable accuracy when compared with the experimental results. Copyright © 2010 John Wiley & Sons, Ltd.     

复杂应力条件下饱和松砂单调与循环剪切特性的比较研究

本文利用大连理工大学新引进与开发的“土工静力-动力液压-三轴扭转多功能剪切仪”,针对福建标准砂,在不排水条件下同时进行了单调剪切试验与循环剪切试验,进而对其进行了对比分析。通过比较表明,应力-应变关系的应变软化和硬化特性与流滑变形和循环流动特性密切相关,当循环剪切应力水平高于单调剪切过程中应变软化阶段最小强度时将会发生流滑变形。无论在单调剪切中,还是在循环剪切中,稳定状态时的有效偏应力比随着大主应力方向与竖向之间夹角的增大而减小,在中主应力系数相同的条件下,循环剪切中呈现显著剪胀时的有效偏应力比和最终稳定状态时的有效偏应力比峰值分别与单调剪切中达到相变状态时的有效偏应力比和最终稳定有效偏应力比基本上一致。然而不排水条件下单调与循环剪切过程中孔隙水压力的增长特性却并不相同,循环剪切中的最大孔隙水压力随着初始主应力方向角的增大而减小,单调剪切中的最大孔隙水压力却随着主应力方向角的增大而增大。     

川滇地区应变率场分布及其变化特征研究

基于GPS多期复测资料, 利用最小二乘配置方法计算川滇地区应变参数, 分析该区域应变率场分布及其变化特征并探讨其分布与强震关系。 研究结果表明: ① 各时段应变率场空间分布的明显变化应属于大于GPS资料误差的真实地壳构造形变信息; ② 最大剪应变率及第一、 第二剪应变率的结果反映了走滑断裂对区域变形的显著控制; ③ 主应变率, 东西、 南北向应变率场动态结果反映的汶川地震孕震的空间尺度较大; ④ 在本区大致反映北东向与北西向剪切变形的第一剪应变率、 东西向应变率、 南北向应变率及最大剪应变率与6级以上地震对应较好。     

Behavior of large post-liquefaction deformation in saturated Nanjing fine sand

Laboratory tests on the large post-liquefaction deformation of saturated Nanjing fine sand were performed by using a hollow cylinder apparatus. The stress-strain responses and the characteristics of excess pore water pressure after liquefaction were studied. It was found that the relationship between deviatoric stress and axial strain presented a sigmoid curve, and there was a good linearity relationship between normalized pore water pressure and deviatoric stress. On this basis, a constitutive model of stress-strain responses and a dissipation model of excess pore water pressure were established. It was found that the results predicted by the two models were in good agreement with the experimental data. The influence of relative densities and confi ning pressure on the characteristics of liquef ied soil were studied. The results showed the relative densities and initial effective confining pressure all had an important influence on the stress-strain responses of liquefi ed saturated Nanjing fine sand. However, the dissipation model of excess pore water pressure after liquefaction was only affected by the confining pressure.