Characterization of various types of deformation and their corresponding deviatoric stress tensors using microfault analysis

Considering an ideally prefractured material, based on Mohr's representation and Bott's model, we define the geometry and the peculiarities of the different theoretical fault domains which are likely to be reactivated under different tectonic regimes. The theoretical striations associated with the different types of deformation are also calculated. The compressive strike-slip, extensive strike-slip, radial extensive and constrictive types of deformation are specified. In the second part of this paper, using Etchecopar's computer-aided method, a quantitative structural analysis of various types of superficial deformation has been carried out in different study areas (southern France, Greece, Spain, Tunisia and Nigeria). The geometry of the microfault domains, as well as the nature of the associated tensors are determined for each type of regional deformation. The problem of the spatial homogeneity of the tensors deduced by the microtectonic analysis within the framework of a particular tectonic phase is also discussed.     

Upper mantle anisotropy inferred from shear wave splitting beneath the Eastern Indian Shield region

We estimate the shear wave splitting parameters vis-à-vis the thicknesses of the continental lithosphere beneath the two permanent seismic broadband stations located at Dhanbad (DHN) and Bokaro (BOKR) in the Eastern Indian Shield region. Broadband seismic data of 146 and 131 teleseismic earthquake events recorded at DHN and BOKR stations during 2007–2014 were analyzed for the present measurements. The study is carried out using rotation-correlation and transverse component minimization methods. We retain our “Good”, “Fair” and “Null” measurements, and estimate the splitting parameters using 13 “Good” results for DHN and 10 “Good” results for BOKR stations. The average splitting parameters (ϕ, δt) for DHN and BOKR stations are found to be 50.76°±5.46° and 0.82 ± 0.2 s and 56.30°±5.07° and 0.95 ± 0.17 s, and the estimated average thicknesses of the anisotropic layers beneath these two stations are ∼ 94 and ∼109 km, respectively. The measured deviation of azimuth of the fast axis direction (ϕ) from the absolute motion of the Indian plate ranges from ∼8° to 14°. The measured deviation of azimuth of the fast axis direction (ϕ) from the absolute motion of the Indian plate ranges from ∼8° to 14°. The eastward deviation of the fast axis azimuths from absolute plate motion direction is interpreted to be caused by induced outflow from the asthenosphere. Further, the delay time found in the present analysis is close to the global average for continental shield areas, and also coherent with other studies for Indian shield regions. The five “Null” results and the lower delay time of ∼0.5–0.6 s might be indicating multilayer anisotropy existing in the mantle lithosphere beneath the study area.     

Convergence analysis of fixed stress split iterative scheme for anisotropic poroelasticity with tensor Biot parameter

We perform a convergence analysis of the fixed stress split iterative scheme for the Biot system modeling coupled flow and deformation in anisotropic poroelastic media with tensor Biot parameter. The fixed stress split iterative scheme solves the flow subproblem with all components of the stress tensor frozen using a multipoint flux mixed finite element method, followed by the poromechanics subproblem using a conforming Galerkin method in every coupling iteration at each time step. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The convergence analysis is based on studying the equations satisfied by the difference of iterates to show that the fixed stress split iterative scheme for anisotropic poroelasticity with Biot tensor is contractive. We also demonstrate that the scheme is numerically convergent using the classical Mandel’s problem solution for transverse isotropy.     

Elastic stress and strain in jointed rock masses by means of crack tensor analysis

Summary An elastic stress-strain relation is formulated in terms of crack tensors which makes it possible to take into account explicitly the effect of joints on elastic behavior of rock masses. The present study is to discuss some related topics which may be encountered in its practical application. Two problems are solved by incorporating the elastic stress-strain relation into a program for three-dimensional finite element analyses; i. e., stress concentration by surface loading and displacement by excavation of an intersecting tunnel. Validity of the results is checked by comparing them with a laboratory model test and a field test, with the following conclusions: The overall distribution of stress definitely depends on a joint stiffness ratio (i. e., normal stiffness to shear stiffness). If the ratio is chosen as unity, the stress concentration occurs mainly in the direction parallel to major joints. If the ratio is high, say 10, then the stress concentrates along the perpendicular as well as the parallel directions to major joints. It can be said, on the basis of the fairly good agreement of the calculations using the high stiffness ratio with the field and laboratory measurements, that the elastic solution by crack tensors provides a practical tool for estimating the stress and strain in strongly jointed rock masses.     

On the capillary stress tensor in wet granular materials

This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based on numerical experiments using the discrete element method, compared with a microstructural elastoplastic model. Water effects are taken into account by adding capillary menisci at contacts and their consequences in terms of force and water volume are studied. Simulations of triaxial compression tests are used to investigate both macro and micro‐effects of a partial saturation. The results provided by the two methods appear to be in good agreement, reproducing the major trends of a partially saturated granular assembly, such as the increase in the shear strength and the hardening with suction. Moreover, a capillary stress tensor is exhibited from capillary forces by using homogenization techniques. Both macroscopic and microscopic considerations emphasize an induced anisotropy of the capillary stress tensor in relation with the pore fluid distribution inside the material. Insofar as the tensorial nature of this fluid fabric implies shear effects on the solid phase associated with suction, a comparison has been made with the standard equivalent pore pressure assumption. It is shown that water effects induce microstructural phenomena that cannot be considered at the macro level, particularly when dealing with material history. Thus, the study points out that unsaturated soil stress definitions should include, besides the macroscopic stresses such as the total stress, the microscopic interparticle stresses such as the ones resulting from capillary forces, in order to interpret more precisely the implications of the pore fluid on the mechanical behaviour of granular materials. Copyright © 2009 John Wiley & Sons, Ltd.     

Variation of limiting lateral soil pressure with depth for pile rows in clay

Pile group interaction effects on the lateral pile resistance are investigated for the case of a laterally loaded row of piles in clay. Both uniform undrained shear strength and linearly increasing with depth shear strength profiles are considered. Three-dimensional finite element analyses are presented, which are used to identify the predominant failure modes and to calculate the reduction in lateral resistance due to group effects. A limited number of two-dimensional analyses are also presented in order to examine the behaviour of very closely spaced piles. It is shown that, contrary to current practice, group effects vary with depth; they are insignificant close to the ground surface, increase to a maximum value at intermediate depths and finally reduce to a constant value at great depth. The effect of pile spacing and pile–soil adhesion are investigated and equations are developed for the calculation of a depth dependent reduction factor, which when multiplied by the limiting lateral pressure along a single pile, provides the corresponding variation of soil pressure along a pile in a pile row. This reduction factor is used to perform p–y analyses, which show that, due to this variation of group effects on the lateral soil pressures with depth, the overall group interaction effects depend on the pile length. Comparisons are also made with approaches used in practice that assume constant with depth reduction factors.     

基于断层擦痕侧伏角公式的构造应力张量反演

利用Aleksandrowski推导的断层擦痕侧伏角公式,提出了一种改进的构造应力张量反演法。根据不同应力比值下构造应力与断层擦痕侧伏角的关系,利用最小二乘法,详细推导了构造应力张量的反演方法,最后利用Matlab软件编制程序实现了该计算过程。在此基础上,现场调查了江西武山铜矿北矿带的断层滑动数据,利用上述改进方法反演了该地区的构造应力张量方向特征。将上述反演结果与由震源机制解获得的最新构造应力场结果进行对比分析,并结合研究区断层的展布特征及所在的地质构造背景,获得了该地区自晚侏罗世以来的构造应力场特征,表明该地区构造应力场具有一定的稳定性。改进后的构造应力张量求解过程及工程应用表明,将Aleksandrowski的图示法和Etchecopar等的反演法结合起来反演构造应力张量,是对已有方法的改进,具有更加简单、实现容易等特点,计算结果比较符合实际。     

Pleistocene landscapes in central Iberia inferred from pollen analysis of hyena coprolites

New pollen data from hyena coprolites from central Spain are presented. The fossil faecal material has been recovered from two karstic systems in different localities, Villacastín and Los Torrejones, which are both around 1000 m a.s.l. The combined findings of bone remains and coprolites in both locations suggest the following chronology: late Middle Pleistocene for Villacastín and early Upper Pleistocene for Los Torrejones. The environments inferred from pollen are broadly in keeping with evidence from associated vertebrate fossil remains, and include a shifting mosaic of open and wooded habitats with abundant pine and juniper species, steppe‐grassland areas with composites and chenopods, and enclaves with mixed oak forests. However, Los Torrejones appears to have been less forested than Villacastín. The abundance of oaks in Villacastín may imply the presence of refugia within an interconnected network of several enclaves during the glacial stages in the Upper Pleistocene. A possible explanation for the patchiness of the landscape may be in the role of herbivores, although the long distances and variety of habitats that hyenas had to roam through could be another explanation for the heterogeneous pollen contents in their dung. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

砂泥岩裂隙岩体埋深和岩性对渗透性影响分析

采用表征岩体渗透性的单位吸水量ω为参数,有效地分析了砂泥岩裂隙岩体中相对埋深和岩性对渗透性空间分布规律的影响.研究区内,在不同深度单位吸水量的最大值和最小值相差3-4个数量级,渗透性表现出显著的随机特征.通过将压水试验数据离散化并在不同深度上取logω的平均值,凸现了渗透性的结构特征.ω均值在一定范围内随相对深度表现出负指数分布规律;剔除logω的线性趋势项后,logω残差表现出与地层内部岩性相对应的规律.此外,研究还发现,渗透性参数随相对深度呈负指数分布规律是由含裂隙的砂岩介质引起的.这些规律为裂隙岩体的渗流计算和模拟奠定了基础.文章所提出的对压水试验数据离散化并在不同深度取均值以找出渗透性和深度关系,以及去除线性趋势项研究渗透性和岩性之间关系等方法具有广泛的应用价值.     

一种基于数值应力场的强度各向异性边坡稳定性分析方法

提出了一种基于数值应力场下的边坡临界滑动面和临界坡高的分析方法。该分析方法首先利用有限元得到边坡内部较为精确的应力场,再通过在边坡内部模拟类似于链式反应过程中粒子产生和运动规律,在此基础上完成临界滑动面的搜索。主要结论如下：（1）提出了一种基于数值应力场的边坡临界滑动面的搜索方法,该方法可在不对边坡滑动面形状和位置进行干预的情况下完成潜在破坏路径的搜索。（2）通过对算法中区域与边界、激发源、产物扩散路径、路径权值4方面要素进行合理控制,可使算法在具有较高精度的同时又能保证较好的分析效率。（3）算法能较为方便地考虑真实应力条件下地层强度各向异性对边坡稳定性的影响,并能对临界坡高进行很好的分析。（4）通过具体算例对本文算法的计算结果进行验证,将所得结果与PSO和Monte Carlo两种方法得到结果进行对比,对本文方法的可靠性进行了验证,取得了较好的效果。     

基于深度加权的重力梯度张量数据的3D聚焦反演

针对重力梯度数据聚焦反演结果中存在的"上漂"现象,在经典Tikhonov正则化理论框架下,引入最小支撑泛函数对反演模型进行约束以避免反问题解的不稳定,并针对重力梯度数据聚焦反演中存在的趋肤效应,在模型目标函数中引入指数深度加权函数。通过理论模型,对部分重力梯度张量分量进行了单独以及联合聚焦反演,验证了基于深度加权的聚焦反演方法的有效性,并将该反演方法运用到涩北一号气田区的实际数据中,反演结果较好地反映出气田位置。     

Incorporation of incomplete fault-slip data into stress tensor inversion

A fault-slip datum used in the stress tensor inversion techniques is composed of fault orientation, slip orientation and the sense of slip. Sometimes the latter two items are not available. This paper proposes a method to deal with such incomplete fault-slip data. Firstly, the constraints on stress state from full and incomplete data are theoretically specified. The admissible stresses are expressed by the probability distributions in the parameter space. The objective function of inversion is given by superposing the probability distributions for all data including full and incomplete ones. Finally, the peaks of the objective function are detected to enumerate possible solutions. The validity of the present method is tested by simulated data. The incorporation of incomplete data can enhance the detectability of stress states and expands the applicability of stress tensor inversion.     

An example of stress tensor distribution deduced from the aftershocks of the November 23, 1980 southern Italy earthquake

The total inversion algorithm (Tarantola and Valette, 1982) is applied to a set of focal mechanisms corresponding to the aftershocks of the southern Italy November 23, 1980 earthquake (M_s = 6.9), and the elements of several stress tensors are computed. The obtained complex distribution of stress for this region is analyzed, and two zones around the main event, corresponding to areas of tension and compression distributed at different depths, are delimited. A stress tensor was sought for a third region, corresponding to events which occurred along the strike of the main event and with magnitudes greater than 2.2, but with ambiguous results.     

MIS 5a/5b时期亚洲夏季风变化的高分辨率石笋记录

由于深海氧同位素阶段5时期 (Marine Isotope Stage 5, MIS 5)高分辨率的亚洲夏季风记录较少,限制了对该时期亚洲夏季风变化的认识。本文利用重庆金佛山羊口洞石笋的δ18O记录,重建了MIS 5a/5b时期平均分辨率为38年的亚洲夏季风演变历史。发现该时段亚洲夏季风在千年—百年尺度上与北大西洋地区气候变化存在紧密联系。得益于误差小于0.4%的230Th测年结果,本文标定了中国间冰阶(Chinese Interstadial, CIS)21的开始时间为84.6±0.3 ka BP,CIS 22的起止时间分别为91.2±0.3 ka BP和88.9±0.3 ka BP。此外,羊口洞石笋记录的CIS 21和CIS 22的变化模式与格陵兰记录不同,而与南极冰芯记录呈反相对应,可能表示在此阶段亚洲夏季风受到了南半球气候变化的影响。      

The representation and calculation of the deviatoric component of the geological stress tensor

A new diagram for the representation of stress states is proposed and compared with Nadai's stress diagram. The diagram is a graph whose axes are labelled as the differences of the principal stresses (σ₂-σ₃ as ordinate axis, σ₁-σ₂ as the abscissa; where σ₁ > σ₂ > σ₃ are the principal stresses). The design of the plot has been deliberately modelled on that of the ‘log Flinn’ diagram which is used to represent finite strain ellipsoids. The position of the plotted stress state on this diagram depends on the nature of the deviatoric (non-hydrostatic) component of the stress tensor. The distance of the plotted stress from the origin corresponds broadly to the departure of the stress from a hydrostatic state and the parameter R, defined as the gradient of the line joining the plotted state to the origin, expresses the type of symmetry possessed by the stress tensor.It is explained how the diagram can be used to represent calculated palaeostresses and, in particular, how the parameter R can be found directly from some existing methods of stress analysis currently in use.Besides its proposed function to represent the results of such analyses it is felt that the use of the diagram may make clear the essential elements of the definitions of well-known terms used to describe particular stress states (e.g. plane stress, triaxial stress, axial compression, etc.).     

Mammoth tooth enamel growth rates inferred from stable isotope analysis and histology

Mammoth (Mammuthus sp.) teeth are relatively abundant in Quaternary deposits from Eurasia and North America, and their isotopic compositions can be used to reconstruct past seasonal patterns in precipitation, diet, and migration. Strategies for collecting and interpreting such data, however, are strongly dependent on growth rates, which can vary among species, individuals, and within teeth. In this study, we use histological and isotopic measurements to determine enamel growth rates for a Columbian mammoth (Mammuthus columbi) tooth in two directions. Using histology, the growth rate through the enamel thickness (ET; perpendicular to the height of the tooth) is estimated at 0.8 to 1.5 mm/yr. Isotopic sampling through the innermost 0.36 mm of the ET recovered less than half a period of variation (i.e., half an inferred year of growth), which is consistent with the histological estimate for ET growth rate. A combination of histological and isotopic measurements suggests that the enamel extension rate (growth in the height of the tooth) is 13–14 mm/yr. Knowledge of enamel growth rates should improve the design and interpretation of future isotopic studies of mammoth teeth. The combination of histological and isotopic measurements may also prove useful in determining growth rates for other extinct taxa.