Correlation Between Compositional Parts Based on Symmetric Balances

Correlation coefficients are most popular in statistical practice for measuring pairwise variable associations. Compositional data, carrying only relative information, require a different treatment in correlation analysis. For identifying the association between two compositional parts in terms of their dominance with respect to the other parts in the composition, symmetric balances are constructed, which capture all relative information in the form of aggregated logratios of both compositional parts of interest. The resulting coordinates have the form of logratios of individual parts to a (weighted) “average representative” of the other parts, and thus, they clearly indicate how the respective parts dominate in the composition on average. The balances form orthonormal coordinates, and thus, the standard correlation measures relying on the Euclidean geometry can be used to measure the association. Simulation studies provide deeper insight into the proposed approach, and allow for comparisons with alternative measures. An application from geochemistry (Kola moss) indicates that correlations based on symmetric balances serve as a sensitive tool to reveal underlying geochemical processes.     

Comparison between iterative solution of symmetric and non‐symmetric forms of Biot's FEM equations using the generalized Jacobi preconditioner

Finite element discretization of Biot's consolidation equations can produce a symmetric indefinite system (commonly used in geomechanics) or a non‐symmetric system. While this difference appears to be minor, however, it will require the selection of entirely different Krylov subspace solvers with potentially significant impact on solution efficiency. The former is solved using the symmetric quasi‐minimal residual whereas the latter is solved using the popular bi‐conjugate gradient stabilized. This paper presents an extensive comparison of the symmetric and non‐symmetric forms by varying the time step, size of the spatial domain, choice of physical units, and left versus left–right preconditioning. The generalized Jacobi (GJ) preconditioner is able to handle the non‐symmetric version of Biot's finite element method equation, although there are no practical incentives to do so. The convergence behaviour of GJ‐preconditioned systems and its relation to the spectral condition number or the complete spectrum are studied to clarify the concept of ill‐conditioning within the context of iteration solvers. Copyright © 2007 John Wiley & Sons, Ltd.     

Finite volume discretization with imposed flux continuity for the general tensor pressure equation

We present a new family of flux continuous, locally conservative, finite volume schemes applicable to the diagonal and full tensor pressure equations with generally discontinuous coefficients. For a uniformly constant symmetric elliptic tensor field, the full tensor discretization is second order accurate with a symmetric positive definite matrix. For a full tensor, an _M-matrix with diagonal dominance can be obtained subject to a sufficient condition for ellipticity. Positive definiteness of the discrete system is illustrated. Convergence rates for discontinuous coefficients are presented and the importance of modeling the full permeability tensor pressure equation is demonstrated.     

含单一贯通破裂面岩石注浆试验及加固机制分析

针对单一贯通结构面注浆加固影响围岩承载力的问题,提出了一种制作含单一贯通破裂面岩样的方法,并对此种岩样分别注入超细水泥和环氧树脂材料,进而借助RMT-150 C试验系统探究了固结体单/三轴压缩下强度及变形特征,最后,采用理论分析结合电镜扫描手段,揭示了结构面注浆微观固结机制。研究发现,三轴加−卸载条件下制备的破裂结构面更接近工程实际,符合试验要求;从应力−应变特征曲线来看,注超细水泥试件表现出阶段性,注环氧树脂试件曲线较为平滑;从强度特征来看,围压影响程度明显高于注浆材料的选择;注浆加固手段可提高岩体的残余强度,随着围压的提高,残余强度提高系数越不明显,固结体峰值强度愈发接近完整岩石峰值强度;从破坏特征来看,注超细水泥试件主破裂面沿原始破裂面剪切滑移,注环氧树脂试件主破裂面为新的贯通破裂面;最后,以摩尔−库仑准则为理论基础,建立了注浆材料黏结力与结构面强度提高系数关系式,发现结构面强度提高系数与浆液黏结力呈线性关系。与试验结果的对比表明,该公式较为合理,可为深部围岩支护优化提供参考。     

二维非恒定渗流的有限元并行计算

建立了二维非恒定渗流的有限元并行计算模型,在windows操作系统下实现了基于消息传递的二维渗流的有限元并行计算。模型采用广义极小残余算法(GMRES)对方程组进行并行迭代求解,通过分析数据执行时的相关性和检验算法结构的固有串行性,将原有串行算法中的算法元直接并行化。对溪洛渡上游围堰的渗流分析进行了并行数值模拟,并针对水位骤降情况下非恒定渗流进行了并行计算,证明了模型的合理性。对模型进行了加速比测定,可以看出并行计算的效率随着问题规模的增加而逐渐提高。     

Systematics of internal zircon morphology in major Variscan granitoid types

The internal morphologies of zircon crystals from different types of granitoids (alkaline, calcalkaline and anatectic) are revealed by cathodoluminescence imaging and are described in terms of growth rates of the crystal faces relative to each other. Zircons in the alkaline granitoids are characterized by high and constant growth rates of {010} relative to the pyramidal forms and by symmetric grwoth of {011}. Zircons in the calcalkaline and anatectic granitoids are characterized by fluctuating or gradually decreasing relative growth rates of {010}, by asymmetric and highly variable growth of {011}, and by a tendency of {110} to become grwoth-inhibited. Corrosion events are interspersed during zircon growth in the calcalkaline magmas. In the calcalkaline and anatectic magmas, a discontinuity breaks the morphological evolution at late stages of crystallization. The discontinuity coincides with a sharp drop in cathodoluminescence. The growth behaviour of each crystal form is analysed and compared with predictions made by the periodic bond chain (PBC) theory. It is argued that the relative growth rate of {010} depends on supersaturation, that the growth rates of {011} faces are changed in response to different ratios of adsorbing cations (Na, K, Al), and that {110} faces become growth-inhibited by the adsorption of H₂O or trace elements enriched in the residual liquid. Morphological and chemical discontinuities at late stages of crystallization are reasonably explained by the formation of larger growth units (from smaller ionic entities) in the residual liquid. Important factors controlling the zircon morphology in different types of granitoids are: high cooling rates (alkaline magmas), magma mixing (calcalkaline magmas), enrichment of H₂O and trace elements in residual liquids (calcalkaline and anatectic magmas), and the major element chemistry of the magma, possibly the ratio of Na and K to Al (agpaicity).     

Effective block diagonal preconditioners for Biot's consolidation equations in piled‐raft foundations

The finite element (FE) simulation of large‐scale soil–structure interaction problems (e.g. piled‐raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi‐minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over‐relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled‐raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over‐relaxation, and ILU preconditioners in simulating piled‐raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.     

Strength Properties of Sandy Soil–Cement Admixtures

Soil stabilization with cement is a good solution for the construction of subgrades for roadway and railway lines, especially under the platforms and mostly in transition zones between embankments and rigid structures, where the mechanical properties of supporting soils are very influential. These solutions are especially attractive in line works where other ground improvement techniques are extensive and, therefore, very expensive. On the other hand, the economic and environmental costs of such works should be optimized with good balances between excavation and embankment volumes. For this purpose, the improvement of locally available soils can bring great advantages, avoiding a great amount in borrowing appropriate material, as well as the need of disposing huge volumes in deposits. This paper focus on the characteristics of two soils, Osorio sand and Botucatu residual sandstone, which can be converted to well acceptable materials for this purpose, if stabilized with cement. The study of soil stabilization with cement relies on the quantification of the influence of percentage of cement and porosity adopted in the admixing process for different state and stress conditions. This influence will be evaluated from the analysis of unconfined compression strength (UCS or q _u ) test results. This experimental framework will enable a good definition of mechanical parameters used in design of foundations and subgrades of railways platforms and for their execution quality control.     

结构性花岗岩残积土的剪切屈服特性试验研究

为研究结构性花岗岩残积土的剪切屈服特性,对未扰动和重塑花岗岩残积土及作比较的掺水泥的重塑土进行了一系列不同围压下的三轴排水对比试验。结果表明,未扰动花岗岩残积土与掺水泥重塑土在剪切过程中的屈服点可以从归一化的剪切切向刚度 与轴向应变 在双对数坐标下的关系曲线中确定;固结压力 对未扰动残积土与掺水泥重塑土的屈服特性都有显著影响, 越大,等向固结作用对土体结构的破坏越严重,剪切开始阶段的初始归一化刚度会相应地越小,屈服时的轴向应变也越小;当固结压力达到足够大时,土体结构被等向固结作用完全破坏,剪切过程中没有结构性屈服现象发生, 曲线与重塑土的 曲线重合;重塑土在不同固结压力下的 曲线重叠,不随固结压力而变化,剪切过程中没有结构性屈服现象发生。     

SPH procedures for modeling multiple intersecting discontinuities in geomaterial

A methodology is developed in SPH framework to analyze the behavior of preexisting multiple intersecting discontinuities or joints in rock material. The procedure does not require any additional unknowns to represent discontinuities and to capture velocity jump across them. Instead, a discontinuity is represented by a set of joint particles placed along the discontinuity plane, in which relative velocity and traction vector is evaluated, obeying the Mohr–Coulomb friction law with zero tension constrain. For failure of continuous rock material, the Drucker–Prager yield criterion with tensile cracking is employed in the elastic‐plastic constitutive model. Free‐sip, no‐slip, and symmetric boundary conditions are also implemented in SPH framework for proper representation of physical system. The paper analyzes behavior of a rock sample having a discontinuity plane under uniaxial loading and compares velocity and stress with a theoretical solution derived considering effective vertical stiffness of the joint planes. The efficacy of the proposed method is successfully demonstrated by solving another two problems of jointed rock mass under uniaxial and gravitational loading conditions.Copyright © 2014 John Wiley & Sons, Ltd.     

A nonlinear microseismic source location method based on Simplex method and its residual analysis

Source location is one of the most valuable features of the microseismic technique due to its ability to delineate the unstable areas. In this paper, the precise formulas of the station residual and event residual are derived for the L1 norm statistical standard and the L2 norm statistical standard based on the residual analysis. Then, the error space for microseismic source location is proposed and analyzed. Based on the above research, a nonlinear microseismic source location method using the Simplex method is developed. This new method can search the microseismic source directly in the error space through four deformations of the simplex figures, and it is able to make use of both P-wave and S-wave velocities. Finally, the performance of the Simplex microseismic source location method is tested and verified by laboratory experiments. Test results show that the Simplex microseismic source location method can improve the accuracy and stability of the source location greatly when P-wave and S-wave velocities are involved simultaneously and correctly. The results also demonstrate that the L1 norm statistical standard always provides more accurate and reliable solutions than the L2 norm statistical standard when there are some major but isolated errors in the input data. However, none of the optimization methods are able to function when the errors in the input data are systematic and extreme, which indicates that an early detection and correction of these errors is of primary importance for microseismic source location.     

数量化理论Ⅰ的稳健性处理及其在矿产定量预测中的应用

多元回归有两个缺陷:(1)自变量的限制条件过为苛刻;(2)稳健性差。这两个缺陷对矿产定量预测有极为不利的影响。为此,笔者应用现代统计学新成果——稳健性统计理论和数量化理论I进行了较系统地研究:选用残差余弦值和及残差绝对值和分别作为目标函数,首次提出了最小化残差余弦值和的数量化理论I和最小化残差绝对值和的稳健性数量化理论I,并给出相应的解法;通过对实际资料的处理、计算与结果的分析、对比,得出定量预测方法——最小化残差绝对值和数量化理论I稳键性好,预测效果最佳的结论。     

水体蒸发过程中稳定同位素分馏的模拟

通过对非平衡条件下水体蒸发中稳定同位素分馏机制的分析, 模拟了蒸发水体中稳定同位素比率的变化及与温度、大气湿度的关系. 在瑞利模式中, 剩余水中的稳定同位素随剩余水比例f的减小不断富集, 富集的速率与温度呈反比. 在动力蒸发条件下, 稳定同位素的分馏不仅与相变温度有关, 而且受大气湿度和液-气相之间物质交换的影响. 在动力蒸发过程中, 相对湿度越小, 剩余水中稳定同位素比率随 f的变化越快. 当相对湿度较大时, 在经历了一段时间蒸发后的剩余水中的δ将不随 f变化. 蒸发水体达到稳定状态的速率主要取决于大气的相对湿度. 当温度约20℃时, 在瑞利平衡条件下模拟的蒸发线与全球大气水线较接近. 在非平衡蒸发条件下, 蒸发线的梯度项和常数项与温度和相对湿度呈正比.     

On a new law of faulting along tectonic wedges: Cosserat explanation of the preferred (paleo)stress states in the Earth's crust

Cosserat extension of the Gauss stress-strain inversion method and multiple-slip method (MSM) are used to analyse 18 examples of natural wedge faulting observed in Slovenia. Based on additional numerical tests we show that kinematic incompatibility of slip along intersecting faults (wedges) has a significant effect on the state of stress in the Earth's crust. The slip direction along intersecting faults (wedges) can only be subparallel to the intersection direction between the faults. The normal stress on the wedges is then equal to the intermediate principal stress (eigenvalue) of the symmetric part of the stress tensor. This equality is very fundamental and could potentially be interpreted as a new law of faulting along tectonic wedges and non-planar faults. In the Cosserat theory of wedge faulting we also define two stress criteria, these are the weak and the strong stress conditions. The weak stress condition is related to the frictional reactivation of the wedges. It defines two limit values of the stress parameter and intermediate principal stress of the symmetric part of the stress tensor. The strong stress condition is related to the brittle faulting along tectonic wedges. It relates the angle of internal friction to the value of the stress parameter and the intermediate principal stress of the symmetric part of the stress tensor. For the value of the angle of internal friction larger than zero, the stress parameter is less than 0.5, which is in agreement with numerical and empirical observations described in this paper.     

地震层速度在盆地分析中的应用

讨论了地震层速度在喾盆地分析中的应用,论述了速度分析的基本原理,介绍了用相对 剩余层速度进行碉性分析的方法,通过实例说明了速度分析的应用效果。指出层速度剖面图能明显地反映构造现象,层速度平面图能可靠地用于盆地构造分析,相对剩余层速度平面图能有效地预测岩性的变化,为沉积相和沉积体系分析提供可靠的依据。     

Application of a high-cycle accumulation model to the analysis of soil liquefaction around a vibrating pile toe

High residual pore pressure observed in the vicinity of piles driven in saturated soil indicates that the soil around the pile may be liquefied. In the present paper, the problem of deformation of saturated sand around a vibrating pile is formulated with the use of a high-cycle accumulation model capable of describing a large number of cycles. The problem is solved numerically for locally undrained conditions in spherically symmetric formulation suitable for the lower part of a cylindrical closed-ended pile near the toe. The aim of the study is to calculate the evolution of the liquefaction zone around the pile for a large number of cycles. A parametric study is carried out to show how the growth of the liquefaction zone depends on the pile displacement amplitude, the relative soil density, the effective stress in the far field and the pore fluid compressibility.     

Residual strength of slip zones of large landslides in the Three Gorges area, China

Slip zones of the large landslides in the Three Gorges area are commonly composed of fine-grained soils with substantial amount of coarse-grained particles, particularly gravel-sized particles. In this study, residual strength of the soils from slip zones of these landslides were examined in relation to their index properties based on a survey of 170 landslides. It was found that laboratory-determined residual friction angle using gravel-free fraction of the disturbed soils from the slip zones was closely related to clay content, liquid limit and plasticity index. On the other hand, in-situ residual friction angle of these soils (i.e. including gravel fraction) showed very weak correlations with clay content and Atterberg limits, but was largely dependent on gravel and fines (clays + silts) contents, increasing with gravels and decreasing with fines, and displayed strong linear correlation with the ratio of gravel to fines contents. These observations indicate that among the index properties, clay content and Atterberg limits can be used to estimate residual strength of the soils finer than 2 mm, but they are not appropriate evaluate the residual strength of the soils containing considerable amount of gravel-sized particles. For the latter, particle size distribution (particularly the ratio of gravel to fines contents) appears to be a useful index. Additionally, it was found that there was no identifiable correlation between relative abundance of individual major clay minerals and residual friction angles of both gravel-free fraction of disturbed and in-situ soils, suggesting that influence of clay minerals on residual strength of these soils can not be simply evaluated based on their abundance.     

The concept of residual stress in rock

The purpose of this paper is to clarify the concept of residual stress in rock. Residual stress is stress near a point in a body subjected to zero external tractions and to zero temperature gradients, excluding body forces. Thus, residual stresses can develop in rock if there are local phase transformations, inelastic strains, or differences in thermal or elastic properties. In these cases, residual stresses can result from changes in temperature, applied stress or configuration of the body.Analysis of residual stresses at the scale of mineral grains within a polycrystalline aggregate such as rock is virtually intractable. One can, however, obtain important insights into residual stresses within bodies with widely spaced sources of residual stress, such as inclusions, and within bodies comprised of multilayers. The analyses indicate that patterns of residual stress in rock can be expected to be extremely complicated. For example, study of residual stresses in a body containing a circular inclusion indicates that:

1. (1) There is a single state of residual stress within an inclusion but the state within the surrounding medium is variable. Thus, values of residual stress within rocks reported in the literature generally are of minor value because the sizes and shapes of the sources and the positions of the measurements relative to the positions of sources of residual stresses in the bodies have not been determined.

2. (2) Residual stresses within an inclusion can be tensile or compressive, even though the applied stresses were compressive, depending upon the source of residual stress.

3. (3) The magnitudes and orientations of residual stresses in an isolated body of rock containing one or more inclusions depends upon the size and shape of the body. The same general conclusions are derived from an analysis of residual stresses in a simple multilayered body.

4. (4) In addition, however, the anisotropy of a multilayered body tends to cause principal residual stresses to parallel the layers rather than to parallel the applied stresses that were responsible for inducing the residual stresses. Thus, without identifying the sources of residual stresses in a body, one cannot infer the directions of principal tectonic stresses that might have been responsible for the residual stresses.

Comparison of the theoretical results with measurements of change of residual stress in blocks of granite, with maximum dimensions of 2.5 m in the field and 0.2 m in the lab oratory, suggests that sources of residual stress are inhomogeneous elements or elements of inelastic deformation within the blocks that are smaller than the blocks themselves, but larger than individual mineral grains. The sources of residual stress are unknown in these granites.     

Effects of coarse-grained materials on properties of residual soil

Residual soils are generally characterised by a low coefficient of permeability and high shrinkage potential. Several soil improvement methods can be applied to overcome these problems, including mixing the residual soil with coarse-grained soils. In order to study the effects of varying coarse-grained materials on the hydraulic properties and shrinkage characteristics of residual soils, a local residual soil was mixed with different percentages of a gravelly sand and a medium sand. The hydraulic properties and shrinkage potential of the residual soil and the soil mixtures were investigated. The measurements showed that increasing the amount of coarse-grained materials increased the saturated permeability and reduced the shrinkage potential of the residual soil mixture. Increasing the amount of coarse-grained materials in the residual soil produced changes in several key parameters of soil-water characteristic curve (e.g., the slope, the air-entry value, the residual matric suction, and the residual volumetric water content), as well as the unsaturated permeabilities of the soil mixtures.