变形构造分析的定量化与摩尔圆的引用与发展

20世纪60年代，与板块构造学说建立的同时，在构造地质学中还有一项革新，就是变形构造分析的定量化，从定性描述走向定量计算。定量化的重要标志就是将力学中的摩尔圆引入构造地质学，并且使其改进和发展，在构造地质分析中建立了有限应变摩尔圆，适应了大变形的分析，又建立了极摩尔圆，适应一般剪切的分析。我国地质学家在其中也做出了自己的贡献。     

岩石有限应变测量的莫尔圆图解网法

通常进行的应变测量需经过繁杂的数学计算或莫尔圆作图才能获得应变结果。本文介绍了笔者新设计的莫尔圆图解网及其使用方法。它可以快速准确地作出莫尔圆,进而求得应变结果,也可用于求解应力莫尔圆问题。     

有限应变测量的关键原理——摩尔圆

20世纪60年代,在板块理论建立的同时,对变形岩石和矿田构造作定量分析以替代定性分析的有限应变测量方法也建立了起来。定量分析的主要标志是将摩尔圆方法从力学引入到地质学,同时也引入矿田构造分析中,并且得到改进与发展。有限应变摩尔圆为分析岩石大变形而建立,极摩尔圆随后为分析广布于野外岩石中的一般剪切变形而建立。我国著名学者李四光在此之前将应力摩尔圆和库仑准则从力学领域介绍到构造地质学,尔后一些中国学者为改进和发展极摩尔圆方法作出了自己的贡献。本文以浅显的方式解释摩尔圆的基本概念和作图方法,附带做些练习和解答。     

Cylindrical cavities and classical rat‐hole theory occurring in bulk materials

The phenomenon of stable cylindrical cavities known as rat‐holes in stockpiles and hoppers is well known but is not properly understood, and existing theory is unsatisfactory, in that it is believed not to properly incorporate actual material properties. Here the classical rat‐hole theory of Jenike and his coworkers is re‐examined, with a view to examining the validity of the so‐called ‘stable rat‐hole equation’, which is widely used in practice. For certain plastic regimes, new exact analytical solutions are determined for two special values of the angle of internal friction. One of the exact results may be used as the basis of an approximate solution valid for small angles of internal friction. Further, these exact and approximate solutions are compared with a full numerical solution of the governing differential equations. One of the approximations used by Jenike and his coworkers is shown to be invalid. Copyright © 2000 John Wiley & Sons, Ltd.     

The algebraic evaluation of two-dimensional finite strain rosettes

Arrays or rosettes of lines along which the extension or relative extension can be determined constitute finite strain gauge rosettes. Expressions for the principal strains and their orientation in terms of three nonparallel gauge extensions can be established in a suitable form for algebraic evaluation, thus replacing graphical methods based on Mohr construction. Three types of strain rosette problems, including one which utilizes angles, are particularly relevant to the study of deformed rocks. These, together with their relation to grid methods, are discussed and simple examples of their use given. Finally, an approach to the problem of finding best-fitting solutions to overdetermined regular strain rosettes is discussed.     

Mohr circles for strain,simplified

The Mohr circle is a well known representation of two-dimensional strain. It is commonly used to illustrate strain algebra, or derive a strain ellipse from particular strain data. The established sign convention is positive (anticlockwise) shear strain on the upward ordinate, after Brace. However, in practice, confusion may easily arise from inconsistent conventions in standard text books. A Mohr-circle convention is proposed here which represents clockwise shear strain on the upward γ ordinate (i.e. upside-down). It simplifies the Mohr circle by representing both single and double angles in their natural sense. Single angles may be traced from rock to Mohr circle directly which is not the case for the Brace circle. Deformed brachiopods and stretched belemnites are used to illustrate this simplified Mohr circle. The pole to the Mohr circle is a useful addition which allows strain data to be represented in their true orientation. The pole method only works on the γ clockwise-up Mohr circle. The Mohr circle is useful to demonstrate simple-shear geometry and algebra. Successive Mohr circles with poles may be used to map strain across a heterogeneous simple-shear zone.     

软土地区注浆成型螺纹桩抗拔承载力的计算

注浆成型螺纹桩采用后注浆技术形成桩侧螺纹,有利于在软土地区施工,目前已开始应用。基于螺纹桩上拔过程中螺牙附近土体的应力条件改变,采用摩尔应力圆分析螺牙附近破坏滑裂面的开展,得到了螺牙间距与螺牙突出尺寸的比值与滑裂面展开角之间的关系,给出了螺牙间土体从圆柱形滑裂面破坏向圆台形滑裂面破坏的判别条件。根据滑裂面的开展,将螺纹桩的抗拔承载力计算分为3种情况,采用极限平衡法得到了相应的螺纹桩抗拔承载力计算公式。最后,通过与有限元数值模拟以及实际工程算例对比,验证了文中方法的合理性。     

空间物理学的回顾和展望

空间物理学是一门重要的迅速发展的学科。回顾了过去百年中发生的重大空间物理学事件。空间物理学已成功地迈过了探索阶段 ,未来是要搞清一些基本的科学问题。这些问题的解决需要观测研究、理论分析、数值模拟和环境预报的紧密合作 ,才能促成空间物理学的飞跃发展。     

运动学涡度在藏南冈底斯岩浆带中段谢通门-曲水韧性剪切带中的应用

一般剪切带主要由纯剪切和简单剪切共同作用,不同的剪切带及不同的构造位置两者所占有的比例不同。利用运动学涡度(Wk)可以定量地分析两者间的比值大小。本文通过极莫尔圆法和有限应变轴率Rs/石英c轴组构法对冈底斯岩浆带中段谢通门-曲水滑覆型韧性剪切带的运动学涡度进行了计算,两种方法获得了较为一致的结果。通过极莫尔圆法,对剪切带中的9组糜棱岩样品进行了运动学涡度计算,获得了Wk=0.73~0.96,平均值Wk=0.83。运用有限应变轴率Rs/石英c轴组构法对4个样品进行了分析,得到Wk=0.85~0.93,均值为0.88,两种方法获得了较为一致的应变结果。还根据极莫尔圆图解,计算了该韧性剪切带的减薄量S=0.09~0.35,平均减薄量为0.20。研究表明该韧性剪切带为典型的以简单剪切为主伴有部分纯剪切的一般剪切,该剪切带的形成可能与拉萨地体在中新世时从挤压到侧向伸展的转换有关。该剪切带变形特征和运动学涡度的确定深化了对藏南冈底斯地区的构造演化过程的理解,并对青藏高原中南部的地质研究具有推进作用。     

岩土材料剪切破坏点安全系数的研究

剪切破坏是岩土材料失效的一种主要的形式。针对这种形式强度安全考虑的点安全系数可以考察结构中各部分的安全情况,是结构安全分析的一种重要参考,尤其在由关键点控制的结构中显得尤为重要。摩尔库伦剪切破坏准则在岩土材料研究中被广泛应用,将基于该准则的点安全系数定义在三维广义Mohr空间中推广,得到了适用于不同剪切破坏失效准则的点安全系数定义,同时,在三维广义Mohr空间中推导,得到了岩土材料剪切破坏最小点安全系数的求解方法;最危险截面上偏应力和剪应力的关系,该最危险截面与最小点安全系数对应;以及在一定整体安全度下的失效条件。应用该定义及方法,可以研究判断不同岩土材料剪切破坏的安全情况,从而提高工程建设质量。     

亚干变质核杂岩的运动学涡度与剪切作用类型

运用极摩尔圆法、张量分析法和应力取向分析法对内蒙亚干变质核杂岩的剪切作用类型进行了定量分析。相关韧性剪切带的运动学涡度值为 0.53-0.87, 表明相关的剪切作用为减薄型一般剪切。其间的差异,表明主期以简单剪切为主,递进变形过程中, 纯剪切组分增加, 这很可能与因晚期脆性断层引起的位移分解作用有关。同向伸展褶劈理的取向与剪切带边界的夹角既不等于两流脊间的夹角,也不等于其值之半,但可据以确定主应力方向,从而确定两流脊间的夹角和对应的运动学涡度     

张量CSAMT数据处理技术初步研究与示范应用

面对大深度和三维探测,标量CSAMT(controlled source audio-frequency magnetotellurics)已显力不从心,而张量CSAMT正逐渐成为研究热点。在前人研究基础上,笔者就张量CSAMT数据处理方面提出Mohr圆分析和传统坐标旋转两种处理技术,并首次创新性地使用我国自主研发的综合电法仪开展了张量CSAMT示范应用。结果表明:Mohr圆分析和传统坐标旋转法相结合应用效果良好,可定性挖掘地下地质体的纵向和横向构造特征,主轴方位的视电阻率和阻抗相位与目标体对应良好,并且电阻率反演结果与钻孔等地质资料综合分析对建立试验区的地质地球物理模型是有益的。     

三轴试验尔包络线模型拟合

在王星辉提出的三轴强度指标回归求值方法的基础上,对该方法进行了改进与完善.严格采用数学方法对包络线的线性模型及曲线模型中的抛物线、对数模型进行了详细求解,并对试验数据的可靠性进行了判断.提出了各种包络线模型的优选优化方法,并给予了实例说明.由实例可知,试验数据虽满足相关系数要求,但线性模型并非最优模型;线性化求解的对数...     

地基承载力确定的一种方法

根据三轴和直剪试验的特点并以Mohr强度理论为基础建立了Mohr包线的曲线形式。基于弹性理论导出了条形地基在均布荷载作用下塑性区方程,根据方程可以确定临塑荷载及塑性区的范围。与基于直线型Mohr-Coulomb准则建立起来的塑性区方程相比,该方程能反映土体抗剪强度增长随正应力增加逐渐趋缓的特点。算例分析表明：按两种方法计算得出的临塑荷载相差不大,塑性区连成一片时的荷载也基本一致;两种方法得出的塑性区的形状极为相似;随荷载增加,塑性区向下发展的速度比按传统方法得出的结果稍慢。     

单剪条件下主应力大小及主应力轴方向

对单剪条件下的应力莫尔圆变化过程进行详细分析,将莫尔圆从初始状态到破坏状态的大、小主应力变化过程看做由若干个等增量步组成,从而推导出任意剪应力状态与初始状态对应的小主应力差值与两者大主应力差值的比为一常数,该常数可以根据初始状态莫尔圆和破坏时对应的莫尔圆确定。推导出单剪条件下任意剪应力对应的大、小主应力及主应力轴方向的表达式。讨论了土体材料参数及法向应力对主应力轴偏转过程的影响以及大、小主应力与剪应力的关系。结果表明：在土体材料参数一定的条件下,主应力轴方向由应力比唯一确定;法向应力一定,土体的摩擦角越小,相同剪应力对应的主应力偏转角越大;剪切起始阶段,主应力变化缓慢,随着剪应力增大,主应力急剧变化至土样破坏时保持不变。     

运动学涡度和极摩尔圆的基本原理与应用

运动学涡度是岩石递进变形中非同性的一种量度，利用其对韧性剪切带进行应变分解，确定剪切作用类型是当今构造地质学研究的较新课题。极摩尔圆同时适用共轴和非共为形，是应变分析的一种有利工具，并特别适用于从应变测量数据求取运动学涡度；从力学理论角度对运动学涡度进行了系统而简明的论述，地极摩尔圆的原理进行了推导，提出了它们在韧性剪切带应变分析中的应用。     

极摩尔圆法计算二维平均运动学涡度

通过有限应变椭圆长短轴比(R_s)和长轴与剪切面夹角(α)构建极摩尔圆,本文计算得出二维平面应变平均运动学涡度(W_m)计算公式为W_m=cos ,并以此绘制了W_m关于R_s和α的等值线投影图。公式计算和有限应变数值投影都是计算平均运动学涡度的简捷有效的方法。极摩尔圆计算提供了判定剪切类型(简单剪切,纯剪切,减薄一般剪切,增厚一般剪切)的两种方法:α值判定瞬时应变剪切类型; R_s×tan²α值判定有限应变剪切类型。     

Study of the interaction between dry granular flows and rigid barriers with an SPH model

This study uses an incompressible smoothed‐particle hydrodynamics model to investigate the interaction between dry granular material flows and rigid barriers. The primary aim is to summarise some practical guidelines for the design of debris‐resisting barriers. The granular materials are modelled as a rigid‐perfectly plastic material where the plastic flow corresponds to the critical state. The coupled continuity equation and momentum equation are solved by a semi‐implicit algorithm. Compared with flows in controlled flume experiments, the model adequately reproduces both the kinetic of the flows and the impact force under various conditions. Then the numerical simulations are used to study the detailed interaction process. It is illustrated quantitatively that the interaction force consists of two parts, ie, the earth pressure force caused by the weight of the soil and a dynamic force caused by the internal deformation (flowing mass on top of a dead zone). For the estimation of impact load, this study suggests that an increased earth pressure coefficient depending on the Froude number should be incorporated into the hydrostatic model.     

Scaling the 3-D Mohr circle and quantification of paleostress during fluid pressure fluctuation – Application to understand gold mineralization in quartz veins of Gadag (southern India)

In this study, orientations of 157 quartz veins occurring in metabasalts of the Gadag region (Dharwar craton, southern India) are used to plot the 3-D Mohr stress circle, which provides information about relative stress/fluid pressure (P_f) conditions, as well as stress state during P_f fluctuation. To scale the 3-D Mohr circle, vein orientation data are integrated with (a) available estimates from fluid inclusions of highest recorded P_f (390 MPa) and lowest recorded P_f (50 MPa) and (b) intrinsic rupture criterion that empirically quantify rock properties. Based on the scaled 3-D Mohr circle, the absolute magnitudes of the three principal stresses are quantified for high and low P_f. Of 157 veins investigated here, 14 veins are identified as having favourable orientation for dilation at high as well as low P_f. These 14 veins have a mean strike of 150°, which is similar to the orientation of the gold-bearing quartz lodes reported in the region. The effective normal stress (σ′_n = σ_n−P_f) prevalent during dilation of fracture/fabric anisotropy with 150° strike is calculated to be −11.5 MPa at high P_f, and −1.0 MPa at low P_f. Thus, it is interpreted that in the Gadag region, a change in σ′_n of 10.5 MPa prevailed during P_f fluctuation and associated separation of gold from the fluid.     

高压下尾矿材料幂函数型摩尔强度特性研究

高压下尾矿材料的强度特性是高尾矿坝稳定性分析的基础。理论推导了幂函数型摩尔（Mohr）强度通式 须满足的条件为 , , ;基于高压三轴试验研究了尾矿材料的强度特征,研究表明：幂函数型摩尔强度包络线能较好地反应尾矿材料在高压下的强度特征;尾矿材料在高压作用下试验前、后的颗粒分析结果表明：当围压达到某一阈值时,尾矿材料在剪切过程中将发生颗粒破碎,对于德兴铜矿尾粉砂,阈值为1 200 kPa;对于德兴铜矿尾亚砂,阈值为1 600 kPa。研究成果可为高尾矿坝坝体稳定性评价提供理论依据。