Vertical vibrations of a rigid circular body on a non-homogeneous half-space interrupted by a frictionless plane

An exact formulation is presented for the problem of a rigid circular body performing harmonic vibrations on an elastic half-space whose shear modulus increases linearly with depth and is interrupted at some finite depth by a frictionless horizontal plane. The static case is derived in the limit of zero frequency vibrations while the known result for the uninterrupted half-space is recovered in either extreme limit of the horizontal frictionless plane coinciding with the surface or when it is pushed down to an infinite depth. It is shown that the maximum effect of the interruption occurs when the frictionless plane is at a depth where the shear modulus is about 1·6 times the surface shear modulus. Furthermore, this maximum effect is equivalent to a reduction of about 5 per cent of the surface shear modulus or a reduction of about 2½ per cent in the natural frequency of the rigid body on an uninterrupted half-space. The important conclusion, therefore, is that irrespective of the depth at which a half-space isso interrupted, the surface shear modulus is still the dominant parameter and that both the increase in shear modulus with depth and the interruption are not only secondary but also opposing effects.     

层状半空间中洞室对入射平面SV波的散射

利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面SV波的散射问题。通过自由场反应分析,求得假想洞室边界上各点位移和各单元应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面SV波的放大作用。结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。     

均匀半空间有限长接地导线源地面电场响应特征

本文分析了导线对可控源音频大地电磁勘探中电场的影响。在分析过程中,将有限长直接地导线源在层状介质中激发的电场的x分量分解为接地电极贡献的传到部分和通电长导线形成的感应部分,分别计算出在均匀半空间条件下,两部分及总电场随频率和收发距的变化规律。通过对计算结果的分析可见：在小收发距时,电场实部在低频区完全由接地电极部分贡献,在高频区由通电导线部分决定;电场虚部在低频区完全由通电导线部分决定,在高频区由接地电极部分和通电导线部分共同决定,且数值近似相等。在大收发距时,电场实部在低频区完全是由接地电极部分贡献,在高频区由接地电极部分和通电导线部分共同决定,且数值近似相等;电场虚部在低频区由通电导线贡献,在高频区由接地电极部分和通电导线部分共同决定,且数值近似相等。从上述分析可以看出,作为大收发距电磁法代表的可控源音频大地电磁法,其观测数据是由接地两端的传导分量和通电导线感应分量组成,并且感应分量贡献与传导贡献相当。由于导线敷设的非直线形,而引发与直导线理论不一致的结果。因此在数据采集工作中,必须考虑导线形状。同时要注意选择合适的收发距和工作频率,尽量把通电导线的影响降到最低。     

非黏性土泊松比试验研究

土体泊松比是反映土体侧向变形的重要参数,但是目前的研究应用与模型参数的重要性不相符.通过基于局部变形测量的三轴试验,分析了泊松比的变化规律:在相同的成样方法和控制密度条件下,同一种材料的颗粒排列组合结构基本类似,在不同围压条件下的试样变形规律基本保持一致;随主应力比的增加,切线泊松比也随之增加,建立泊松比与主应力比之间的关系更符合泊松比取值规律.     

Poisson's ratio in the oceanic crust — a review

Laboratory samples from the upper oceanic crust (tholeiitic basalt flows) that have not been significantly weathered, hydrothermally altered or fractured have a typical Poisson's ratio of 0.30 ( ) and a compressional velocity of 6.0 km s⁻¹; from the middle crust (dolerite sheeted dykes) a ratio of 0.28 ( ) and a velocity of 6.7 km s⁻¹; from the lower crust (gabbro) a ratio of 0.31 ( ) and a velocity of 7.1 km s⁻¹; and from the uppermost mantle a ratio of 0.24 ( ) and a velocity of 8.4 km s⁻¹. These sample values are representative of the large scale insitu values for the middle and lower crust and for the upper mantle. The upper crust is modified by several processes that decrease the velocity and generally increase Poisson's ratio: (1) the formation of an irregular layer of low temperature weathering generally less than 50 m thick; (2) large scale porosity in the form of drained pillows and lava tubes, of talus and rubble and of large open fractures; (3) where there was a high sedimentation rate over the ridge that formed the crust, hydrothermal alteration and intercalation of basalt and sediments. The Poisson's ratios of both high velocity sediments and of crystalline continental crustal rocks generally are significantly lower than the ratios of oceanic crustal rocks of similar compressional wave velocity. Thus, the use of shear wave velocities should permit the separation of these different formations which frequently cannot be distinguished on the basis of compressional wave seismic refraction data alone.     

岩体负泊松比试验研究

高分子材料领域已经研制出一些具有负泊松比效应的材料,而岩石材料中负泊松比现象十分罕见.基于国内首条在建海底隧道--厦门东通道海底隧道工程而开展的岩体室内动力测试和静力测试工作中,均观察到了泊松比为负值的现象.利用品粒转动模型,对此特殊试验现象的成因给出了初步解释,并得到了岩体试样泊松比值的合理计算方法.     

Composition and tectonic evolution of the Chinese continental crust constrained by Poisson's ratio

We have measured both P- and S-wave velocities (V_p and V_s) and Poisson's ratios (υ) of 60 typical ultrahigh pressure (UHP) metamorphic rock samples from the Chinese Continental Scientific Drilling (CCSD) main and pre-pilot holes and surface outcrops in the Sulu–Dabie orogenic belt at hydrostatic confining pressures up to 850 MPa. The experimental results, together with those compiled in Handbook of Seismic Properties of Minerals, Rocks and Ores [ Ji, S.C., Wang, Q., Xia, B., 2002. Handbook of Seismic Properties of Minerals, Rocks and Ores. Polytechnic International Press, Montreal, 630 pp.], reveal that except for monomineralic rocks such as quartzite, serpentinite, anorthosite, limestone, and marble the rest of the rock types have Poisson's ratios falling along an upward convex curve determined from the correlations between elastic moduli and density. Poisson's ratios increase with density as the lithology changes from granite, felsic gneiss and schist, through diorite–syenite, intermediate gneiss and metasediment, to gabbro–diabase, amphibolite, and mafic gneiss, and then decrease as the rocks become ultramafic in composition. Eclogite has a higher density but a lower Poisson's ratio than peridotite. The results were applied to constrain the crustal composition and tectonic evolution of the Chinese continental crust based on crustal thickness (H) and Poisson's ratio (υ) from 248 broadband seismic stations, measured using teleseismic receiver function techniques. The North China, Yangtze, South China and Northeast China blocks and Songpan–Ganzi Terrane are dominated by low (υ < 0.26) and moderate (0.26 ≤ υ < 0.28) υ values (> 70%), suggesting the dominance of felsic composition in the crust. The Lhasa terrane, Qiangtang terrane, and Indochina block are characterized by high proportions (33–42%) of measurements with very high υ values (≥ 0.30 and H is found for the South China block, Northeast block, Lhasa block, Qiangtang terrane and Indochina block, indicating either tectonic thickening of the felsic upper and middle crust by folding and thrusting or the removal of mafic layers from the lower crust into the upper mantle by delamination.     

弹性半空间夹杂群对平面SH波散射的快速多极多域边界元法模拟

结合快速多极子展开技术,发展一种高精度快速多域间接边界元方法,用于求解弹性半空间大规模夹杂群对平面SH波的二维散射。数值检验表明,该方法能够高效精确地求解大规模多域散射问题,同时可大幅度降低计算存储量,据此在普通电脑上可实现数百万自由度二维多域出平面散射问题快速求解,进而分别针对半空间中均匀分布和随机分布的夹杂群,探讨了夹杂群刚度、形状对其周围平面SH波散射的影响规律。研究结果表明:由于弹性波的多次散射相干,使得夹杂群对平面SH波的散射与单夹杂体存在显著差异,总波场空间分布特征和位移频谱特征更为复杂;平面SH波散射特性主要取决于夹杂体的材料软硬程度、几何形状特征和入射波的角度、频率。另外,研究方法和分析结论可为半空间复杂不均质体对SH波散射正、反演分析提供新的技术手段和理论依据。     

低幅应变条件下粉质黏土泊松比的非线性特征

对哈尔滨原状粉质黏土进行共振柱试验,通过扭转及弯曲试验得出相应的弹性模量E、剪切模量G、泊松比ν,旨在分析低幅应变下粉质黏土泊松比随应变发展的非线性特征。试验结果表明：随着应变的增大,粉质黏土剪切模量与弹性模量均出现衰减,但二者衰减并不同步,剪切模量先于弹性模量发生衰减;泊松比随着应变的增大而增大,并随着围压的升高而降低;在半对数坐标系下,泊松比与归一化剪切模量 近似呈线性关系,基于此提出低幅应变下泊松比预测模型。理论推导证明：低幅应变下ν- 曲线呈线性具有其必然性;随着应变的发展和 值的降低,ν- 曲线由斜率一定的线性段过渡到斜率逐渐降低的非线性段,并最终趋近于一定值。基于理论推导建立了泊松比预测模型参数与Hardin-Drnevich模型参数的关系,由此可依据低幅应变下ν- 曲线形态对较高应变下泊松比进行预测,实例验证表明该方法预测结果较好,具有一定应用价值。     

Response to harmonic wave excitation of finite or infinite elastic plates on a homogeneous or layered half-space

The soil–structure interaction of elastic plates on homogeneous or layered soils excited by horizontally propagating waves is analysed. Large plates are modelled by a combined finite-element boundary-element method (FEBEM), whereas the response of infinitely long plates is calculated by a numerical integration in the frequency–wavenumber domain. The finite-element boundary-element method yields the complete soil–plate transfer function of frequency and distance whereas the frequency–wavenumber solution of the infinitely long plate can serve as an approximation for long distances on a finitely long plate. The soil–plate transfer function starts to decrease strongly at the coincidence frequency, where the bending stiffness equals the plate inertia. A strong decrease follows at mid frequencies and a strong reduction of less than 0.1 of the ground vibration is reached at high frequencies. Rules for the characteristic frequencies are derived from the numerical results clearly indicating the strongest influence of the soil stiffness and the weaker influence of the bending stiffness of the plate. The influence of the mass, length and width of the plate are shown to be limited in case of realistic parameters, but it should be noted that the reduction effects are less effective for layered soils and for nearer observation points.     

华南地壳及壳幔过渡带泊松比及其地质意义

地震波泊松比蕴涵着丰富的地质信息,根据泊松比可以识别地壳岩石的基性程度,进而分析地球动力学与成矿背景。本文搜集整理了国家地震科学数据共享中心等数据平台自20世纪80年代至2017年底的天然地震震相资料,经过数据筛选,得到华南研究区内M≥2.0级地震事件11410个。通过最小二乘法拟合数据的走时-震中距关系直线方程,得到Pg波平均波速6.11 km/s,Sg波平均波速3.60 km/s,首波Pn波平均波速8.06 km/s,Sn波平均波速4.59 km/s。在此基础上,求得华南地壳平均波速比Vp/Vs为1.697,由公式计算得到华南地壳的平均泊松比为0.234,壳幔界面附近的平均波速比Vp/Vs为1.756,计算得到壳幔界面附近的平均泊松比为0.260。走时反演给出的泊松比结果显示扬子地块、华夏地块以及东南沿海地壳的物性差异。华夏地块与扬子地块之间存在大面积的低泊松比异常区,与江南造山带存在良好的对应关系;而东南沿海、钦杭成矿带泊松比明显较高,解释为幔源物质注入地壳的结果。     

Stratified subsoil modelled by a cross-anisotripic elastic half-space

A method of analysing horizontally stratified subsoil by using as a substiutive model a homogeneous anisotropic elastic half-space is presented. the material parameters for the substitutive model are dependent on the geometric and mechanical properties of the stratified soil.     

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi‐analytical and numerical solutions that involve interaction between a circular opening and specific systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole. Copyright © 2000 John Wiley & Sons, Ltd.     

层状饱和土体中排桩对简谐荷载隔振效果分析

根据Biot理论,利用已有的传递、透射矩阵法得到层状饱和土体内部受竖向圆形分布荷载作用下的基本解,再由Muki虚拟桩法,建立了频域内层状土-桩的第二类Fredholm积分方程。通过离散方法求解积分方程,得到了评价隔振效果的振幅比。与已知文献结果比较,验证了方法的正确性。数值结果表明：对于同种类型的振源,采用相同的隔振系统,在上软下硬的多层土体中的隔振效果比在上硬下软的土层中要好。采用较长的桩或刚度较大的桩,或桩之间的距离加密都可得到好的隔振效果。     

Quasi-static deformation of a layered half-space by a long strike-slip fault

Theoretical expressions for the surface displacement and shear stress caused by a long strike-slip dislocation in an elastic layer overlying an elastic half-space are derived and the correspondence principle is used to obtain the quasi-static response when the half-space is Maxwell-viscoelastic. Variation of the surface displacement and shear stress with horizontal distance is studied for various times and vertical extents of the fault. It is seen that the quasi-static response differs significantly from the corresponding elastic response.     

基于现场实测的缓倾硬性结构面连通率统计

通过对缓倾角硬性结构面数据的分析、判别,现场实测结构面几何特征的各基本要素,如结构面坐标、结构面产状、结构面间距、结构面的连续性、结构面迹长等,运用三维空间投影图解,最终求解结构面连通率,取代以往现场用线连通率经验判断的传统模式。本方法已应用于水电工程施工过程,效果良好。     

Plane strain deformation of a multi-layered poroelastic half-space by surface loads

The Biot linearized quasi-static theory of fluid-infiltrated porous materials is used to formulate the problem of the two-dimensional plane strain deformation of a multi-layered poroelastic half-space by surface loads. The Fourier-Laplace transforms of the stresses, displacements, pore pressure and fluid flux in each homogeneous layer of the multi-layered half-space are expressed in terms of six arbitrary constants. Generalized Thomson-Haskell matrix method is used to obtain the deformation field. Simplified explicit expressions for the elements of the 6 × 6 propagator matrix for the poroelastic medium are obtained. As an example of the possible applications of the analytical formulation developed, formal solution is given for normal strip loading, normal line loading and shear line loading.     

The effect of Poisson's ratio and the far-field boundary conditions on the accuracy of finite element calculations

It is shown that a finite element calculation which approximates an ‘infinite medium’; problem by a mesh with finite boundaries will yield greater accuracy when stress boundary conditions are applied on the far-field boundary than is obtainable with displacement boundary conditions. In particular, with Poisson's ratio close to 0.5, the accuracy of the latter model is severely impaired, whereas the stress boundary condition model is unaffected for Poisson's ratio of 0.49 and a reasonable mesh. The eight-node quadratic isoparametric element displays superb accuracy for the axisymmetric thick cylinder with either type of boundary condition.     

层状场地中局部不均体对平面P波的散射

利用间接边界元方法,在频域内求解了层状场地中局部不均体对平面P波的散射。利用精确的土层动力刚度矩阵进行自由场反应分析,求得位移和应力响应。通过计算虚拟分布荷载的格林影响函数,求得相应位移和应力;根据边界条件确定虚拟分布荷载,最终得到问题的解答。研究了入射P波时,不均体宽度、埋深、厚度、入射角、入射频率度等参数对地表位移幅值的影响,并与相应自由场的结果进行了比较。不均体对P波散射有重要影响,在工程场地地震安全性评价中,应合理考虑局部不均体对场地设计地震动参数确定的影响。