Frequency dependence of elastic wave speeds at high temperature: a direct experimental demonstration

At sufficiently high temperatures and/or long periods, the elastic behaviour of crystalline material gives way progressively to viscoelastic behaviour associated with the stress-induced migration of crystal defects. This transition is marked by the onset of appreciable strain energy dissipation accompanied by frequency dependence (dispersion) of the shear modulus and elastic wave speeds. Ultrasonic interferometry and torsional forced-oscillation techniques can be used to probe the low-amplitude stress-strain behaviour of fine-grained polycrystalline material in two very different frequency ranges, respectively 10-100 MHz and 1 mHz-1 Hz. Here we demonstrate and apply these two complementary methods in a study of the high-temperature mechanical behaviour of a fine-grained synthetic olivine polycrystal. At the high frequencies of ultrasonic interferometry, the shear wave speed varies linearly with temperature between room temperature and the highest experimentally accessible temperature (1300 °C) in close accord with expectations based on similarly high-frequency studies of the elastic behaviour of single-crystal olivine. However, at teleseismic frequencies (<1 Hz) and temperatures >900 °C, the shear wave speed becomes much more strongly temperature-sensitive reflecting markedly viscoelastic behaviour. Newly emerging laboratory-derived constraints on this viscoelastic enhancement of the temperature sensitivity of seismic wave speeds and its grain-size dependence will provide a more robust interpretation of seismological models for the variation of wave speeds and attenuation within the Earth's interior.     

天山北坡西部雪岭云杉海拔梯度生态弹性变化

基于天山北坡西部温泉哈夏林区间隔100m海拔高度采集的雪岭云杉梯度样本的断面积生长量资料,分析该区域树木生态弹性变化。干旱事件是区域生态弹性最主要的干扰因子,高温事件也是干扰因子之一。干扰因子的强度会造成生态弹性梯度特征的变化。在极端干旱年份,哈夏林区梯度生长弹性特征最显著,即中高海拔为强抵抗力和弱恢复力,而低海拔则呈相反态势,并出现生长衰退现象。中旱事件时不同海拔均为强抵抗力和较强的恢复力。高温年份低海拔呈现弱抵抗力和弱恢复力。在发生持续干旱时,不同海拔高度的树木生长均受到遏制,但低海拔衰退强度大于高海拔区域,高海拔区域树木对干旱的适应能力要强于中低海拔。     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Elastoplastic model with loading memory surfaces (LMS) for monotonic and cyclic behaviour of geomaterials

A new elastoplastic model called loading memory surface based on the critical state concept and the multi‐surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three‐dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three‐dimensional generalization of the well‐known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.     

Elastic fields in two joined transversely isotropic media of infinite extent as a result of rectangular loading

This paper presents the closed‐form solutions for the elastic fields in two bonded rocks induced by rectangular loadings. Each of the two bonded rocks behaves as a transversely isotropic linear elastic solid of semi‐infinite extent. They are completely bonded together at a horizontal surface. The rectangular loadings are body forces along either vertical or horizontal directions and are uniformly applied on a rectangular area. The rectangular area is embedded in the two bonded rocks and is parallel to the horizontal interface. The classical integral transforms are used in the solution formulation, and the elastic solutions are expressed in the forms of elementary harmonic functions for the rectangular loadings. The stresses and displacements in the rocks induced by both the horizontal and vertical body forces are also presented. The numerical results illustrate the important effect of the anisotropic bimaterial properties on the stress and displacement fields. The solutions can be easily implemented for numerical calculations and applied to problems encountered in rock mechanics and engineering. Copyright © 2011 John Wiley & Sons, Ltd.     

非线性弹性模型的改进

本文在邓肯-张模型进行深入探讨的基础上,提出了切线模量实质物理意义是剪切模量的观点,并分别采用应力法和应变法推导了剪切模量和体积模量(或变形模量)公式,还进行了考虑Biot固结非线性弹性油罐地基有限元实例分析。对不同的变形模量计算方法进行了比较,提出了改进的非线性弹性模型。     

节理岩体三维偶应力弹性理论

节理的存在使得岩体的力学特性十分复杂。偶应力理论考虑了介质内颗粒尺度的影响，它以具有一定尺度的微元体为研究对象，引进了偶应力及弯曲曲率的概念，从而考虑了弯曲效应对介质变形特性的影响，可以用来解决岩土工程中的地下洞室底鼓、顶板开裂及反倾向层状岩体的弯曲倾倒等弯曲变形及弯曲破坏问题。本文考虑了节理间距的影响，对节理岩体的空间间题提出了弹性偶应力理论并建立了有限元计算模式，最后通过算例说明用偶应力理论解决上述问题的有效性。     

Transient analysis of wave propagation in non‐homogeneous elastic unbounded domains by using the scaled boundary finite‐element method

The scaled boundary finite‐element method has been developed for the dynamic analysis of unbounded domains. In this method only the boundary is discretized resulting in a reduction of the spatial dimension by one. Like the finite‐element method no fundamental solution is required. This paper extends the scaled boundary finite‐element method to simulate the transient response of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. To reduce the number of degrees of freedom and the computational cost, the technique of reduced set of base functions is applied. The scaled boundary finite‐element equation for an unbounded domain is reformulated in generalized coordinates. The resulting acceleration unit‐impulse response matrix is obtained and assembled with the equation of motion of standard finite elements. Numerical examples of non‐homogeneous isotropic and transversely isotropic unbounded domains demonstrate the accuracy of the scaled boundary finite‐element method. Copyright © 2006 John Wiley & Sons, Ltd.