Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

Reflection of waves from the boundary of a random elastic semi-infinite medium

In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity , where measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ². The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.     

Effects of ageing and overconsolidation on the elastic stiffness of a remoulded clay

Summary Results of resonant column tests were used to determine values of low amplitude shear modulus (G ₀) of a remoulded kaolinite clay for different durations of ageing and for different values of consolidation stress (₀) and overconsolidation ratio (OCR). It was found that after completion of primary consolidation the values of G ₀ increased linearly with the logarithm of time and after a week of confinement the value of normalized rate of secondary increase of shear modulus (N _G ) could be reliably estimated. Values of N _G were found to derease linearly with the logarithm of OCR and with the logarithm of ageing duration. This similarity of behaviour provided a basis for establishing an equivalency between age and equivalent overconsolidation ratio (OCR)_eq. The effects of ₀ and OCR on the value of G ₀ were also established in a functional form that indicated a stronger influence compared to that predicted by the Hardin Equation.     

Atomistic calculations of structural and elastic properties of serpentine minerals: the case of lizardite

The physical properties of the hydrous phyllosilicate lizardite have been investigated by atomistic simulation using the GULP code based on transferable semi-empirical interatomic potentials. Lizardite behavior was first investigated during structure relaxation at room temperature. The Helmholtz free energy is minimum for an equilibrium structure that is in agreement with experiment. The bulk, shear, and Young modulii for lizardite were calculated along with the Poisson ratio. From the shear and bulk modulii, we also calculated translational and longitudinal acoustic wave velocities that are important quantities for tectonophysics models. As expected, lizardite is stiffer in the a direction parallel to the layers than in the c perpendicular direction; the variation of the unit cell parameters with pressure is in good agreement with experiment. The cohesive energy between two successive layers along c direction was calculated at 0.33 eV (i.e., 0.11 eV per OH bond) in good agreement with recent ab initio calculations. Upon pressure and temperature variations, we evidenced that structural changes are mainly pressure induced; pressure being accommodated by a decrease of the c parameter up to 10 GPa. We also found that the change of slope in the derivative of the c cell parameter with respect to pressure occurring around 2 GPa originates from the bending of the interlayer hydroxyl groups with respect to the layer normal direction.     

A non-linear stress-stiffness model for geomaterials at small to intermediate strains

A double exponential fitting model (DEFM) capable of expressing the non-linear stress-stiffness relationship of geomaterials has been proposed by Shibuya et al. (1997). The model comprises two material constants; the elastic stiffness at very small strains and the strength, together with other free parameters to determine the complete stress-stiffness relationship. In this paper, the capability of the original function used for DEFM in simulating the tangent stiffness-stress relationship of geomaterials is first discussed. Second, the methods for determining the free model parameters, as well as its conversion to obtain a stress-strain relationship are proposed. The applicability of DEFM to predicting non-linear stress-stiffness relationship is examined in detail in a total of forty-nine fitting cases of compression test data on sedimentary rock, artificial soft rock and soft clay. It is found that the DEFM is effective in expressing the non-linear stress-stiffness relationship of various kinds of geomaterials at small to intermediate strains, say less than 0.5%. The superiority of this model compared to other fitting models currently in use is also demonstrated in some of the fitting cases.     

有限弹性变形地壳中的地震波

地壳由半无限大的基岩上一层厚度为H^-的表土层组成，入射地震波为垂直的SH波，产生水平地面运动。当浅源大地震发生时，在极震区以外行波传播产生地面运动将使地壳介质有非线性的有限弹性变形。用小参数摄动法使非线性控制方程为线性化的小参数各阶控制方程，得出头两阶线性控制方程的解析解。     

论上海软土地基⑦⑧⑨层压缩模量Es的定值问题

上海地区深部土层⑦⑧⑨层埋深在30～70m。对其压缩模量Es的定值问题,现行《上海市地基基础设计规范》(DGJ08 11 1999)(后文中简称《规范》)长期以来确定室内试验E0 1～0 2值为沉降计算值,导致沉降计算值与建(构)筑物实际沉降量之间相差2～8倍。为符合规范的变形要求,设计人员不得不采取桩加粗、加长、加密的办法,从而造成桩基投资的极大浪费。为了正确认识深部土层的Es值,上海岩土工程界进行了多种形式的试验研究。近年来,笔者结合上海高、大、深、重建(构)筑物的工程实践,深入进行上海深部⑦⑧⑨层压缩模量Es的试验研究,获得许多新的认识,对其定值问题作了研究,提出⑦⑧⑨层的建议值,供同行参考研讨。     

Determination of silica sand stiffness

Site investigation and evaluation of properties of soil or rock are important aspects of geotechnical design. Determination of the ground stiffness is one of the important parameters in geotechnical engineering. Since the measurement of shear modulus is very sensitive to soil disturbance, especially for sand, determination of the stiffness of soil in the field is more reliable than in laboratory tests on sampled specimens. Measurement of shear modulus is one of the most common applications of self-boring pressuremeter testing. As an in situ device, the pressuremeter provides a unique method for assessing directly the in situ shear modulus of a soil. This paper describes a laboratory study of silica sand stiffness, which varies with stress level and strain amplitude. The results show that the elastic shear modulus value is mainly dependent on the value of the mean effective stress and relative density.     

弹性波CT技术及应用

弹性波ＣＴ技术是一种新的物探方法。本文简单地介绍了该技术的方法原理及影响图像重建的因素，并以实例说明了弹性波ＣＴ技术在煤矿井下的应用效果