Soil reaction to lateral harmonic pile motion

The analytical representation of dynamic soil reaction to a laterally-loaded pile using 3D continuum modeling is revisited. The governing elastodynamic Navier equations are simplified by setting the dynamic vertical normal stresses in the soil equal to zero, which uncouples the equilibrium in vertical and horizontal directions and allows a closed-form solution to be obtained. This physically motivated approximation, correctly conforming to the existence of a free surface, was not exploited in earlier studies by Tajimi, Nogami and Novak and leads to a weaker dependence of soil response to Poisson's ratio which is in agreement with numerical solutions found in literature. The stress and displacement fields in the soil and the associated reaction to an arbitrary harmonic pile displacement are derived analytically using pertinent displacement potentials and eigenvalue expansions over the vertical coordinate. Both infinitely long piles and piles of finite length are considered. Results are presented in terms of dimensionless parameters and graphs that highlight salient aspects of the problem. A detailed discussion on wave propagation and cutoff frequencies based on the analytical findings is provided. A new dimensionless frequency parameter is introduced to demonstrate that the popular plane-strain model yields realistic values for soil reaction only at high frequencies and low Poisson's ratios.     

Elasticity of CaSnO3 perovskite

The elastic properties of CaSnO₃ perovskite have been measured by both ultrasonic interferometry and single-crystal X-ray diffraction at high pressures. The single-crystal diffraction data collected using a diamond-anvil cell show that CaSnO₃ perovskite does not undergo any phase transitions at pressures below 8.5?GPa at room temperature. Ultrasonic measurements in the multianvil press to a maximum pressure of ～8?GPa at room temperature yielded S- and P-wave velocity data as a function of pressure. For a third-order Birch-Murnaghan EoS the adiabatic elastic moduli and their pressure derivatives determined from these velocity data are K _S0=167.2±3.1?GPa, K ^′ _S0=4.89±0.17, G ₀=89.3±1.0?GPa, G ^′ ₀=0.90±0.02. The quoted uncertainties include contributions from uncertainties in both the room pressure length and density of the specimen, as well as uncertainties in the pressure calibration of the multianvil press. Because the sample is a polycrystalline specimen, this value of K _S0 represents an upper limit to the Reuss bound (conditions of uniform stress) on the elastic modulus of CaSnO₃ perovskite. If the value of αγT is assumed to be 0.01, the value of K _S0 corresponds to K _T0=165.5±3.1?GPa. The 10 P-V data obtained by single-crystal diffraction were fit with a third-order Birch–Murnaghan equation-of-state to obtain the parameters V ₀=246.059±0.013 ų, K _T0=162.6±1.0?GPa, K ^′ _T0=5.6±0.3. Because single-crystal measurements under hydrostatic conditions are made under conditions of uniform stress, they yield bulk moduli equivalent to the Reuss bound on a polycrystalline specimen. The results from the X-ray and ultrasonic experiments are therefore consistent. The bulk modulus of CaSnO₃ perovskite lies above the linear trend of K ₀ with inverse molar volume, previously determined for Ca perovskites. This prevents an estimation of the bulk modulus of CaSiO₃ perovskite by extrapolation. However, our value of G ₀ for CaSnO₃ perovskite combined with values for CaTiO₃ and CaGeO₃ forms a linear trend of G ₀ with octahedral tilt angle. This allows a lower bound of 150?GPa to be placed on the shear modulus of CaSiO₃ by extrapolation.     

V型河谷地应力研究

介绍了河谷地应力研究现状 ,利用弹性理论和变分原理 ,研究了V型河谷岩体地应力问题 ,得到了河谷岩体中由于自重应力和构造应力引起的复杂应力场。应用本文结果 ,不仅可以方便绘制各种应力图件 ,而且可以较为精确地得到河谷区域任意指定点的应力值 ,从而为区域稳定性和岩体稳定性评价 ,为水电工程、地下硐室设计以及边坡工程等提供必要的岩体力学资料。本文方法数值实现简单 ,编程容易 ,计算快 ,精度高 ,可应用推广.     

几个力学概念在构造地质学中的应用

本文对构造地质学中常用的几个力学概念在使用中出现的误解和问题进行了讨论,阐述了笔者的看法和建议,以期重新引起地学工作者应用力学的原理和方法解决地质构造问题的兴趣和热情,并期待更多的地质学家能正确地运用力学的相关知识探讨和解决地球动力学领域中的诸多疑难问题。     

P-wave velocities of polymineralic rocks: comparison of theory and experiment and test of elastic mixture rules

We compare the P-wave velocities (Vp) of 696 dry samples measured at pressures up to 0.6–1.0 GPa with values calculated from the volume fraction and room pressure elastic constants of each constituent mineral using 16 averaging methods. The exceptional large number of samples covers almost all common lithologic types of igneous and metamorphic rocks. The calculated Vp data are in good agreement with laboratory values measured at about 300 MPa, even though elastic constants of only 22 common minerals are used in the computation. The mean Vp of a polymineralic rock is exclusively controlled by the volume fractions of its constituent minerals while grain shape and crystallographic preferred orientations, anisotropy and other perturbations have minimum effects. The mean Vp can be fairly well predicted as long as a relevant mixture rule is used and the volume fraction is accurately determined for each mineral. However, none of the mixture rules can simultaneously produce the best fit to measured P-wave velocities for all the lithologic types. One method may work well for one lithology but poor for other lithology. Even for a given lithology, an averaging method may yield good agreement at moderate pressure but poor agreement at high pressure. Applications of an inappropriate mixture rule will potentially cause the misinterpretation of the crust and mantle Vp data in terms of mineralogical compositions and structures.     

A visualization system for mineral elasticity

The authors have developed an efficient visualization system to gain insight into large collections of mineral elasticity data produced by an increasing number of both theoretical calculations and experiments. The system allows us to visualize multivariate elastic moduli (i.e., elastic constant tensors) and their variation with composition, pressure and temperature. Moreover, it supports visualization of elastic wave propagation in an anisotropic medium by rendering the wave velocity data, which are calculated as a function of propagation direction in a three-dimensional space. This paper describes the design, implementation and application of the visualization scheme we have developed for mineral elasticity. In particular, our scheme exploits a combination of parallel coordinates, star plot, scatter plot and polygon-surface rendering techniques, which are implemented using OpenGL, GLUI and C++. The result is a highly portable and flexible interactive visualization system. For illustration, the elastic properties of several important oxide and silicate minerals are successfully visualized as a function of pressure and temperature.Reviewed by: D. Yuen, G. Erlebacher     

Piezomagnetic fields produced by dislocation sources

Tectonomagnetic modeling based on the linear piezomagnetic effect is reviewed with special attention to dislocation models. Stacey's scheme was the prototype for such modeling, as proposed in his first seismomagnetic calculations in 1964. The linear piezomagnetic law is presented, in which the stress-induced magnetization is expressed as a linear combination of stress components. The Gauss law for magnetic field and the Cauchy-Navier equation for static elastic equilibrium are combined through linear piezomagnetism and the Hooke law to yield the basic equation for piezomagnetic potential. A representation theorem for its solution is given by surface integrals of the displacement and its normal derivative over the strained body.A Green's function method is developed to compute the piezomagnetic field produced by a dislocation surface in an elastic half-space. Volterra's formula for piezomagnetic potential is derived by modifying Stacey's scheme for tectonomagnetic modeling. The Green's functions for the problem are called elementary piezomagnetic potentials, which are defined as potentials produced by elementary dislocations. Special consideration is required to construct the elementary piezomagnetic potentials, because the stress field around a point dislocation has a singularity of orderr ^–3. The integral representing elementary piezomagnetic potentials is not uniformly convergent. Owing to inappropriate convergency, the Green's functions obtained in an earlier study led to a puzzling outcome. Revised Green's functions give consistent results with those obtained so far by numerical integrations. Generally the piezomagnetic field produced by dislocation sources is weak in the case of a homogeneous earth model. Two enhancement effects for piezomagnetic signals are suggested: one due to inhomogeneous magnetization and the other via bore-hole observations.     

Winkler model for lateral response of rigid caisson foundations in linear soil

A generalized spring multi-Winkler model is developed for the static and dynamic response of rigid caisson foundations of circular, square, or rectangular plan, embedded in a homogeneous elastic. The model, referred to as a four-spring Winkler model, uses four types of springs to model the interaction between soil and caisson: lateral translational springs distributed along the length of the caisson relating horizontal displacement at a particular depth to lateral soil resistance (resultant of normal and shear tractions on the caisson periphery); similarly distributed rotational springs relating rotation of the caisson to the moment increment developed by the vertical shear tractions on the caisson periphery; and concentrated translational and rotational springs relating, respectively, resultant horizontal shear force with displacement, and overturning moment with rotation, at the base of the caisson. For the dynamic problem each spring is accompanied by an associated dashpot in parallel. Utilising elastodynamic theoretical available in the literature results for rigid embedded foundations, closed-form expressions are derived for the various springs and dashpots of caissons with rectangular and circular plan shape. The response of a caisson to lateral static and dynamic loading at its top, and to kinematically-induced loading arising from vertical seismic shear wave propagation, is then studied parametrically. Comparisons with results from 3D finite element analysis and other available theoretical methods demonstrate the reliability of the model, the need for which arises from its easy extension to multi-layered and nonlinear inelastic soil. Such an extension is presented in the companion papers by the authors [Gerolymos N, Gazetas G. Development of Winkler model for lateral static and dynamic response of caisson foundations with soil and interface nonlinearities. Soil Dyn Earthq Eng. Submitted companion paper; Gerolymos N, Gazetas G. Static and dynamic response of massive caisson foundations with soil and interface nonlinearities—validation and results. Soil Dyn Earthq Eng. Submitted companion paper.].     

Estimation of rock engineering properties using hardness tests

In engineering projects such as tunnels, dams, foundations, and slope stability, the strength and elastic properties of the intact rock affect both the project design and the construction operation. It is sometimes expensive and time consuming to perform direct tests to evaluate the engineering properties (such as strength, modulus of elasticity, and Poisson's ratio) of the intact rock. The purpose of this work is to investigate the relationships between the engineering properties of the intact rock and the different types of hardness (Schmidt, shore scleroscope, abrasion, and total hardness), which are relatively cheap and easy to evaluate. In this study, dolomite, dolomitic limestone, and shale rocks were used. For simplicity, linear statistical analyses were performed. The results show that there are good relationships between the engineering properties of the intact rock and its hardness. Also, the results of this study are compared well with the results obtained by other investigators conducted on different types of rocks.     

根据2001年Mw 78可可西里强震InSAR同震测量结果反演东昆仑断裂两侧地壳弹性介质差异

利用2001年 Mw 78 可可西里强震InSAR同震测量结果，反演了青藏高原北部东昆仑断裂两侧地壳弹性介质差异.InSAR测量结果显示断层南侧的同震位移比北侧的大20％～30%.根据人工地震反射剖面建立岩石圈模型，以断层两侧杨氏模量差异和震源破裂深度为反演变量，通过有限元方法模拟实测得到的同震位移剖面.反演得到最佳断层破裂深度为20～22km，断层南侧杨氏模量相对北侧比值为81%～92%.结果表明，断层两侧弹性介质性质存在明显差异，由于构造运动作用，断层南部地壳不及北部地壳坚硬.前人利用地震层析成像和大地电磁测深等手段推断青藏高原内昆仑山断裂以南可可西里－羌塘地块地壳内广泛发育低速高导层，我们通过形变场力学分析得到与此相一致的结果.