双相各向同性介质弹性波高精度波场分离数值模拟方法     

陈可洋 《内陆地震》2011,25(3):215-228

为了便于研究双相介质固流相混合弹性波场中纵横波波场的传播规律,提出了基于交错网格的Biot双相各向同性介质弹性波动方程高精度波场分离正演数值模拟方法.采用高阶交错网格有限差分法来构建一阶双曲型双相各向同性介质弹性波动方程正演算子实现波场正演,并在每一步递推过程中,分别计算出同相和流相分量相应的散度场(纯纵波场)和旋度场...  相似文献   

Differential equations governing slip-induced pore-pressure fluctuations in a water-saturated granular medium     

Richard M. Iverson 《Mathematical Geology》1993,25(8):1027-1048

Macroscopic frictional slip in water-saturated granular media occurs commonly during landsliding, surface faulting, and intense bedload transport. A mathematical model of dynamic pore-pressure fluctuations that accompany and influence such sliding is derived here by both inductive and deductive methods. The inductive derivation shows how the governing differential equations represent the physics of the steadily sliding array of cylindrical fiberglass rods investigated experimentally by Iverson and LaHusen (1989). The deductive derivation shows how the same equations result from a novel application of Biot's (1956) dynamic mixture theory to macroscopic deformation. The model consists of two linear differential equations and five initial and boundary conditions that govern solid displacements and pore-water pressures. Solid displacements and water pressures are strongly coupled, in part through a boundary condition that ensures mass conservation during irreversible pore deformation that occurs along the bumpy slip surface. Feedback between this deformation and the pore-pressure field may yield complex system responses. The dual derivations of the model help explicate key assumptions. For example, the model requires that the dimensionless parameterB, defined here through normalization of Biot's equations, is much larger than one. This indicates that solid-fluid coupling forces are dominated by viscous rather than inertial effects. A tabulation of physical and kinematic variables for the rod-array experiments of Iverson and LaHusen and for various geologic phenomena shows that the model assumptions commonly are satisfied. A subsequent paper will describe model tests against experimental data.  相似文献   

Finite volume coupling strategies for the solution of a Biot consolidation model     

《Computers and Geotechnics》2014

In this paper a finite volume (FV) numerical method is implemented to solve a Biot consolidation model with discontinuous coefficients. Our studies show that the FV scheme leads to a locally mass conservative approach which removes pressure oscillations especially along the interface between materials with different properties and yields higher accuracy for the flow and mechanics parameters. Then this numerical discretization is utilized to investigate different sequential strategies with various degrees of coupling including: iteratively, explicitly and loosely coupled methods. A comprehensive study is performed on the stability, accuracy and rate of convergence of all of these sequential methods. In the iterative and explicit solutions four splits of drained, undrained, fixed-stress and fixed-strain are studied. In loosely coupled methods three techniques of the local error method, the pore pressure method, and constant step size are considered and results are compared with other types of coupling methods. It is shown that the fixed-stress method is the best operator split in comparison with other sequential methods because of its unconditional stability, accuracy and the rate of convergence. Among loosely coupled schemes, the pore pressure and local error methods which are, respectively, based on variation of pressure and displacement, show consistency with the physics of the problem. In these methods with low number of total mechanical iterations, errors within acceptance range can be achieved. As in the pore pressure method mechanics time step increases more uniformly, this method would be less costly in comparison with the local error method. These results are likely to be useful in decision making regarding choice of solution schemes. Moreover, the stability of the FV method in multilayered media is verified using a numerical example.  相似文献   

Consolidation analysis of non-homogeneous soil by the weak form quadrature element method     

《Computers and Geotechnics》2014

A weak form quadrature element formulation for consolidation analysis of non-homogeneous saturated soil is established based on Biot’s theory. Numerical examples are given, and the results are compared with the analytical solutions available or those from the commercial finite element software ABAQUS, demonstrating accuracy and rapid convergence of quadrature element solutions. The disparity between various treatments of non-homogenous soil is discussed, and the effectiveness and advantages of the quadrature element formulation in consolidation analysis of non-homogeneous soil are demonstrated.  相似文献   

Unsaturated hydro-mechanical-chemo coupled constitutive model with consideration of osmotic flow     

《Computers and Geotechnics》2013

Since low permeability rock has the potential to behave as an actual semi-permeable osmotic membrane, chemical osmosis may have an effect on water flow and needs to be accounted for in analysis. Hence, an advanced fully coupled formulation for modelling unsaturated hydro, chemical and mechanical effects is here presented based on modified mixture theory. Firstly, the classical Darcy’s law has been modified to include the chemical potential. Secondly, the mechanical deformation, which affects the permeability, has been coupled with the water and chemical flows by using Helmholtz free energy and the Gibbs–Duhem equation. Finally, an illustrative numerical example with relevance to radioactive waste disposal has been analysed to investigate the performance of the coupled formulation and the relative influence of parameters.  相似文献   

Biot固结理论中连续性方程形式的讨论     

张凯  周辉  冯夏庭  房敬年  张元刚 《岩土力学》2009,30(11):3273-3277

对于Biot固结方程中的连续性方程形式,不同的研究者存在分歧。在详细分析了Biot推导固结方程的过程后,发现其在推导固结方程时用到的弹性应变能密度函数存在错误。为了得到正确的连续性方程,采用两种思路进行了分析：①通过对土体单元变形的分析,得到了考虑土体颗粒和流体可压缩性的连续性方程;②按照Biot推导固结方程的思路,通过修正推导过程中用到的弹性应变能密度函数得到了连续性方程。上述两种思路得到的连续性方程是等价的,同时将上述连续性方程和其他研究者通过质量守恒得到的连续方程进行了对比,结果是一致的,从而确定了连续性方程的正确形式,并澄清了目前在Biot固结方程中的连续性方程上存在的分歧,所得结论可为固结方程的解析或数值计算提供依据。  相似文献   

紫坪铺水库造成孔隙弹性耦合变化及其对2008年汶川地震触发作用          下载免费PDF全文

陶玮  Timothy Masterlark  沈正康  Erika Ronchin  张永 《地球物理学报》2014,57(10):3318-3331

位于川西地区龙门山断裂带附近的紫坪铺水库于2005年9月开始蓄水.约2.7年后,2008年5月12日,M_w7.9级汶川地震在龙门山断裂带上发生,两事件在时间和空间上的接近,揭示其可能相互关联,但前人的诸多研究给出了不同甚至是相反的结果.本研究基于完全耦合孔隙弹性理论,利用二维有限元模型(FEM),模拟水库蓄水造成的区域孔隙压力场和应力场的演化过程,基于库仑应力演化探讨其对龙门山断裂带活动的影响.模拟结果显示紫坪铺水库蓄水打破了原来的区域孔隙压力平衡,形成孔隙压力梯度源,向周围地壳传播;进而造成龙门山断裂带上库仑应力正值范围不断扩大,由浅入深影响到整条断层,尤其对浅层范围的加载作用明显,达上百千帕,为整个断层面的失稳提供了基础.震源区域库仑应力呈持续增长趋势,汶川地震发震前,增长了约数千帕~数十千帕,即使初期库仑应力为负,在未来某时刻库仑应力仍可能由负转正,并不断增大.通过计算汶川地震震源及其附近区域内相对于多种可能断层倾角的库仑应力,发现库仑应力随断层倾角增大而增加.因此整体来看,紫坪铺水库蓄水对龙门山断裂带起加载作用,有可能触发地震.对紫坪铺库区周围的小震分析也显示,蓄水以来小震明显增多、且不同时段小震发生密集区与水库距离逐渐增大,与孔隙压力扩散趋势一致.以上结果表明紫坪铺水库的蓄水增加了汶川地震的危险性.  相似文献   

Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only     

Naohiro Nakamura 《地震工程与结构动力学》2008,37(4):495-515

The author has studied the transform method of complex stiffness, which is strongly dependent on frequency, to the time domain. In this paper, new transform methods that use only the real part or the imaginary part data are proposed. By applying them to example problems, it is confirmed that the accuracy of the proposed methods is almost high in both causal and noncausal cases. These methods can also be thought as a standby for the Hilbert transform, because the undefined part is easily calculated by the recovering complex function from the obtained impulse response. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

多层地基非轴对称Biot固结的理论解   总被引：1，自引：1，他引：0  

王全胜  艾智勇 《岩土力学》2008,29(Z1):645-649

提出了一种新方法来推导多层地基非轴对称Biot固结问题的传递矩阵,相应的理论推导工作量较少。基于柱坐标系下非轴对称Biot固结的基本方程,通过引入中间变量,并对坐标 进行Fourier级数展开,对时间 和坐标 进行Laplace-Hankel变换,得到了6×6阶和2×2阶的两组常微分方程;然后,两组常微分方程进行关于 的Laplace变换和逆变换,得到了单层地基非轴对称Biot固结问题的传递矩阵;结合边界条件和连续条件,运用传递矩阵法得到多层地基非轴对称Biot固结问题在Laplace-Hankel变换域内的解,通过Laplace-Hankel逆变换得到了该问题物理域的真实解答。编制了计算程序,并进行了数值计算与分析。该方法具有计算速度较快的特点,方便工程应用。  相似文献   

Linearized amplitude variation with offset and azimuth and anisotropic poroelasticity     

Xinpeng Pan  Guangzhi Zhang  Xingyao Yin 《Geophysical Prospecting》2019,67(7):1882-1897

The normal-to-shear weakness ratio is commonly used as a fracture fluid indicator, but it depends not only on the fluid types but also on the fracture intensity and internal architecture. Amplitude variation with offset and azimuth is commonly used to perform the fluid identification and fracture characterization in fractured porous rocks. We demonstrate a direct inversion approach to utilize the observable azimuthal data to estimate the decoupled fluid (fluid/porosity term) and fracture (normal and shear weaknesses) parameters instead of the calculation of normal-to-shear weakness ratio to help reduce the uncertainties in fracture characterization and fluid identification of a gas-saturated porous medium permeated by a single set of parallel vertical fractures. Based on the anisotropic poroelasticity and perturbation theory, we first derive a linearized amplitude versus offset and azimuth approximation using the scattering function to decouple the fluid indicator and fracture parameters. Incorporating Bayes formula and convolution theory, we propose a feasible direct inversion approach in a Bayesian framework to obtain the direct estimations of model parameters, in which Cauchy and Gaussian distribution are used for the a priori information of model parameters and the likelihood function, respectively. We finally use the non-linear iteratively reweighted least squares to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of the proposed approach, and the real data illustrates the stabilities of estimated fluid indicator and dry fracture parameters in gas-saturated fractured porous rocks.  相似文献