Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.

基于各向异性和极化介质的2.5维CSAMT正演数值模拟

传统的CSAMT在进行正、反演数值模拟时通常假设地下介质为电各向同性且无IP效应的介质,而实际的地下介质往往同时存在电各向异性和IP效应,因此开展各向异性和IP效应共同作用下的CSAMT电磁场响应特征的研究势在必行。文中基于含源的Maxwell方程组,推导了2.5维各向异性介质的电磁场偏微分方程,采用伽辽金有限元法实现了各向异性的2.5维CSAMT数值模拟,进而讨论了欧拉角和各向异性系数对2.5维CSAMT响应的影响。通过引入Cole-Cole模型分别研究了不同极化参数对CSAMT响应的影响,最后讨论了各向异性和IP效应同时存在时的电磁场响应特征。研究结果表明,各向异性和IP效应均会对CSAMT的响应结果产生较为严重的影响。当各向异性和IP效应同时存在时,根据欧拉角和主轴电阻率的取值,二者的效果将相互叠加或抵消。文中的研究结果对于提高CSAMT资料处理与解释精度具有重要的理论意义。

2.5D forward modeling and inversion of frequency-domain airborne electromagnetic data

Frequency-domain airborne electromagnetics is a proven geophysical exploration method.Presently,the interpretation is mainly based on resistivity-depth imaging and onedimensional layered inversion;nevertheless,it is difficult to obtain satisfactory results for two- or three-dimensional complex earth structures using 1D methods.3D forward modeling and inversion can be used but are hampered by computational limitations because of the large number of data.Thus,we developed a 2.5D frequency-domain airborne electromagnetic forward modeling and inversion algorithm.To eliminate the source singularities in the numerical simulations,we split the fields into primary and secondary fields.The primary fields are calculated using homogeneous or layered models with analytical solutions,and the secondary（scattered） fields are solved by the finite-element method.The linear system of equations is solved by using the large-scale sparse matrix parallel direct solver,which greatly improves the computational efficiency.The inversion algorithm was based on damping leastsquares and singular value decomposition and combined the pseudo forward modeling and reciprocity principle to compute the Jacobian matrix.Synthetic and field data were used to test the effectiveness of the proposed method.

2.5-D modeling of cross-hole electromagnetic measurement by nite element method

A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the 2-D conductive structures. Computing costs are considerably minimized by reducing the full three-dimensional problem to a series of two-dimensional problems. This is accomplished by transforming the problem into y-wave number （Ky） domain using Fourier transform and the y-axis is parallel to the structural strike. In the Ky domain, two coupled partial differential equations for magnetic field Hy and electric field Ey are derived. For a specific value of Ky, the coupled equations are solved by the finite element method with isoparametric elements in the x-z plane. Application of the inverse Fourier transform to the Ky, domain provides the electric and magnetic fields in real space. The equations derived can be applied to general complex two-dimensional structures containing either electric or magnetic dipole source in any direction. In the modeling of the electromagnetic measurement, we adopted a pseudo-delta function to distribute the dipole source current and circumvent the problem of singularity at the source point. Moreover, the suggested method used isoparametric finite elements to accommodate the complex subsurface formation. For the large scale linear system derived from the discretization of the Maxwell＇s equations, several iterative solvers were used and compared to select the optimal one. A quantitative test of accuracy was presented which compared the finite element results with analytic solutions for a dipole source in homogeneous space for different ranges and different wave numbers Ky. to validate the addressed the effects of the distribution range τ of the homogeneous medium. code and check its effectiveness. In addition, we pseudo-delta function on the numerical results in

Analytical Model of Elastic Modulus and Coefficient of Thermal Expansion for 2.5D C/SiC Composite

To make better use of 2.5D C/SiC composites in industry, it is necessary to understand the mechanical properties. A finite element model＇of 2.5D composites is established, by considering the fiber undulation and the porosity in 2.5D C/SiC composites. The fiber direction of warp is defined by cosine function to simulate the undulation of warp, and based on uniform strain assumption, analytical model of the elastic modulus and coefficient of thermal expansion （CTE） for 2.5D C/SiC composites were established by using dual- scale model. The result is found to correlate reasonably well with the predicted results and experimental results. The parametric study also demonstrates the effects of the fiber volume fraction, distance of warp yarn, and porosity in micro-scale on the mechanical properties and the coefficients of thermal expansion.

Numerical simulation of high-speed train induced ground vibrations using 2.5D finite element approach

An efficient 2.5D finite element numerical modeling approach was developed to simulate wave motions generated in ground by high-speed train passages. Fourier transform with respect to the coordinate in the track direction was applied to re-ducing the three-dimensional dynamic problem to a plane strain problem which has been solved in a section perpendicular to the track direction. In this study, the track structure and supporting ballast layer were simplified as a composite Euler beam resting on the ground surface, while the ground with complicated geometry and physical properties was modeled by 2.5D quadrilateral elements. Wave dissipation into the far field was dealt with the transmitting boundary constructed with fre-quency-dependent dashpots. Three-dimensional responses of track structure and ground were obtained from the wavenumber expansion in the track direction. The simulated wave motions in ground were interpreted for train moving loads traveling at speeds below or above the critical velocity of a specific track-ground system. It is found that, in the soft ground area, the high-speed train operations can enter the transonic range, which can lead to resonances of the track structure and the sup-porting ground. The strong vibration will endanger the safe operations of high-speed train and accelerate the deterioration of railway structure.

A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities

Dynamic responses of track structure and wave propagation in nearby ground vibration become significant when train operates on high speeds. A train-track-ground dynamic interaction analysis model based on the 2.5D finite element method is developed for the prediction of ground vibrations due to vertical track irregularities. The one-quarter car mode,1 is used to represent the train as lumped masses connected by springs. The embankment and the underlying ground are modeled by the 2.5D finite element approach to improve the computation efficiency. The Fourier transform is applied in the direction of train＇s movement to express the wave motion with a wave-number. The one-quarter car model is coupled into the global stiffness matrix describing the track-ground dynamic system with the displacement compatibility condition at the wheel-rail interface, including the irregularities on the track surface. Dynamic responses of the track and ground due to train＇s moving loads are obtained in the wave-number domain by solving the governing equation, using a conventional finite element procedure. The amplitude and wavelength are identified as two major parameters describing track irregularities. The irregularity amplitude has a direct impact on the vertical response for low-speed trains, both for short wavelength and long wavelength irregularities. Track irregularity with shorter wavelength can generate stronger track vibration both for low-speed and high-speed cases. For low-speed case, vibrations induced by track irregularities dominate far field responses. For high-speed case, the wavelength of track irregularities has very little effect on ground vibration at distances far from track center, and train＇s wheel axle weights becomes dominant.

3D finite element prediction of chip flow, burr formation, and cutting forces in micro end-milling of aluminum 6061-T6

Abstract Predictive models for machining operations have been significantly improved through numerous methods in recent decades. This study proposed a 3D finite element modeling （3D FEM） approach for the micro end-milling orAl6061-T6. Finite element （FE） simulations were performed under different cutting conditions to obtain realistic numerical predictions of chip flow, burr formation, and cutting forces. FE modeling displayed notable advantages, such as capability to easily handle any type of tool geometry and any side effect on chip formation, including thermal aspect and material property changes. The proposed 3D FE model considers the effects ofmiU helix angle and cutting edge radius on the chip. The prediction capability of the FE model was validated by comparing numerical model and experimental test results. Burr dimension trends were correlated with force profile shapes. However, the FE predictions overestimated the real force magnitude. This overestimation indicates that the model requires further development.

用正演数值计算方法开展双侧向测井对裂缝的响应研究

采用有限元分析软件ANSYS对裂缝的双侧向测井视电阻率与裂缝孔隙度、泥浆电阻率、裂缝倾角和基岩电阻率的关系进行了计算 .在大量正演数据的基础上得出双侧向测井响应反演公式和裂缝孔隙度计算公式 ,提出更为精细的裂缝倾角的弹性划分模型 ,用双侧向视电阻率值近似估算裂缝倾角的方法 ,提高了利用双侧向测井求裂缝产状与裂缝孔隙度 (裂缝宽度 )的精度 .

基于非结构化网格的2.5-D直流电阻率自适应有限元数值模拟(英文)

2.5-D直流电阻率有限元数值模拟中,模型的剖分及加密主要通过手动实现.另外,采用的单元类型比较规则如矩形单元等,不易实现复杂模型的模拟.为解决上述问题,文中提出了一种自适应有限元算法.算法中采用稳健的后验误差估计来自动预测下一次网格的单元尺寸,直到设定的迭代条件满足为止.另外,采用非结构化三角形单元实现了任意复杂模型的灵活剖分.基于此,利用垂直接触面模型分析和对比了不同自适应策略的效率.通过对比发现,点源附近的单元得到了加密以消除源的奇异性.另外,对于任意一种策略,有限元结果均能最终收敛到精确解.最后,模拟了两个模型:2-D单个异常体模型和2-D地形模型.

复杂介质有限元法2.5维可控源音频大地电磁法数值模拟

利用有限元 2 .5维可控源音频大地电磁法 (简称CSAMT)数值模拟方法 ,对 10 0Ωm均匀半空间介质中有限长度的电偶极源产生的电场、磁场及视电阻率、相位特征进行了数值模拟 ,研究了场的空间变化规律 .在一个象限中 ,场的特征存在双叶现象 ,当收发距大于 4个趋肤深度时 ,电阻率较接近介质真实的电阻率 ,这些结果为观测系统和收发距的选择提供了依据 .波数域场的特征表明 ,低波数对源的贡献占较大的比例 .有限元法 2 .5维CSAMT数值模拟的优势在于能较准确地获得复杂介质结构的波场特征 .本文结合直立异常体、倾斜异常体及断陷模型对CSAMT电阻率、相位剖面特征及频率曲线特征的可靠性进行了研究 .数值模拟结果直观地给出了异常体的剖面异常形态 .通过对比研究异常体的剖面异常形态和半空间场的特征进一步说明本文方法和软件在模拟复杂介质结构场特征时是可靠的 .这为认识观测数据 。

地铁运行引起的饱和地基动力响应

基于Biot饱和多孔介质的波动方程,通过对时间的Fourier变换得出频域内的波动方程,结合边界条件利用Galerkin法推导出频域-波数域内的u-w格式的2.5维有限元方程,通过快速Fourier逆变换求得三维时域-空间域内的动力响应.通过计算实例验证了计算模型.建立地铁-隧道-饱和地基动力相互作用模型,分析地铁移动荷载引起的饱和地基动力响应.研究表明,地铁荷载加振频率对振动幅值及衰减规律的影响很大,控制荷载自振频率是减小环境振动的最佳措施.

水平井各向异性地层双侧向测井响应数值模拟

利用三维有限元法对水平井中各向异性地层的双侧向测井响应进行了数值模拟,分别分析了地层各向异性系数、围岩层厚、泥浆侵入对各向异性地层双侧向测井响应的影响。结果表明:水平井中各向异性地层双侧向测井响应主要受到岩层垂向电阻率影响;目的层高阻时各向异性地层受围岩层厚影响大,目的层低阻时各向同性地层受围岩层厚影响大;与各向同性地层相比,泥浆侵入对各向异性地层双侧向测井响应影响更加明显和复杂。

2.5维电磁响应的有限元模拟与波数取值研究

利用有限元法实现了任意方向偶极子源在二维介质中频率域电磁响应的数值模拟,研究了波数取值对模拟结果的影响。通过对构造走向的Fourier变换,将全三维电磁问题,转化为一系列二维问题,并在波数域求解,极大地减小了计算工作量,导出了波数域耦合适用于二维电性介质中任何方向电或磁偶极子响应计算的电磁场方程。针对每个给定的波数,上述耦合电磁场方程用等参有限元方法在x-z平面内求解。采用Fourier逆变换,将波数域解积分,得到空间域电磁场。针对电磁模拟计算中,源点的奇异性,采用具有一定面积的伪δ函数表达源电流分布,使数值解精度得以提高。另外,采用等参有限元,使地下复杂地质体得到准确表达。利用不同波数值对均匀介质与层状介质的模拟结果与解析解的对比,验证了算法的正确性与精度。利用层状介质模型的解析解与数值计算结果的对比,分析了波数的优化取值范围及取值点数对数值模拟结果的影响,考察了算法对非均匀介质的适应性。

基于双二次插值的2.5维FCSEM有限元正演模拟

首先给出2.5维频率域可控源电磁的有限元方程,并详细推导基于矩形剖分及双二次插值的有限元方程的刚度矩阵的求解过程;接着重点研究波数的选取并得到一组精度较高的波数选取方案;然后利用本文基于双二次插值的有限元算法对一个均匀半空间模型进行模拟计算,并将计算结果与解析解对比,验证本文算法的正确性;最后对2个二维地电模型进行有限元模拟,分别得到TE及TM模式下的视电阻率及相位等值线断面图,通过对比分析可知模拟结果均能在不同程度上反映出异常体,从而进一步说明本文算法能够对2.5维频率域可控源电磁进行有效地模拟。

二维海底地层可控源海洋电磁响应的数值模拟

利用等参有限元方法对不同类型的偶极子源在二维海底地层上方产生的电磁场响应进行了数值模拟。通过对构造走向进行Fourier变换,将全三维电磁问题转化为一系列二维电磁问题,并在波数域求解,极大地减小了计算量;导出了适用于二维海底地层中任意方向的电偶极子或磁偶极子响应的波数域电磁场方程,并在x-z平面内采用等参有限元方法求解,利用Fourier逆变换得到空间域海洋电磁响应;采用具有一定面积的伪δ函数表达源电流分布,提高了数值解的精度;利用层状含高阻油气储层和低阻水层模型的数值模拟结果,分析了不同方向的电偶极子源和磁偶极子源的敏感性。模拟结果表明,水平电偶极子激发测得的两个电场分量和一个水平磁场分量,均对海底高阻层响应灵敏,适合于油气储层直接探测;水平磁偶极子激发的两个磁场分量和一个水平电场分量,尽管响应幅度较低,但在高阻储层能产生一定的异常,可以为水平电偶极子激发油气探测提供补充信息。

孔隙水压力对高铁路基动力响应的影响

采用2.5维有限元方法分析孔隙水压力对饱和路基地面振动的影响。根据Biot理论建立饱和多孔介质控制方程,采用双重Fourier变换将控制方程转换为频率-波数域表达式。采用2.5维有限元方法建立饱和路基模型,列车荷载在频率-波数域表示,轨道和路堤采用欧拉梁模拟,采用黏滞阻尼吸波边界减小有限元边界反射。分析列车速度、路基孔隙率和渗透系数对地面振动和孔隙水压力的影响。结果表明:车速较低时,由于饱和路基受孔隙水压力的影响,地面竖向振幅小于弹性地基;车速较高时,孔隙水压力急剧增加,对地面振动影响较大。列车运行速度较高时,饱和地基的孔隙率和渗透系数对孔隙水压力有较大影响。

时间域航空电磁法2.5维有限元模拟

采用三角网格剖分的有限元法,研究了2.5维航空瞬变电磁法正演模拟问题。利用时频变换数值方法将时间域电磁场转换到拉氏域,再利用傅里叶变换将三维问题降维变为2.5维问题,然后由有限元法求解得到拉氏域二维电磁场,逆拉氏变换后得到时间域航空瞬变响应。为了回避正演模拟中总感应磁场在场源处的奇异性问题,采用异常场算法,场源响应通过在微分方程中施加背景电磁场实现。由于瞬变电磁信号具有较大的动态范围,而且需要经过两次正、逆拉氏变换和傅里叶变换,每个环节的计算精度和速度要严格控制在较高的水平上,否则积累误差会非常大。模型计算表明均匀大地和层状大地模型解析解与数值解吻合很好。这证明该算法是正确可行的,可作为研究二维复杂地质体的方法手段。

大型泵站裂缝成因分析及处理

结合南水北调工程中某大型泵站的设计、施工情况,从结构设计、原材料选用、温度控制、混凝土超强、施工工艺及方案等方面对裂缝成因进行了定性分析,并利用三维有限元仿真计算成果对裂缝成因进行了定量分析。总结出大型泵站容易产生裂缝的部位、类型及原因,认为进水流道混凝土降温过程中出现的较大温度应力是早期裂缝出现的直接原因,采用的施工方案和泵送混凝土工艺是导致裂缝出现的间接因素。由于后期养护和保温措施不力产生较大的收缩应力和温度应力是引发中后期裂缝的主要原因。提出了从工程设计、原材料选用、温度控制、施工工艺及方案等方面采取综合防裂措施和处理裂缝的方法。

CSAMT 2.5维有限元数值模拟

对三维场源二维地电模型的正演计算称为2.5维数值模拟。这里从麦克斯韦方程组出发,1分别求解电磁场的一次场和二次场,将三维场源降为二维;2利用傅氏变换将空间域方程转化为波数域,应用有限元求解波数域电磁场方程,引入无限元解决无穷远边界的收敛问题;3根据电磁场值实虚部的曲线特征,按对数等间隔选取21个波数。编写代码计算均匀半空间与解析解结果对比,电阻率的均方相对误差均小于0.5%,证明其有效性。计算了三种地电模型的电磁场响应,对单一高、低阻体和高低阻组合体的模拟效果真实,异常中心位置基本吻合。结果证明,这里的CSAMT2.5-D正演算法可以模拟较为复杂的地电模型,并取得良好的效果。