行波效应下曲线隧道动力响应解析解

隧道曲率变化段是制约隧道结构抗震安全性的关键控制区段,但目前隧道抗震设计仅以横断面剪切变形为主,未考虑隧道沿纵向的曲率半径变化,缺乏针对曲线隧道的纵向抗震简化分析方法。将曲线隧道沿纵向简化为作用在黏弹性地基上的变曲率有限长均质Euler-Bernoulli梁,基于Hamilton原理及黏弹性地基梁理论建立了结构的微分动力控制方程及边界条件,并通过模态叠加法进行求解,推导出任意动载作用下曲线隧道的位移、速度、加速度、弯矩、剪力等动力响应的解析表达式,以行波荷载为例,给出行波效应下曲线隧道动力响应的退化解答。通过与有限元基准模型在相同条件下的对比分析,验证了所推导解析解的正确性。最后应用该解析公式进行参数敏感性分析,揭示了隧道曲率半径、行波波速、行波频率及地层–结构相对刚度比等关键因素对曲线隧道结构动力响应的影响规律。     

地表移动荷载对既有地下隧洞动力影响解析研究

为获得地表移动荷载对地下隧洞的动力影响,首次给出了地表移动荷载作用下半空间隧洞动力响应解析解。地表移动荷载采用移动简谐荷载模拟,含隧洞半空间地基通过各向同性弹性介质模拟。基于弹性地基控制方程在直角坐标系和柱坐标系下基本解及平面与柱面波函数波形转换,结合地基表面和隧洞柱面施加边界条件,在频域中求得移动荷载下半空间弹性地基与隧洞解析解答,并结合快速Fourier逆变换求得隧洞时域动力响应。利用本解析模型,可计算获得地面移动荷载引起的地下隧洞振动影响,通过与已有研究对比,对本模型正确性进行验证。计算分析了不同荷载移动速度与隧洞埋深下,隧洞表面位移、加速度和地基中动应力响应。研究表明,随着荷载移动速度增加,隧道拱顶地基中动应力与振动加速度均显著增加。地基中动应力随隧道埋深增加迅速衰减,隧洞加速度随埋深衰减相对较慢,但当隧洞埋深超过某一临界深度时,隧洞振动可低于我国规范规定限值。在低速范围,隧洞临界深度随荷载速度线性增加,但当荷载速度超过一定值,隧洞临界深度随着荷载速度呈指数型增长。     

行波效应下黏弹性地基梁动力响应解析解

弹性地基梁动力问题通常采用解析法和数值法进行分析,当可以应用解析法计算时效率更高。采用Laplace和Fourier变换,推导得出了黏弹性地基上受恒定轴向压力和横向行波作用下的无限长Euler-Bernoulli梁的解析解。经与数值模拟结果对比,验证了解答的正确性;并以长隧道为应用实例,分析对比了行波频率、波速、轴力和地基刚度对长隧道动力响应的影响,并得出了隧道内力响应受行波频率影响,频率越低,隧道内力响应越大,以及隧道内力响应受行波波速影响,当行波波速接近临界波速时,隧道内力响应明显增大等结论。     

平面SH波激励下的土–隧道动力相互作用的解析解

采用波函数展开法给出了平面SH波入射下均匀半空间中埋置刚性衬砌隧道动力响应的解析解,并对问题的边界条件进行了验证。研究表明,土–隧道相互作用的机理和土–基础–地上结构相互作用有明显区别。土–隧道相互作用导致隧道动力响应小于相应自由场的动力响应,且前者的反应谱峰值周期有一定程度的降低。入射波角度、入射频率、以及隧道埋深对隧道动力响应和地表动力响应有显著影响,而隧道质量的影响则比较小。     

Responses of a cylindrical lined tunnel due to internal dynamic load in two distinct mediums: Ideal elastic and saturated porous medium

The dynamic responses of a lined tunnel subjected to dynamic loading is one of the key issues that needs to be addressed prior to the design and construction of tunnels. While the tunnel lining and surrounding soil are commonly designed in ideal explosion-proof engineering as ideal elastic media to simplify the problem, in reality; soils are porous geo-materials. Therefore, the concern is whether this practice is more conservative or close to the reality, in contrast to the scenario where the surrounding soil is assumed as a saturated porous medium. This study investigates the differences and relationships between the dynamic responses of the lining structures in two immensely disparate media: ideal elastic medium and porous saturated medium. Firstly, to avoid the complexity of 3D numerical studies, 3D analytical solutions for the responses of the lined tunnel in both the ideal elastic medium and porous medium due to internal dynamic loading are derived using Fourier and Laplace transforms. Also, the differences between the dynamic responses (e.g., the radial displacement, radial effective stress, and hoop effective stress) of the lining structures in two media are determined to assess the rationality of assuming that the soil around the lined tunnel is an infinite elastic compressible medium. Finally, the influence of the porosity on the dynamic response of a cylindrical lined tunnel subjected to dynamic loads is examined.     

考虑土体三维波动效应时黏性阻尼土中桩的纵向振动特性及其应用研究

从三维轴对称土体模型出发,考虑土体三维波动效应,对黏弹性支承桩在任意竖向激振力作用下与土体的耦合作用特性进行了研究。假定桩为竖直、弹性、等截面体,土为线性黏弹性体,其材料阻尼为黏性阻尼。利用拉普拉斯变换,将定解问题转换到拉普拉斯域内求解。通过引入势函数,将土体位移进行分解,从而将土体动力平衡方程进行解耦,求解得到土体的振动模态形式,再利用该解,以小应变条件下桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到拉普拉斯域内桩的位移函数解析解,进而可得到桩顶速度导纳函数解析解,采用卷积定理和傅里叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。基于所得解对速度导纳曲线和速度反射波曲线进行了量纲一的参数讨论,以揭示桩的纵向振动特性,为基桩动测提供理论和实践上的指导。     

移动简谐荷载作用下饱和土体中圆形隧道和轨道结构的动力分析

采用解析法研究了移动简谐荷载作用下饱和土全空间中圆形衬砌隧道和轨道结构的动力响应,用无限长圆柱壳模拟衬砌,用Biot饱和多孔介质理论模拟土体,用Euler梁理论模拟钢轨、浮置板并组成周期性的两层叠合梁单元,结合轨道与衬砌仰拱处的力和位移连续条件,实现轨道结构与衬砌及周围饱和土体的耦合。通过算例分析了荷载移动速度、自振频率对轨道结构位移、饱和土体位移及孔压的影响,对比了连续浮置板轨道和离散浮置板轨道的动力特性。结果表明:离散浮置板轨道情形下,轨道结构和饱和土体响应频谱中存在由荷载周期通过不连续浮置板而引发的参数激励;荷载自振频率接近轨道结构固有频率时产生共振,对轨道结构和饱和土位移、孔压响应均有较大影响;离散浮置板轨道和连续浮置板轨道动力特性有显著差异,当荷载频率接近有限长浮置板形成驻波的频率时,二者对应的自由场响应区别明显;增大衬砌厚度可以显著减小饱和土位移响应。     

Vertical dynamic interactions of poroelastic soils and embedded piles considering the effects of pile-soil radial deformations

The paper presents an analytical solution for the vertical dynamic interaction analysis of a poroelastic soil layer and an embedded pile with the consideration of pile-soil radial deformations. The soil is treated a three-dimensional porous continuum and described by the Boer’s poroelastic model, while the pile is treated as a two-dimensional rod with both radial and vertical deformations of which the equation of motion is derived by the Hamilton’s variational principle. Without the introduction of potential functions, first take the volumetric strain of soil skeleton and pore fluid pressure as intermediate variables to deal with the equations of motion for the soil and then use the separation of variables to solve the equations of motion for the soil and the pile. By imposing the boundary and continuity conditions of the pile-soil system, the dynamic impedance in frequency domain and the velocity response in time domain of the pile top are obtained. The present solution is then verified by comparing with the corresponding finite element model computation results and the existing solutions. The effects of the pile-soil parameters on the dynamic characteristic of the pile-soil system are also analyzed. Some significant conclusions are drawn, which can provide useful reference for related engineering practice.     

内源爆炸荷载作用下饱和土中圆形衬砌隧道的瞬态响应解答

内源爆炸荷载作用下隧道的动力响应,经常被简化为以爆源为中心的二维平面应变问题,其实际上是一个三维岩土工程问题。为评价隧道爆源及周围区域的爆炸破坏,采用Laplace和Fourier变换,提出一种在内源爆炸荷载作用下,饱和土体中圆形衬砌隧道的瞬态响应精确解答。基于Biot波动理论,将周围土体和衬砌结构分别看成饱和两相介质和弹性介质,推求了Laplace和Fourier变换域内爆炸荷载作用下衬砌和周围饱和土体的动力响应解析解。利用Laplace和Fourier反变换的数值方法,进行了爆炸荷载作用下衬砌和周围土体的动力响应数值分析。结果表明:与简化的二维平面应变模型相比,基于三维模型得到的切向应力、径向位移和孔隙水压力较小;隧道的动力响应随时间而迅速减小,并随着与爆源距离的增加,而在径向和轴向上呈指数衰减。     

基于解析层元法的成层半平面地基移动荷载动力响应研究

解析层元法具有较高的计算效率和数值稳定性,为此基于解析层元法研究移动荷载作用下层状各向同性地基的平面应变动力响应问题。假定研究坐标系随移动荷载同步移动,移动荷载相对于移动坐标系处于相对静止状态,从而将移动荷载作用下的动力问题转化为准静态问题。结合移动坐标系下的控制方程和傅里叶变换方法,推导出单层有限厚度和半空间土体在傅里叶变换域内的解析层元。根据有限层法原理组装各土层的解析层元得到总刚度矩阵,再结合边界条件求解总刚度矩阵方程在积分变换域内的解。然后,利用傅里叶积分逆变换将变换域内的解答转换为物理域内的解。最后,通过算例验证本文理论的正确性,并分析荷载移动速度、荷载作用深度、成层性及地基加固厚度与加固效果等对成层地基动力响应的影响。研究表明:地基的竖向位移和竖向应力随荷载移动速度的提高而不断增大,当移动速度接近土体的剪切波速时,地基竖向位移和竖向应力均迅速增加;移动荷载作用下地基的成层性对土体的竖向位移有较大的影响,且主要受地基表层土体性质的影响;表层土体的加固对减小地基沉降有显著效果,随着加固效果的增加,地表沉降的减小量逐渐降低。     

地铁列车荷载作用下轨道系统及饱和土体动力响应分析

 为研究地铁列车运行引起的轨道系统及饱和土体动力响应问题,建立了地铁列车–轨道结构–衬砌–饱和土体耦合分析模型,其中列车荷载用一系列符合列车几何尺寸的移动常荷载或移动简谐荷载模拟,轨道结构中的钢轨和浮置板简化为无限长弹性Euler梁。基于弹性理论和Biot多孔介质理论,采用2.5维有限元法分别模拟衬砌和饱和土体,结合轨道与衬砌仰拱处的力和位移连续条件,实现浮置板轨道系统与衬砌及周围饱和土体的耦合,并通过快速Fourier逆变换(IFFT)进行波数展开获得三维时域–空间域内的动力响应。研究结果表明,随着常荷载移动速度和移动简谐荷载自振频率的提高,地表振动水平显著增大;移动常荷载产生的地表响应最大值在荷载正上方,其空间衰减率保持恒定;移动简谐荷载产生的地基振动大于移动常荷载产生的地基振动,响应最大值在列车运行线路两侧一定范围内;在移动简谐荷载作用下,钢轨速度谱与地表速度谱分布在以简谐荷载自振频率为中心的一段范围内。     

悬挂建筑结构动力参数优化及地震响应分析

建立了高层悬挂建筑结构减振体系的简化计算模型和运动方程,进行了频域内的参数优化和位移时程分析与计算。经过参数优化的悬挂建筑结构具有良好的减振避震性能。提出了能同时对悬挂建筑主、次结构的动力响应进行多目标优化的参数分析方法,该方法可以使得悬挂建筑主结构的频域和时域内的位移动力响应分别比普通巨型框架结构降低24%和50%以上,同时次结构的动力响应也达到一个理想的水平。     

弹性半空间中衬砌隧道对瑞利波的散射

 采用一种高精度的间接边界积分方程法,对弹性半空间中衬砌隧道对入射瑞利的二维散射问题进行求解分析。结果表明：衬砌隧道和非衬砌隧道对瑞利波的散射具有显著的差别,衬砌刚度对波的散射规律具有重要影响。隧道附近地表动力响应和隧道衬砌动应力集中主要取决于衬砌和围岩的刚度比、隧道的埋深和直径、入射波频率等因素。对于柔性衬砌,浅埋隧道对低频瑞利波会产生显著的位移放大效应;对于刚性衬砌,衬砌内壁的动应力集中效应十分明显。整体上看,随着埋深的增大,隧道周围波的散射逐渐减弱。     

土岩变化地层长隧道纵向地震响应解析解

土岩地层交界面是制约长隧道结构抗震安全的关键控制节点,但现有设计方法均未考虑隧道沿其纵向的地层变化。基于隧道的动力响应特点提出力学模型,将隧道沿纵向简化为两段处于不同地层条件中的半无限长弹性地基梁。通过求解结构的位移微分控制方程,推导出土岩变化地层长隧道纵向地震响应的解析表达式,并引入位移相位角模拟行波效应,提出了面向工程设计的土岩变化地层长隧道纵向抗震简化分析方法。通过与有限元基准模型在相同条件下的对比分析,验证了该方法的有效性。最后应用该解析公式进行参数敏感性分析,揭示了结构刚度、地层剪切波速比等关键因素对土岩变化地层隧道结构地震响应的影响规律:隧道结构刚度越大,结构内力响应越剧烈,隧道地层突变段的内力峰值差越大,地层突变的影响范围也随之变宽;地层剪切波速比越大,隧道地层突变段的内力峰值差越大,但地层突变的影响范围却不受影响。     

层状地基上预应力弹性板的竖向振动特性研究

基于解析层元法和经典弹性薄板理论,提出了一种求解层状地基与预应力弹性板竖向动力相互作用的计算方法。从地基的基本解和弹性薄板动力方程出发,借助Hankel积分变换,并结合地基与弹性板在接触面上的相容条件,得到变换域内地基与弹性板的动力耦合方程。通过求解耦合方程和数值逆变换,得到频域内预应力弹性板的位移解。与已有文献的结果进行对比,验证提出方法及计算程序的正确性及有效性。最后,通过算例分析,探讨了板–土刚度比和板径向预应力对预应力弹性板竖向动位移的影响。     

三维非均质土中粘弹性桩-土纵向耦合振动响应

在考虑土体三维非均质性情况下,对变截面粘弹性桩的动力特性进行研究.首先,结合边界条件,利用复刚度传递平面应变土体模型求得纵向不同性质桩侧土层的复刚度,进而对各段变截面桩身从下往上逐段推导得到单桩桩顶受纵向激振力作用下的桩基振动的频域响应解析解;然后,利用卷积定理和Fourier逆变换得到桩顶的时域响应半解析解;最后,研...     

基坑施工对下卧地铁隧道上抬变形影响的简化理论分析

为了合理地分析基坑施工对下卧已建地铁隧道上抬变形的影响,首先,将软土地基考虑为三参量H-K黏–弹性体,推导了自由边界半无限黏–弹性空间体在内部集中荷载作用下的Mindlin时域解,并采用积分、叠加的方法,提出了一种用于计算基坑开挖及工程降水所引起的邻近隧道附加应力的方法;然后,将已建隧道视为Pasternak黏–弹性地基上的欧拉伯努利长梁,建立了隧道在附加荷载作用下的平衡微分方程,求得了隧道纵向附加变形和内力的表达式;最后,将所提方法运用于某近接既有地铁隧道的基坑工程中,并与三维数值模拟流变分析结果和现场实测结果进行了对比分析。研究发现:提出方法能较好地反映软土隧道变形随时间的发展趋势;隧道纵向附加变形、曲率和弯矩的解析解与数值解基本一致,且上抬变形的解析解与实测值能较好地吻合;成果可为基坑施工对邻近隧道的影响分析及保护措施的制定提供一定的理论依据。     

地下隧道在临近隧道爆破作用下的安全评估

A numerical simulation method is proposed to evaluate the underground tunnel safety against explosion in adjacent tunnels. The dynamic constitutive relation used for rock material in the present study consists of a continuum damage model with the damage scalar depending on an equivalent tensile strain, a modified piecewise linear Drucker-Prager strength model allowing for the material strength degradation with damage, and a modified linear equation of state. The numerical model is calibrated by simulation of independent field explosion tests. Parametric study regarding the effect of the adjacent tunnel distance on the dynamic responses of underground tunnel is carried out. Failure zone around the explosion tunnel, and stress, strain and velocity on the adjacent tunnel wall are calculated. Safe separation distance between the adjacent tunnels is predicted and compared with empirical result.     

A dynamic stiffness-based framework for harmonic input estimation and response reconstruction considering damage

In structural health monitoring (SHM), the measurement is point-wise but structures are continuous. Thus, input estimation has become a hot research subject with which the full-field structural response can be calculated with a finite element model (FEM). This paper proposes a framework based on the dynamic stiffness theory, to estimate harmonic input, reconstruct responses, and to localize damages from seriously deficient measurements. To begin, Fourier transform converts the dynamic equilibrium equation to an equivalent static one in the frequency domain, which is under-determined since the dimension of measurement vector is far less than the FEM-node number. The principal component analysis has been adopted to “compress” the under-determined equation, and formed an over-determined equation to estimate the unknown input. Then, inverse Fourier transform converts the estimated input in the frequency domain to the time domain. Applying this to the FEM can reconstruct the target responses. If a structure is damaged, the estimated nodal force can localize the damage. To improve the damage-detection accuracy, a multi-measurement-based indicator has been proposed. Numerical simulations have validated that the proposed framework can capably estimate input and reconstruct multi-types of full-field responses, and the damage indicator can localize minor damages even with the existence of noise.     

SAFETY ASSESSMENT OF UNDERGROUND TUNNEL SUBJECTED TO ADJACENT TUNNEL EXPLOSION

A numerical simulation method is proposed to evaluate the underground tunnel safety against explosion in adjacent tunnels. The dynamic constitutive relation used for rock material in the present study consists of a continuum damage model with the damage scalar depending on an equivalent tensile strain, a modified piecewise linear Drucker-Prager strength model allowing for the material strength degradation with damage, and a modified linear equation of state. The numerical model is calibrated by simulation of independent field explosion tests. Parametric study regarding the effect of the adjacent tunnel distance on the dynamic responses of underground tunnel is carried out. Failure zone around the explosion tunnel, and stress, strain and velocity on the adjacent tunnel wall are calculated. Safe separation distance between the adjacent tunnels is predicted and compared with empirical result.