Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves

Combining the wave function expansion method and conformal transformation method, the dynamic stress around a non-circular tunnel with imperfect interface subjected to anti-plane shear waves is derived. The non-circular tunnel is mapped into an annular region, and the analytic solutions of stress and displacement solutions are expanded in terms of wave functions. By introducing the spring-type interface model, the coefficients are determined by satisfying the imperfect bonding conditions around the concrete lining. The distribution of tangential stresses on the imperfect interface is graphically illustrated, and the interacting effect of imperfect interface and incident wavelength is discussed in detail. The imperfect interface is revealed as a key factor dominating the seismic responses of a tunnel.     

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。     

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。     

内源爆炸荷载作用下无限弹性土体中圆柱形衬砌隧道的瞬态响应解答

内源爆炸荷载产生的振动响应对地下衬砌隧洞的安全非常重要。采用Fourier变换和Laplace变换,推导出内源爆炸荷载作用下无限弹性空间中圆柱形衬砌孔洞的瞬态动力响应无量纲解答,利用Fourier和Laplace逆变换数值方法,计算分析内爆炸荷载产生的振动在衬砌和周围弹性介质中的分布和传播衰减规律。计算结果表明,爆源中心处衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力最大,向左右两侧迅速衰减,在6倍衬砌内径处衰减为0;衬砌内表面径向位移、切向应力和衬砌外表面土体径向位移、切向应力时程曲线峰值爆源中心处最大,离爆源中心越远,峰值越小,且在t~*=10时衰减为0。     

爆炸荷载作用下饱和土中隧道的瞬态动力响应

用解析方法研究了爆炸荷载作用下饱和土中圆形隧道的动力响应问题。模型假定饱和土体中的圆形隧道中心处发生爆炸,爆炸荷载采用简化形式,衬砌运动方程基于Flügge壳体理论,饱和土采用Biot波动方程,通过引入两个势函数,在Laplace变换域中推导了爆炸荷载作用下圆形隧道位移和应力响应的表达式。利用Laplace数值逆变换得到爆炸荷载作用下衬砌与土体的时域计算结果,分析了排水条件对位移、应力变化的影响,并讨论了饱和土参数、衬砌和土的相对刚度的影响。数值结果表明,爆炸荷载作用下,不排水条件下应力和位移的响应幅值比排水条件下有所增大;饱和土参数
对土体应力的幅值有明显的影响;衬砌与土的相对刚度越大,土体位移和应力响应的幅值越小,衰减的速度也越快。     

侧向荷载下剪力墙问题的解析解

剪力墙是高层建筑结构的主要抗侧力构件之一。本文利用结构的对称条件,采用半逆解法得到了自重和水平荷载作用下剪力墙结构的应力解析解,并较好地满足了边界条件,可供结构设计参考。     

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.     

水平动荷载作用下海洋大直径管桩动力响应解析解

考虑桩–土–流体耦合振动,研究了谐和激振水平动荷载作用下的海洋大直径管桩振动响应问题.将桩周和桩芯海水考虑为无黏性不可压缩流体建立其控制方程求得海水速度势解析表达式,继而得到作用于桩身动水压力表达式.将土体看作黏弹性介质建立桩周土和桩芯土控制方程,对土体方程直接解耦求解,得到桩周土和桩芯土位移和抗力表达式.利用桩–土体...     

类矩形盾构隧道纵向等效抗弯刚度解析解

结合类矩形盾构隧道截面特点,分别对中性轴位于截面上部边缘(环缝完全闭合)、截面上拱部、截面腰部和截面下拱部4种情况进行分析,并进一步考虑螺栓预紧力和环缝影响范围,推导得到类矩形盾构隧道的纵向等效抗弯刚度解析解,并对影响纵向等效刚度的相关因素进行探究.研究表明:当施加弯矩小于环缝启动弯矩时,环缝全部闭合,等效纵向抗弯刚度...     

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。     

An approximate ANN-based solution for convergence of lined circular tunnels in elasto-plastic rock masses with anisotropic stresses

An approximate solution is presented for predicting the convergence of lined circular tunnels in elasto-plastic rock masses with anisotropic in situ stresses. The basic idea which led to derivation of the solution is function approximation using Artificial Neural Networks (ANNs). A suitable data base including 2500 convergence values is prepared by innovative combination of Design of Experiments technique and Finite Difference Method. Then, an ANN with optimum architecture and appropriate training algorithm is used to learn the underlying phenomena involved in the problem from the data. The explicit form of the solution for calculation of convergence is elicited from the trained ANN. Subsequently, the ANN-based solution is validated against analytical and numerical solutions. Finally, the limitations associated with the solution are discussed.     

平面Rayleigh波入射下饱和土中浅埋隧道复合式衬砌的动力响应

基于Biot波动理论,采用Fourier-Bessel级数展开法,建立了平面Rayleigh波入射下,饱和土中浅埋隧道复合式衬砌的散射力学模型,求解了频域内复合式衬砌的动应力集中系数、孔压集中系数的解析解,通过参数化分析,研究了Rayleigh波在不同入射频率作用下,内衬和外衬的刚度比、厚度比、隧道埋深等因素对复合式衬...     

Analytical solution for deep rectangular structures subjected to far-field shear stresses

Underground structures located in seismic areas have to support the static loads transferred from the surrounding ground under normal working conditions, as well as the loads imposed by any seismic event. Typically underground structures have cross section dimensions much smaller than the wave length of ground peak velocities, in which case inertial forces can be neglected and the structure can be designed using a pseudo-static analysis, where the seismic-induced loads or deformations can be approximated by a far-field shear stress or strain. Current close-form solutions for deep rectangular structures subjected to a far-field shear stress are approximations that do not consider all the relevant variables. An analytical solution is presented in this paper for deep rectangular structures with a far-field shear stress. Complex variable theory and conformal mapping have been used to develop the solution, which is applicable to deep rectangular structures in a homogeneous, isotropic, elastic medium. The solution shows that the deformations of the structure depend on the relative stiffness between the structure and the surrounding ground, and on the shape of the structure. The analytical solution has been verified by comparing its predictions with results from a finite element method and from previously published data.     

Rock mass response for lined rock caverns subjected to high internal gas pressure

The storage of hydrogen gas in underground lined rock caverns (LRCs) enables the implementation of the first fossil-free steelmaking process to meet the large demand for crude steel. Predicting the response of rock mass is important to ensure that gas leakage due to rupture of the steel lining does not occur. Analytical and numerical models can be used to estimate the rock mass response to high internal pressure; however, the fitness of these models under different in situ stress conditions and cavern shapes has not been studied. In this paper, the suitability of analytical and numerical models to estimate the maximum cavern wall tangential strain under high internal pressure is studied. The analytical model is derived in detail and finite element (FE) models considering both two-dimensional (2D) and three-dimensional (3D) geometries are presented. These models are verified with field measurements from the LRC in Skallen, southwestern Sweden. The analytical model is inexpensive to implement and gives good results for isotropic in situ stress conditions and large cavern heights. For the case of anisotropic horizontal in situ stresses, as the conditions in Skallen, the 3D FE model is the best approach.     

多层介质寒区公路隧道保温层厚度计算的一种解析方法

新疆天山的玉希莫勒盖隧道处于高海拔季节性冻土地区,为防止冻害的发生,需要对所需保温层厚度进行研究。针对这一问题建立计算模型,采用Laplace积分变换的方法得到了由于保温作用而没有相变发生时寒区隧道温度场的解析分析方法;通过与stehfest方法对比分析,基于高斯正交法则和快速Fourier变换的Den Iseger方法具有更好的稳定性和准确性,采用该数值反演方法进行Laplace逆变换的求解。根据对玉希莫勒盖隧道的分析表明,保温层、衬砌与围岩中的温度都随着大气温度呈简谐振动;现场采用的5 cm厚保温层内外温差达9.63℃,不能保证该隧道围岩不发生冻胀现象;要保证其在设计年限内不发生冻胀所需要的最小保温层厚度为27 cm;通过对相关物理参数的分析表明：对流换热系数对固体介质的表面温度的最值影响较大,但对保温层厚度的影响较小;随着年平均气温的升高所需保温层的厚度越小,保证的安全年限越长,厚度也越大;随着地层温度的升高,所需保温层厚度逐渐减小;最后对年平均气温和地层温度的不同组合情况进行拟合分析,得出保温层厚度与这两因素的相关关系,可为该地区其他隧道的设计提供参考。     

复合荷载作用下钢梁弯扭屈曲临界弯矩研究

基于由完备的复合荷载作用下钢梁弯扭屈曲总势能方程推导的平衡微分方程,采用Galerkin法推导了考虑横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式,建立了等效弯矩系数的计算理论。依据等效弯矩系数的计算理论确定了7种常见工况的等效弯矩系数理论计算式并给出了6种特殊工况的Cb实用计算式,从Cb计算式的计算精度、适用范围和形式三个方面对国内外文献的Cb计算式进行对比,验证了等效弯矩系数理论的正确性并提出了Cb计算式的选用准则,最后通过2个数值算例验证了复合荷载作用下钢梁临界弯矩Mcr计算式的正确性和Cb计算式选用准则的合理性。结果表明：考虑了横向荷载作用点高度和横截面不对称参数的复合荷载作用下钢梁弯扭屈曲临界弯矩的计算式形式简单、物理意义明确且便于计算;Cb实用计算式的适用范围广且精度高;等效弯矩系数的选用准则合理、有效。     

地震波斜入射地下隧道地震响应：2.5维FE-BE耦合模拟

针对地震波斜入射导致的非一致地震激励结构地震响应问题,提出了地下隧道三维地震响应分析的一个2.5维有限元–边界元（FE-BE）耦合分析方法,该耦合方法具有分析效率高和计算精度高的优势。利用有限元模拟隧道结构,并引入弹簧单元考虑衬砌管片接头的影响;半无限土域利用基于场地三维动力刚度矩阵和移动斜线荷载格林函数的边界元方法模拟。通过与文献结果比较验证了耦合方法的正确性。利用该2.5维FE-BE方法,以某盾构隧道为例,研究了斜入射地震波作用下隧道结构的三维地震响应,着重分析了管片接头对隧道衬砌地震变形和内力的影响,并讨论了通过对隧道衬砌整体刚度进行折减（等效均质圆环模型）来考虑管片接头影响的方法的适用性。研究表明,管片接头对隧道地震响应有重要影响,随接头刚度减小隧道衬砌变形呈增大趋势,但衬砌内力显著减小;而且,对于管片接头刚度较大的情况,等效均质圆环模型可以在一定程度上反映管片接头对隧道结构地震响应的影响,但可能导致隧道纵向弯矩的低估。     

多风向多目标等效静风荷载分析方法及应用

针对大跨空间结构中多振型参与风振响应特点和工程应用需要,提出针对多个风向的多目标等效静风荷载分析方法。根据所有风向的平均风荷载（或者风振响应极值）分布之间的相似性指标,将所有风向分为若干个风向区,计算各风向区的风振包络响应;在每个风向区内,选择平均风荷载分布和结构主导振型惯性力作为构造多目标等效静风荷载的基本向量,根据最小二乘法,得到基本向量的最优组合系数,从而得到针对多个风向、多个等效目标的等效静风荷载。将该方法用于某大型科技新馆,分析结果表明：根据各风向下屋面平均风压系数分布间的相关系数,36个风向角仅需分成3个风向区,且各风向区等效静风荷载作用下的静力响应与实际动力响应包络响应吻合较好,验证了所提方法的计算精度和工程应用的便利性。