斜坡下考虑支护效应浅埋隧道力学响应的时效解答

针对岩质或黄土浅埋隧道,考虑岩土体黏弹性流变特性和支护效应,给出斜坡下进行隧道施工时的全域时效解答。根据一般黏弹性问题求解方法,采用复变函数方法、Laplace变换、黏弹性叠加关系,用随时间和空间变化支护力体现管片支护效应,导出适用于任意黏弹性模型岩体、任意时刻施加支护的应力与位移。解答与相同模型有限元结果一致,根据解答分析了广义Kelvin黏弹性模型岩体中浅埋隧道开挖时侧压力系数、斜坡倾角、埋深对稳定地表沉陷大小和范围、洞周时效位移、应力的影响,给出可按深埋问题处理时的埋深范围。解答可用于岩质和黄土隧道初步设计中,并为隧道与地下结构相互作用分析两阶段法提供自由位移场。     

垂直界面附近椭圆形夹杂对SH波的散射与地震动研究

利用复变函数法和Green函数法给出了SH波对垂直界面附近椭圆形夹杂散射问题的解析解答。首先,将待求的半空间模型沿垂直边界分割为区域Ⅰ和区域Ⅱ两个直角域。通过保角映射的方法将区域Ⅰ内椭圆形夹杂的外域映射为单位圆外域,并利用镜像方法构造出两个区域内满足直角域边界条件的散射波场及适用的Green函数;其次,利用界面契合思想,通过在界面处添加附加力系的方法建立起满足界面处位移和应力连续条件的无穷代数方程组,并截断有限项求解;最后,给出了求解地表位移幅值的具体算例。结果表明,入射波数、入射角度、夹杂位置、垂直界面以及材料参数都对地表位移幅值的分布有影响。     

SH波上方垂直入射时界面附近椭圆夹杂与裂纹的动态响应

采用Green函数、保角映射等方法分析SH波上方垂直入射时弹性半空间中椭圆形弹性夹杂与任意方位裂纹的相互作用。首先,求解含椭圆形弹性夹杂的弹性半空间内任意一点承受时间谐和出平面线源荷载作用时的位移基本解,即Green函数,再结合裂纹切割法构造裂纹,得到SH波上方垂直入射时椭圆夹杂和裂纹同时存在条件下的位移场与应力场。作为算例,给出大量的数值结果,探讨不同参数情况下弹性夹杂周边动应力集中系数（DSCF）、地表位移及裂纹尖端动应力强度因子（DSIF）的分布规律,结果表明不同参数的变化会对三者的分布带来一定的影响。     

基于边界配点法浅埋隧道开挖引起 周围土体变形的分析

对于浅埋隧道施工引起土层位移的解析解,其边界条件的数学处理上比较困难,因此实际工程的应用中受到限制。为解决这一缺陷,基于弹性力学的Airy应力函数,将半无限平面内土体的应力及位移分布转化为解析函数。然后,采用边界配点的方法,控制地表处的应力边界条件( = 0, = 0)及隧道周边土体的位移边界条件( , )。最后,采用最小二乘法,确定土体应力及位移函数的各项系数,求得浅埋隧道在周边土体产生径向位移的作用下,地表及深层土体位移的半数值半解析解。算例分析表明,该方法可以考虑任意荷载及位移作用的边界条件,能够充分发挥解析法和数值法两者的优点,且计算结果与实测结果较吻合,在预测地表及深层土层位移中具有一定的实用价值,可为进一步采取工程措施控制地层变形提供理论依据。     

含圆柱形弹性夹杂地基沉降量的解析解

研究各向同性地基中含一个圆柱形弹性夹杂的地基沉陷问题。考虑全场的应力、变形特征,运用复变函数的罗朗级数展开技术,构造合适的应力函数,结合夹杂的边界条件和无穷远的性态,获得了全场复势的解析表达。数值结果显示：由于两相材料剪切模量之比的不同,在某个范围内沉陷量大于基底中点沉陷;在这个范围之外,则小于基底中点沉陷。当夹杂埋深为夹杂半径的5倍以上时,就可以运用所得结果,而不致引起太大误差;含圆形隧洞和刚性夹杂的问题可作为特殊情况得到。     

SH波作用下各向异性弹性半空间中浅埋圆孔附近的动应力集中研究

研究了稳态水平剪切（SH）波作用下含有圆柱形孔洞的各向异性弹性半空间的动力响应问题,探讨介质的各向异性对孔附近动应力的影响规律。运用复变函数和多极坐标方法在变换空间中构造出各向异性弹性半空间中圆孔的散射波函数,所构造的散射波函数能够自动满足半空间水平表面上应力自由的边界条件和无穷远处的Sommerfeld辐射条件。根据圆孔表面应力自由的边界条件,采用最小二乘法求解所构造的散射波函数的系数。分析了SH波以不同角度自弹性半空间内入射时,不同介质特性、入射波数和埋深对圆孔附近动应力集中系数的影响。数值结果表明,各向异性弹性半空间中孔附近的动应力比各向同性情况有明显增高。     

考虑椭圆化地层变形影响的浅埋隧道弹性解

研究了浅埋隧道周围地层最终变形的计算问题,提出了考虑椭圆化变形影响的计算模型和浅埋隧道位移边界条件,并利用Airy应力函数得到了该问题弹性解析解。在此基础上,通过算例分析了椭圆化变形对竖向位移和水平位移的影响。结果表明,椭圆化变形对水平位移的影响远大于竖向位移。     

既有路基下浅埋隧道开挖引起地层的位移及应力解析解

在既有公路下进行浅埋隧道开挖会引起地层产生位移,导致地表沉降。为了保证施工安全,快速精确地计算地层位移及应力,有效地控制地表沉降,对浅埋隧道的设计与施工均十分重要。在镜像法原理的基础上,引入等效模量当层法,推导出了在有上覆不同材料下浅埋圆形隧道开挖引起地层位移、应力及地表沉降的解析分布规律。计算结果表明,既有路基下开挖隧道引起地层产生的位移和应力解析解能够很好地体现上层高弹性模量路基对沉降及应力的扩散作用,可以求得隧道开挖后洞周地层包括上覆路基及下卧层中任意位置处的位移、应力以及地表沉降,为在双层地基材料中开挖浅埋隧道引起地层位移及地表沉降的计算提供了一种新的解析方法。     

层状场地中局部不均体对平面P波的散射

利用间接边界元方法,在频域内求解了层状场地中局部不均体对平面P波的散射。利用精确的土层动力刚度矩阵进行自由场反应分析,求得位移和应力响应。通过计算虚拟分布荷载的格林影响函数,求得相应位移和应力;根据边界条件确定虚拟分布荷载,最终得到问题的解答。研究了入射P波时,不均体宽度、埋深、厚度、入射角、入射频率度等参数对地表位移幅值的影响,并与相应自由场的结果进行了比较。不均体对P波散射有重要影响,在工程场地地震安全性评价中,应合理考虑局部不均体对场地设计地震动参数确定的影响。     

层状半空间中洞室对入射平面SV波的散射

利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面SV波的散射问题。通过自由场反应分析,求得假想洞室边界上各点位移和各单元应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面SV波的放大作用。结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。     

Analysis of a point sink embedded in a porous elastic half space

Closed-form solutions are presented for the steady-state distributions of displacement, pore pressure and stress around a point sink embedded in a homogeneous, isotropic elastic half space. These solutions have been evaluated for a typical case of a sink (pump) buried in sand and the magnitude of the settlement of the ground surface has been estimated.     

Soil–pipe interaction due to tunnelling: Assessment of Winkler modulus for underground pipelines

One of the key problems in the implementation of Winkler models to analyze tunnelling effects on existing pipelines lies in the assessment of subgrade modulus under external soil displacement. In this paper, an expression of the Winkler subgrade modulus for a pipeline buried at arbitrary depth and subjected to free soil displacement with arbitrary curve shape is given. Using superposition principle and the Fourier integral, the subgrade modulus of an infinite beam resting on the surface of an elastic half space and buried infinitely are obtained respectively. Then the influence of embedment depth is estimated based on Mindlin and Kelvin solution. The validity of the proposed subgrade modulus is verified by comparison with the results from an elastic continuum solution and two centrifuge model tests for the responses of buried pipeline due to nearby tunnelling. Thereafter, parametric studies are shown to assess the accuracy of the proposed subgrade modulus by comparing with an elastic continuum solution in homogeneous and non-homogeneous soil stratum and the amount of error is estimated.     

On the exact evaluation of displacements within a semi-infinite solid due to a buried line source

Garvin’s variant of the Cagniard technique has been used to evaluate exactly the displacements at points within a homogeneous, isotropic, perfectly elastic, solid half space due to a buried explosive line source. The disturbance at any given time is confined to a region bounded by the free surface of the half space and theP wave front within it. The disturbance associated with the Rayleigh pulse affects a smaller region bounded by the free surface and the PP wave front.     

直角域中凸起和孔洞对SH波的散射与地震动

按照波函数展开法和镜像方法,对直角域中半圆形凸起和圆形孔洞对SH波的散射进行了分析,得到其稳态解。对含孔洞和凸起的直角域做分区,等效为一个含孔洞与凹陷的直角域和一个圆域的契合,其在分界面上满足位移和应力的连续性条件,即契合条件,分别构造两个区域内的位移波函数,按照孔洞边界柱面上的应力自由和契合条件定解波函数展开式的系数。按Fourier级数展开法,得到定解条件的线性代数方程组,截断求解,进而得到问题的解析解。数值算例给出圆形孔洞边沿动应力和地表位移幅值的分布情况,得到直角域自由边界、凸起、孔洞对散射和地震动的影响。     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

Source signature and elastic waves in a half‐space under a sustainable line‐concentrated impulsive normal force

First, the response of an ideal elastic half‐space to a line‐concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature—the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress‐free surface of the half‐space to three points located on the other two boundaries of the solution domain. These four wave‐arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface‐axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface‐axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint‐Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line‐concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd.     

Displacement ring load Green's functions for saturated porous transversely isotropic tri‐material full‐space

Based on the Biot's poroelastic theory and using scalar potential functions both the ring load and point load displacement Green's functions for a transversely isotropic saturated porous full‐space composed of an upper half‐space, a finite thickness middle layer and a lower half‐space is analytically presented for the first time. It is assumed that each region consists of a different transversely isotropic material. The equations of poroelastodymanics in terms of the solid displacements and the pore fluid pressure are uncoupled with the help of two scalar potential functions, so that the governing equations for the potential functions are either a second order wave equation or a repeated wave‐heat transfer equation of sixth order. With the aid of Fourier expansion with respect to circumferential direction and Hankel integral transforms with respect to the radial direction in cylindrical coordinate system, the response is determined in the form of line integrals in the real space, followed by theorem of inverse Hankel integral transforms. The solutions degenerate to a single phase elastic material, and the results are compared with previous studies, where an excellent agreement may be observed with the results provided in the literature. Some examples of displacement Green's functions are finally given to illustrate the solution. Copyright © 2016 John Wiley & Sons, Ltd.