正交各向异性岩体中非圆形水工隧洞的解析解

将围岩和衬砌分别视作均质、连续的线弹性正交各向异性和各向同性体,并充分考虑衬砌的支护滞后效应和隧洞运行时的内水压力作用,运用复变函数方法中的幂级数解法,提出了正交各向异性岩体中任意形状水工隧洞的力学解析方法。以直墙半圆拱形水工隧洞为例,所获得的解析解可精确满足衬砌内边界的应力边界条件以及围岩与衬砌接触面的应力、位移连续条件,同时还将解析结果与ANSYS数值结果对比分析,吻合良好。利用获得的解析解,讨论了围岩开挖面上不同的各向异性程度、不同的弹性对称面角度以及隧洞内不同的水压荷载对衬砌以及围岩上应力和位移分布的影响。     

非圆形隧洞衬砌支护下应力与位移的新解法

以往在利用平面弹性复变函数方法进行衬砌支护作用下非圆形隧洞的力学分析时,一般将洞室外域保角映射到象平面的单位圆外域,并认为可以利用同一个映射函数将衬砌截面映射到象平面的圆环域内。当衬砌厚度很薄时,这种方法是可行的,而当衬砌相对较厚时,利用同一映射函数所得到的衬砌截面形状发生严重失真。为解决此问题,本文引入两套映射函数,分别将洞室外域映射到象平面的单位圆的圆外域,衬砌截面映射到圆环域。这种方法可以适应于不同的衬砌厚度,利用这种方式获得的衬砌截面,在衬砌较厚时仍能保证衬砌厚度相对均匀。在求解解析函数过程中不再采用传统的幂级数解法,而是使用边界配点法,将两套映射函数结合,获得了该问题的应力解和位移解。本文以马蹄形隧洞为例,求解结果与ANSYS软件所得数值解吻合很好,分析了衬砌厚度对隧洞应力和位移的影响。根据本文解答可以方便、快捷地进行相近条件下隧道的初步设计。     

考虑构造应力作用下浅埋圆形隧洞的解析解

基于复变函数方法,通过孔边及地表的应力边界条件,获得了自重应力和构造应力作用下浅埋圆形隧洞的应力和位移解析解,并通过ANSYS有限元软件对解析解进行了验证。引入可以反映地表水平应力大小的0q项,使得该解具有一般性,对地表水平应力分量为0或不为0的情形都可进行求解。分析了隧洞开挖后的应力场及位移场。结果表明,当地表存在水平方向应力时,隧洞的侧壁区域可能会出现切向拉应力,地表水平应力越大,出现的最大拉应力也越大;随着0q的增大,洞顶向上拱起,两侧受挤压向内变形的程度会加剧,地表会出现向上隆起现象,且在洞顶正上方程度为最大。     

软弱围岩条件公路连拱隧道施工方法数值分析

针对软弱围岩条件（Ⅳ级围岩）大跨度连拱隧道施工安全和围岩稳定问题,结合工程实际,采用非线性有限元法,对连拱隧道施工过程进行了数值计算分析,对比了中导洞一核心土和三导洞先墙后拱施工工艺下隧道的位移特征、点安全系数、二次衬砌应力、锚杆和钢拱架轴向应力。实际工程研究表明,中导洞一核心土施工工艺开挖软弱围岩条件大跨度公路连拱隧道是可行的,对类似软弱围岩条件的隧洞施工有一定参考价值。     

深埋隧洞开挖数值模拟分析的纵向模型范围研究

模型范围是影响数值分析计算精度与效率的重要因素,针对深埋隧洞开挖数值模拟分析问题,采用有限差分软件FLAC3D和复合失稳准则,对计算模型的纵向范围取值问题展开研究。首先分析了深埋隧洞开挖过程中围岩纵向变形以及未开挖岩塞对围岩变形的约束作用,然后研究了近端边界和远端边界对监测断面位置处围岩变形的影响,最后采用最小二乘法对多组计算结果进行了位移误差分析,并给出了纵向模型范围的取值建议。研究结果表明,当监测断面距掌子面大于10倍洞径时,未开挖岩塞的约束作用基本消失;远端边界以及近端边界与监测断面的最大位移误差值之间均基本满足幂函数关系,且远端边界对监测点位移误差的影响要大于近端边界;深埋隧洞开挖数值模拟中,纵向模型范围取7.5倍洞径即可满足一般数值分析的精度要求。     

深埋隧洞开挖数值模拟分析的纵向模型范围研究EI北大核心CSCD

模型范围是影响数值分析计算精度与效率的重要因素,针对深埋隧洞开挖数值模拟分析问题,采用有限差分软件FLAC^(3D)和复合失稳准则,对计算模型的纵向范围取值问题展开研究。首先分析了深埋隧洞开挖过程中围岩纵向变形以及未开挖岩塞对围岩变形的约束作用,然后研究了近端边界和远端边界对监测断面位置处围岩变形的影响,最后采用最小二乘法对多组计算结果进行了位移误差分析,并给出了纵向模型范围的取值建议。研究结果表明,当监测断面距掌子面大于10倍洞径时,未开挖岩塞的约束作用基本消失;远端边界以及近端边界与监测断面的最大位移误差值之间均基本满足幂函数关系,且远端边界对监测点位移误差的影响要大于近端边界;深埋隧洞开挖数值模拟中,纵向模型范围取7.5倍洞径即可满足一般数值分析的精度要求。     

隧洞围岩损失位移估计的智能优化反分析

隧洞开挖过程中围岩监测断面的布置一般滞后于掌子面开挖,监测断面布置前围岩已发生的位移称为损失位移。采用优化反分析思路求取损失位移,该思路将损失位移的求解转化为以实测位移与计算位移的误差作为目标函数、岩体力学参数作为决策变量的全局优化反分析问题。针对该全局优化反分析问题是一类高度非线性多峰值且计算代价较高的优化问题,将性能优异的粒子群优化算法与高斯过程机器学习方法相融合,结合FLAC3D数值计算程序,提出隧洞围岩损失位移优化反分析的粒子群-高斯过程-FLAC3D智能协同优化方法。算例研究表明,该方法是可行的,不仅能获得可靠的损失位移预测结果,而且可获取合理的围岩计算模型力学参数,具有全局性好、计算效率高的特点,克服了传统优化反分析方法容易陷入局部最优或过于依赖初始学习样本的局限性。将该方法应用到锦屏二级水电站辅助洞BK14+599断面的损失位移反分析,获得了该断面围岩的损失位移和力学参数,其中,损失位移较大,原因在于岩体开挖后在短时间内弹性变形大。因此,对于地下工程,特别是深部地下岩体工程,在围岩稳定性评价与围岩参数反分析中,损失位移不可忽视,应给予足够重视。     

矩形巷道孔边应力的弹性分析

对已有的矩形巷道孔边应力研究成果进行了归纳,并提出其存在的问题。在此基础上,利用隧洞围岩应力复变函数分析法中的解析函数通式和单位圆外域-洞室外域共形映射函数计算方法,计算了不同跨高比和侧压力系数下的矩形巷道孔边应力,分析并获得了其对孔边应力分布的影响规律。给出了原岩垂直应力分量 和水平分量 单独作用下矩形巷道顶板和侧帮中点的应力集中系数,并与相关研究结果进行了比较分析,结果表明,矩形巷道的计算断面与理论断面边界线间的误差对孔边应力计算值有较大的影响。采用共形映射函数计算方法获得的计算断面更逼近理论断面,采用解析函数通式进行围岩应力计算时不产生精度损失,研究成果更接近于矩形巷道理论值,可供巷道设计及围岩稳定性分析作理论参考。     

单位圆外域到任意开挖断面隧洞外域共形映射的计算方法

将复杂开挖断面为边界的力学问题转化成单位圆为边界的力学问题,是利用复变函数理论开展地下隧洞围岩力学分析的前提。从黎曼存在定理出发,建立了以洛朗级数有限项表示的单位圆外域到任意开挖断面隧洞外域的共形映射函数。根据边界对应原理,将域到域的共形映射问题转化成单位圆周线到任意开挖断面隧洞边界线的共形映射问题。从三角插值理论出发,采用奇偶插值点反复相互迭代对映射函数的求解开展了研究。为快速地进行迭代计算,采用法线逼近法进行计算点（映射点）调整。提出了以映射边界线与实际开挖洞形边界线之间的绝对误差作为迭代计算的收敛条件,保证了共形映射精度。给出了3个开挖断面隧洞映射函数的求解算例,并将研究结果与文献中的方法进行了比较。结果表明,提出的单位圆外域到任意开挖断面隧洞外域共形映射的计算方法具有操作简单、精度高和收敛快等特点。     

深埋长隧洞三维地质力学模型试验研究

为了评价深埋长隧洞围岩的稳定性和隧洞间距的合理性,本文采用三维地质力学模型试验技术,研究在高地应力、高外水压力作用下,隧洞围岩整体稳定性以及相邻洞室开挖的相互影响效应,并与三维弹塑性有限元数值计算结果进行对比验证,研究结果表明:地质力学模型试验成果和数值计算结果基本一致,两者得到的位移场、应力场、屈服区范围都基本吻合。在高地应力、高外水压力作用下,工程所在的Ⅲ类围岩隧洞是可以安全成洞的。采用超载法进行试验和计算可知,在Ⅲ类围岩中极限超载安全系数k＞1.3,开挖隧洞对洞周围岩的位移与应力影响区一般小于1倍洞径范围,隧洞的间距是合适的。     

Analytical Solutions for the Construction of Deeply Buried Circular Tunnels with Two Liners in Rheological Rock

The construction of underground tunnels is a time-dependent process. The states of stress and strain in the ground vary with time due to the construction process. Stress and strain variations are heavily dependent on the rheological behavior of the hosting rock mass. In this paper, analytical closed-form solutions are developed for the excavation of a circular tunnel supported by the construction of two elastic liners in a viscoelastic surrounding rock under a hydrostatic stress field. In the solutions, the stiffness and installation times of the liners are accounted for. To simulate realistically the process of tunnel excavation, a time-dependent excavation process is considered in the development of the solutions, assuming that the radius of the tunnel grows from zero until its final value according to a time-dependent function to be specified by the designers. The integral equations for the supporting pressures between rock and first liner are derived according to the boundary conditions for linear viscoelastic rocks (unified model). Then, explicit analytical expressions are obtained by considering either the Maxwell or the Boltzmann viscoelastic model for the rheology of the rock mass. Applications of the obtained solutions are illustrated using two examples, where the response in terms of displacements and stresses caused by various combinations of excavation rate, first and second liner installation times, and the rheological properties of the rock is illustrated.     

Lined Circular Tunnels in Elastic Transversely Anisotropic Rock at Depth

Closed-form solutions for displacements and stresses of both the liner and the rock are presented for a deep circular tunnel excavated in transversely anisotropic rock above or below the water table subjected to static or seismic loading. The solutions are obtained with the assumption of elastic response of rock and liner, tied contact between rock and liner, impermeable liner, plane strain conditions along the tunnel axis and simultaneous excavation, and liner installation. The liner of a tunnel placed below the water table must support, in addition to the rock stresses, the full water pressure, while a tunnel located above the water table must support only the rock pressures. The solutions presented for static loading show, however, that displacements and stresses of the liner and rock are the same when the tunnel is placed above or below the water table as long as the total far-field stresses are the same. With rapid loading, e.g. seismic loading, excess pore pressures may be generated in saturated rock, which induce a different response than that of a tunnel excavated in dry rock. The analyses indicate that stresses and displacements are more uniform when excess pore pressures are produced, which seems to indicate that pore pressure generation tends to reduce non-uniform response in anisotropic rock.     

Characteristic Curves for Deep Circular Tunnels in Poroplastic Rock

A complete analytical solution for an axisymmetric deep tunnel excavated in a saturated poroplastic rock is presented. Results are found for short- and long-term analyses and for different drainage conditions at the rock–liner interface. In the derivation, the following assumptions are made: (1) circular cross-section, (2) deep tunnel, (3) plane strain conditions on a cross-section perpendicular to the tunnel axis, (4) axisymmetric loading, (5) the rock is saturated, homogeneous and isotropic, and (6) the rock is elastic-perfectly plastic with brittle failure and non-associated flow rule. The results obtained indicate that, if the rock remains elastic during construction, the stresses of the liner and the tunnel deformations are the same for short- and long-term conditions and are independent of the drainage conditions at the rock–liner interface and on the magnitude of Biot’s parameter α. If the rock yields, the stresses in the liner and the tunnel deformations strongly depend on the type of analysis. Effective radial and tangential stresses inside the rock decrease with Biot’s parameter α, while radial displacements increase. The response of the liner in terms of stresses and deformations strongly depends on its stiffness relative to the rock, yielding of the rock, groundwater and drainage conditions, and construction operations, while it is somewhat less sensitive to the rock’s poroplastic properties. Stresses and deformations inside the rock, however, show a much stronger dependency.     

Mechanical Response of Lined and Unlined Heated Drifts

Summary Approximate relations are developed to determine the steady stresses and displacements that may develop in unlined and lined drifts heated above ambient, as representative of conditions in a nuclear waste repository. For a series of parallel, unlined drifts, radial convergence due solely to thermal effects is everywhere null at early-times; at late times it is a maximum inward at springline, and an equivalent maximum outward at crown and invert. Support pressures and hoop stresses are evaluated for a flexible liner placed in intimate contact with the drift wall, following excavation, where a full slip condition is applied at the drift-liner interface. For rock mass moduli of similar order to, or smaller than, the liner modulus, hoop stresses and support pressures are shown insensitive to rock mass parameters. Surprisingly, liner stresses are strongly controlled by liner modulus, liner Poisson ratio, liner thermal expansion coefficient, and instantaneous liner temperature, and only weakly by rock mass modulus. Response is shown independent of thermal expansion coefficient of the rock mass, and temperature distribution beyond the drift wall. The “misfit” expansion of the liner in the drift cavity controls liner stresses that rise linearly with the temperature of the liner, alone. Importantly, the results demonstrate the potential to control magnitudes of thermal stresses by the incorporation of compressible elements within the liner, or within the blocking or backfill behind the liner. Although the results are partly conditioned by the assumptions of a fully flexible liner and full slip conditions at the drift-liner interface, they serve to define the important parametric dependencies in the mechanical response of heated drifts.     

Numerical Analyses of the Influence of Blast-Induced Damaged Rock Around Shallow Tunnels in Brittle Rock

Most of the railway tunnels in Sweden are shallow-seated (<20 m of rock cover) and are located in hard brittle rock masses. The majority of these tunnels are excavated by drilling and blasting, which, consequently, result in the development of a blast-induced damaged zone around the tunnel boundary. Theoretically, the presence of this zone, with its reduced strength and stiffness, will affect the overall performance of the tunnel, as well as its construction and maintenance. The Swedish Railroad Administration, therefore, uses a set of guidelines based on peak particle velocity models and perimeter blasting to regulate the extent of damage due to blasting. However, the real effects of the damage caused by blasting around a shallow tunnel and their criticality to the overall performance of the tunnel are yet to be quantified and, therefore, remain the subject of research and investigation. This paper presents a numerical parametric study of blast-induced damage in rock. By varying the strength and stiffness of the blast-induced damaged zone and other relevant parameters, the near-field rock mass response was evaluated in terms of the effects on induced boundary stresses and ground deformation. The continuum method of numerical analysis was used. The input parameters, particularly those relating to strength and stiffness, were estimated using a systematic approach related to the fact that, at shallow depths, the stress and geologic conditions may be highly anisotropic. Due to the lack of data on the post-failure characteristics of the rock mass, the traditional Mohr–Coulomb yield criterion was assumed and used. The results clearly indicate that, as expected, the presence of the blast-induced damage zone does affect the behaviour of the boundary stresses and ground deformation. Potential failure types occurring around the tunnel boundary and their mechanisms have also been identified.     

隧道开挖问题中的流固耦合模型及数值模拟

隧道工程中的地下水问题是富水地层中普遍存在的重要问题,地下水流动对隧道围岩稳定性有重要影响。给出了描述隧道开挖过程中力学与水力特征及表征方法,根据岩体的基本结构特征及代表性单元体（REV）是否存在提出了流固耦合模型的建立方法;提出了隧道水力耦合数值分析中的耦合计算模型的建立方法;利用数值法研究了隧道开挖渗流与应力耦合问题,得到变形和渗流场的变化规律。结果表明,隧道开挖引起的渗流影响边界大于力学影响边界,由于渗流引起的渗流力增加了围岩的应力、位移,从围岩-支护结构共同作用原理考虑,进行隧道支护结构设计时是应该考虑渗流效应的。     

Bayesian Estimation of Boundary Conditions with Application to Deep Tunneling

An iterative procedure is proposed to determine the far-field state of stress that exists in a rock mass with non-linear behavior around a tunnel. Absolute displacements of the tunnel wall obtained by means of geodetic measurements are used to identify the boundary stress conditions. Previous information is accounted for, so that boundary conditions can be updated at the various stages of a project, as soon as new information becomes available. The application to the 2-D plane strain synthetic model of a tunnel in a yielding rock mass shows the fast convergence of the procedure and the need to use absolute displacements (rather than relative displacements) in order for the identification problem to be well-posed.     

An analytical solution for stresses induced by a post-tensioned anchor in rocks containing two perpendicular joint sets

A new analytical approach for the analysis of stress around a post-tensioned anchor in rock with two perpendicular joint sets is presented. The solution considers nonlinear shear stresses developed along the anchor bond length as well as debonding at the tendon–grout interface. The bearing plate effects are also considered in the analyses. The following assumptions are made: (1) homogeneous and orthotropic elastic rock; (2) half-space rock mass with plane strain conditions; (3) trilinear bond-slip model for the behavior of the tendon–grout interface; (4) an elastic anchor. The employed methodology is to decompose the anchor problem into two problems of simpler loadings: stresses produced under a rigid bearing plate and stresses induced by interfacial shear stresses mobilized along the bond length. Based on the proposed solution, an illustrative example is given and the results show that a large compressive region is formed around the anchor free length. Tensile stress concentrations are also observed around the bond length and near the rock surface outside the bearing plate. A parametric study is also conducted to investigate the effects of joint properties on the induced stresses. The results show that as the number of joints intersecting the anchor axis increases, the magnitude of compressive stresses in the free zone decreases, while the size of compression zone around the anchor increases. To verify the results of the analytical approach, a comparison is made with numerical results obtained by using the finite element method. The analytical solutions compare very well with the results obtained by numerical method.     

新疆西部北天山深埋特长隧道工程区应力场数值模拟

采用隧道工程区应力实测数据、北天山地区现代震源机制解、区域地质构造资料以及岩体物理力学参数作为物理模型边界条件和载荷,对北天山隧道工程区进行三维应力场数值模拟,获得了整个工程区特别是隧道工程重要部位岩体应力分布规律,并依据隧道区应力场模拟结果,结合地质资料进行了隧道工程稳定性分析。