A Simple Method for Analysis of Point Anchored Rockbolts in Circular Tunnels in Elastic Ground

Summary. A simple analytical method for the analysis of point anchored rockbolts is presented in this paper. The solution has been derived for elastic ground and rockbolts, for plane strain conditions, and for tunnels with circular cross section. The method provides accurate results for the rockbolts’ loads and displacements and explicitly includes the connection of the rockbolts to the surrounding ground. The addition of such details to a Finite Element numerical model is critical; otherwise the solution obtained may be dependent on the discretization used and on the stiffness of rockbolts and ground. As an alternative to including details of the rockbolt head and anchor point in the numerical model, which could be computationally very expensive, an equivalent spring constant is proposed. The spring constant is obtained by matching numerical with analytical results for a simple case, but keeping the geometry, material properties, and discretization unchanged.     

Ground response curves for rock excavations supported by ungrouted tensioned rockbolts

Summary A numerical analysis has been developed for the design of ungrouted tensioned rockbolts as support of excavations under axisymmetric conditions. The bolts dimensions (length, crosssection, longitudinal and circumferential spacings), their stiffness, their pre-tension load and the delay of installation are taken into account. Moreover, the method effects three main improvements in the usual theory, taking into consideration: 1. the reaction force transferred to the rock mass in the bolts anchoring zone, 2. the elastic recompression of the carrying ring surrounding the excavation due to the bolts preload, and 3. the relative displacement of the bolts ends which has a repercussion on their tension.Since the usual rock-support interaction analysis is only available when the rock mass and the support behave independently, an alternative solution has been explored for the bolting system (since it cannot be considered as an internal support). It consists to include the effect of the rockbolts into the ground reaction curve.In this paper, the principles of the analysis are explained and a numerical application is taken.     

Elastic Solution for Deep Tunnels. Application to Excavation Damage Zone and Rockbolt Support

Summary  A new formulation is presented for deep circular tunnels in rock with cylindrical anisotropy. The formulation is an exact solution since it satisfies equilibrium, strain compatibility, and the anisotropic constitutive model. Complete solutions have been found for two scenarios: tunnel with excavation damage zone, and tunnel with rockbolt support. The solution is based on the assumption of a deep, circular tunnel in a medium with two homogeneous zones: an inner zone surrounding the tunnel, which is either isotropic or anisotropic, and an outer zone, for the remainder of the medium, which is isotropic. Plane strain conditions, elastic response of rock, rockbolts and support, and simultaneous excavation and support installation are also assumed. For tunnels surrounded by an excavation damage zone with reduced rock properties, the tangential stresses and the radial deformations at the tunnel wall are very sensitive to both the magnitude of stiffness reduction of the damaged rock and the size of the damaged zone. The effect of the rockbolts on the rock is approximated by treating the rockbolt-rock composite as a material with cylindrical anisotropy with stiffnesses related to the properties of the rock and rockbolts, and spacing of the rockbolts. Comparisons between the analytical solution and a numerical method show small differences and provide confidence in the approach suggested.     

Performance of a multi-face tunnel excavated in loess ground based on field monitoring and numerical modeling

In large-span tunneling projects, the mechanical behavior of the rock changes in response to different sequential excavation methods (SEMs) of advancing the tunnel face. The double side drift method (DSDM), which is a development of SEM, was widely used in loess tunnels with large cross sections in China for its ability to limit ground displacement. This paper presents the deformation characteristics of large-span loess tunnels of the high-speed railway line in China. Field monitoring and numerical simulations were conducted to determine the optimal construction approach and reveal the deformation properties of large-span loess tunnels in China. The construction approaches, support measures, ground surface, and subsurface deformation characteristics associated with DSDM are demonstrated. The ground surrounding the loess tunnel underwent vertical settlement at the arch part and at the ground surface because of the metastable structure of the loess. This study provides an in-depth illustration of the influence of face-advancing sequences on ground displacement induced by tunneling, which helps us implement the most effective SEMs.     

Solutions for Displacement and Stress in Strain-Softening Surrounding Rock Incorporating the Effects of Hydraulic–Mechanical Coupling and Rockbolts Effectiveness

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering.     

高路堤下涵洞地基处理现场测试与数值模拟研究

山区高速公路高填方涵洞工程应用广泛,由于地基处理不当造成的涵洞病害屡见不鲜。结合现场实测成果和有限元数值模拟结果,分析了涵洞结构物的受力状态及地基受力、变形特性,讨论了地基刚度、不均匀沉降对涵洞受力的影响和埋深效应对地基承载力的影响。研究结果表明：涵洞基底与相同标高下涵洞外侧路基基底土压力相差不大,地基设计时可按二者相等考虑;地基刚度越大,涵洞顶部土压力越大,对涵洞结构物强度要求就越高,地基处理中应尽量避免使用刚性桩复合地基。根据研究结果,提出了高路堤下涵洞地基的设计方法。     

地铁暗挖施工引起的管线与地层沉降关系研究

依托北京地铁4号线公益西桥站工程,建立结构-地层-管线三维弹塑性数值模型,基于管线周边地层沉降及地表沉降实测数据分析,研究西南出入口暗挖施工上方管线周边地层变形规律。通过现场实测数据、数值模拟及经验公式计算结果综合对比,分析了管线刚度对地层变形抵制作用的影响。研究表明：管土相对刚度小于0.18时,管线与土体沉降差小于5%,可用经验公式计算出的管线轴线处地层沉降代替管线沉降。随管线刚度的增大,管线对土体变形的抑制作用逐渐增强,沿深度方向地层沉降量增大速率减小,并会出现负增长,甚至出现地层沉降小于地表沉降的情况。通过对数值计算结果的拟合分析,提出了刚性接头管线与地表沉降比和管土相对刚度的经验公式。工程实例应用结果表明,计算值与实测值偏差小于4%,验证了该方法的适用性。     

穿越地裂缝带地铁隧道结构分段长度优化研究

目前西安地铁建设中过地裂缝带隧道均采取分段设缝的结构措施,而隧道结构分段长度的优化问题是地铁隧道穿越地裂缝带设防的关键。本文以西安地铁斜交穿越地裂缝带为工程背景,通过分段设缝的地铁隧道斜交跨地裂缝带的有限元数值模拟,研究了斜交跨地裂缝带地铁隧道分段设缝的合理模式及分段隧道的合理长度。计算结果表明:对缝设置模式下分段设缝隧道结构塑性区范围较小,集中在隧道拱底、拱脚;而悬臂设置模式下塑性区分布范围大且较为复杂,不利于进行衬砌加强。地铁隧道穿越地裂缝带衬砌结构宜采取分段设缝的对缝设置模式,跨地裂缝带的分段隧道合理长度为15 m,位于地裂缝主变形区内的分段隧道长度可按10～15 m考虑,而穿越地裂缝主变形区之外的地铁隧道分段长度可根据轨道调坡及隧道防水等其他要求适当增加。研究成果可为地裂缝发育的城市地铁隧道结构设计及其他地下空间开发提供重要的理论依据和技术参考。     

Study on Optimization of Crossheading Support and Lateral Stress Evolution Law with Shallow Buried Soft Rock

In a shallow-buried coal mine, the original support scheme of large crossheading has features of excessive strength and resource waste. Firstly, various optimization schemes are obtained through permutation and combination, and verified through numerical simulation. Additionally, under the premise of ensuring safety and economy, the optimal scheme is determined as A3B3: For the roof support, there are 5 rockbolts in each row, with spacing of 1100 × 1000 mm. Row-spacing between anchor cables is 2200 × 2000 mm. There is 1 bolt per row for each sidewall, 1050 mm from the roof and with the spacing of 1400 mm. In order to study the evolution of lateral abutment pressure during the dynamic load stage, FLAC3D was applied. The plastic zone range from coal seam excavation to model equilibrium is analyzed. Finally, the rationality of the design is verified by analyzing the observed of borehole television and roadway displacement.

     

Design of tabular excavations in foliated rock: an integrated numerical modelling approach

Summary This paper presents a rock mechanics design methodology applicable to steeply dipping orebodies typical of many underground hardrock mines. The first stage in the design process is the characterization of the rock mass using bothin situ and laboratory data. The effects of anisotropy on rock mass behaviour are discussed with reference to laboratory and field observations. The second stage involves the use of a number of selected numerical modelling techniques to investigate ground response in the near-field rock mass surrounding the mining excavations. This study shows that the use of several numerical methods in conjunction, allowing for the advantages of each method to be maximized, provides a more comprehensive analysis of the different facets of stope design. This approach differs from those in the literature which seek to compare the different numerical methods in order to select just one method best suited for a problem. The design methodology employed emphasizes the importance of developing an understanding of ground deformation mechanisms as opposed to predicting absolute behaviour.     

大直径钢管桩承载力的非线性分析

推导了砂土地基中闭口管桩的沉桩影响半径以及刚性桩的横向承载力（矩）。通过使用MATLAB程序对单桩轴向刚度的分析,得出了其与桩周单位深度土的等效刚度系数、桩端土的等效刚度系数、钢管桩的壁厚、桩径、桩长、桩身弹性模量等参数之间的一些关系,从而为此类桩的优化设计提供了理论依据。在此基础上通过桩身荷载传递的双曲线函数模型以及相关参数,在已知（假定）桩身压缩量的情况下求出相应的桩顶轴力。     

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.     

大荷载原煤仓天然地基沉降监测及分析

为了真实反映大荷载原煤仓天然地基沉降变形随上覆荷载的变化特征及规律,确保工程安全,在研究区场地建立了一套沉降监测系统,跟踪测试了建设施工及运营期间荷载作用下原煤仓地基土的沉降变形,并依据实际监测结果,通过"规范方法"及"三维数值分析方法"进行了验证。结果表明:原煤仓地基实际变形满足规范要求的允许值,证明采用第四系湖积砂层作为天然地基方案是可行的;地基土实际沉降主要集中在运营期间,建设及施工阶段所占比例较小（10%~27%）,而规范计算该阶段沉降所占比例在40%以上;在沉降计算及预测过程中考虑基础刚度的影响,所得基底土压力分布及沉降计算结果更符合现场实际。研究结果可为类似工程场地设计、建设及安全施工提供理论依据及参考。      

搅拌桩加固挤土效应及在地铁隧道保护中的应用

在减小地基变形进行的深层搅拌桩加固时,加固本身的挤土效应对隧道变形产生了影响。为此,模拟了搅拌桩（DCM）侧向挤土效应的4种荷载模式,结合实测资料并采用数值试验验证了侧向挤土荷载模式的合理性。进一步应用该模式,通过有限元模拟了搅拌桩的加固挤土效应,分析讨论了不同加固顺序对地面变形,隧道变形以及长期蠕变变形的影响,结论表明,搅拌桩加固对地面环境影响是不可忽略,隧道周围搅拌桩施工顺序对隧道变形影响较大,搅拌桩加固后长期蠕变效应相对加固过程的变形很小。     

复用回采巷道护巷煤柱合理宽度研究

为解决高瓦斯工作面双U型巷道布置中煤柱损失大、相邻工作面复用回采巷道维护困难的难题,综合采用理论分析、数值计算和现场试验的方法,研究得到煤柱宽度对相邻两工作面之间煤柱内复用巷道围岩应力分布和变形特征的影响规律：随着巷道一侧煤柱宽度的增加,巷道围岩垂直应力峰值向一侧移动,并逐渐远离巷道;当巷道一侧煤柱较小时,巷道以窄煤柱帮变形和顶板下沉为主,随着煤柱宽度增加,底鼓增大并成为巷道主要变形。以煤柱内应力峰值比值为指标,分析煤柱宽度与巷道稳定性的关系,并将不同宽度煤柱进行了稳定性分区。研究成果成功应用于工程实践,为类似条件下巷道布置提供依据。     

A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability

In this paper we consider the numerical solution of a coupled geomechanics and a stress-sensitive porous media reservoir flow model. We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with respect to the L ²-norm for the pressure and for the average fluid velocity and with respect to the H ¹-norm for the deformation. Estimates with respect to the L ²-norm for mean stress, which is of special importance since it is used in the computation of permeability for poro-elasticity, can be derived using the estimates in the H ¹-norm for the deformation. We start by deriving error estimates in a continuous-in-time setting. A cut-off operator is introduced in the numerical scheme in order to derive convergence. The spatial grids for the discrete approximations of the pressure and deformation do not need be the same. Theoretical convergence error estimates in a discrete-in-time setting are also derived in the scope of this investigation. A numerical example supports the convergence results.     

西安地铁2号线隧道穿越地裂缝带的设防参数

基于西安地裂缝成因、基本特征和未来活动趋势分析,通过几何缩比为1：5的地裂缝活动模型试验和地裂缝活动对盾构隧道影响的数值模拟计算,研究了西安地铁2号线隧道正交穿越地裂缝带的设防参数。通过分析地裂缝年平均活动速率和历史最大活动量,确定了与地铁2号线相交的各条地裂缝的最大垂直位移量的预测值和设计建议值。模型试验和数值模拟结果表明,正交条件下地铁隧道在地裂缝活动地段的设防宽度为60 m,即上盘为35 m,下盘为25 m;沿隧道纵向地裂缝两侧地层变形规律呈现台阶状突变变形,隧道纵向设计可将上盘视为整体下降来考虑;地铁隧道穿越地裂缝带必须分段设缝以适应地裂缝的变形,其分段长度在地裂缝主影响区按10 m进行设防,在一般影响区可按10～15 m进行分段设防。研究结果可为地铁隧道穿越地裂缝带的结构设计提供参考。     

复杂环境中大规模桩筏基础的优化设计方法研究

变刚度优化设计对于复杂环境中的大规模桩筏基础始终是一个重要难题。基于有限元分析提出一种两阶段优化设计方法,该方法首先根据传统均匀布桩方案的桩顶应力分布对群桩进行分区,然后依据每个子区域桩顶应力之间的关系确定基桩数量调整系数,最后通过调整桩间距来改变各子区域的基桩数量,从而实现变刚度优化设计。运用该方法对多层土体中承担非均匀上部结构荷载的大规模桩筏基础进行变刚度优化设计,计算结果表明优化设计后筏板的差异沉降、平均整体弯矩和群桩顶部的差异应力均显著降低。该方法计算简单,应用范围广,且不受复杂土层条件、非均匀上部结构荷载以及桩基础规模大小形状的限制。     

近区锚喷结构的爆破振动特性研究

选用水泥砂浆和玻璃钢分别模拟岩石和锚杆,浇筑2.5 m×1.8 m×2.1 m尺寸的岩体模型,通过模型试验研究近区锚喷结构在掏槽爆破作用下的振动特性。利用测试锚杆测得不同设置情况锚杆上的应变波。试验结果表明,端锚锚杆中部锚固段与锚杆尾部自由段测得的振动波形和变形形式完全不同,中部锚固段振动幅值稍大;在不设置喷层和预应力时,尾部自由段的应变波规律性更强,且持续时间长;随着离爆源距离的增加,锚杆的振动频率和幅值衰减明显,但振动持续时间则稍有增长;通过小波变化的时频方法分析应变波的能量,临近工作面锚杆的振动能量大,但能量分布分散,振动时间有限,稍远的锚杆虽振动能量小,但能量集中,持续时间长;两种不同能量对锚喷结构产生不同的损坏模式。试验和实践发现,爆破容易造成附近喷层的损坏和锚杆的失效,钢纤维混凝土可增加喷层的抗动载性能,调整支护工艺也是减小爆破影响的有效方法。     

Cluster spacing optimization of multi-stage fracturing in horizontal shale gas wells based on stimulated reservoir volume evaluation

The multi-stage fracturing in horizontal well is a common technique for shale gas reservoir exploitation, in which cluster spacing governs the fracturing performance. Undersized cluster spacing might make the stimulated reservoir volume (SRV), activated by the respective hydraulic fracture, excessively overlap with each other, while oversized cluster spacing might leave a large unstimulated volume between neighboring hydraulic fractures; in either case, fracturing would be inefficient. Previous design of cluster spacing has failed to maximize the SRV due to the absence of a dynamic SRV evaluation model. A numerical model of SRV evaluation in shale reservoir was established by integrating four main modules, including fracture propagation, reservoir pressure distribution, formation stress distribution, and natural fracture failure criterion. Then, a method to optimize cluster spacing was developed with the goal of maximizing SRV. In order to validate this method, it was applied in Fuling shale gas reservoir in Southwest China to determine the optimal cluster spacing. The sensitivity of key parameters on the optimal cluster spacing has been analyzed. This research proposed a compelling cluster spacing optimization method, which could reduce the uncertainty in cluster spacing design, and provides some new insights on the optimal design of multi-stage fracturing in horizontal shale gas well.