Updating the models and uncertainty of mechanical parameters for rock tunnels using Bayesian inference

Rock mechanical parameters and their uncertainties are critical to rock stability analysis, engineering design, and safe construction in rock mechanics and engineering. The back analysis is widely adopted in rock engineering to determine the mechanical parameters of the surrounding rock mass, but this does not consider the uncertainty. This problem is addressed here by the proposed approach by developing a system of Bayesian inferences for updating mechanical parameters and their statistical properties using monitored field data, then integrating the monitored data, prior knowledge of geotechnical parameters,and a mechanical model of a rock tunnel using Markov chain Monte Carlo(MCMC) simulation. The proposed approach is illustrated by a circular tunnel with an analytical solution, which was then applied to an experimental tunnel in Goupitan Hydropower Station, China. The mechanical properties and strength parameters of the surrounding rock mass were modeled as random variables. The displacement was predicted with the aid of the parameters updated by Bayesian inferences and agreed closely with monitored displacements. It indicates that Bayesian inferences combined the monitored data into the tunnel model to update its parameters dynamically. Further study indicated that the performance of Bayesian inferences is improved greatly by regularly supplementing field monitoring data. Bayesian inference is a significant and new approach for determining the mechanical parameters of the surrounding rock mass in a tunnel model and contributes to safe construction in rock engineering.     

海底隧道围岩位移全曲线研究

限于施工现场条件,目前的隧道量测位移均是隧道实际位移的一部分,而隧道量测全位移则少有研究。以厦门海底隧道工程为依托,对隧道开挖各部拱顶下沉监测数据进行了回归分析,得出了海底隧道CRD1和CRD3部拱顶下沉未监测到位移的第1部分Y1。采用三维有限差分程序研究海底隧道各部位移全曲线,得出了掌子面到达研究断面前发生位移所占比例。根据实测资料得出海底隧道CRD1部和CRD3部拱顶下沉未监测到的位移第2部分Y0。将Y0和Y1与实测部分Ym相加,即得到隧道位移全曲线。     

An improved numerical approach in surrounding rock incorporating rockbolt effectiveness and seepage force

The solutions of stress and displacement of a circular opening excavated in brittle and strain-softening rock mass incorporating rockbolts effectiveness and seepage force are presented in this study. The evolution equation is reconstructed for the strength parameters that incorporate these factors. Based on the evolution equation, an improved numerical method and stepwise procedure are presented which are compatible with the Mohr–Coulomb (M–C) and the generalized Hoek–Brown (H–B) failure criteria, respectively. Then given three interaction mechanisms between rockbolts and surrounding rock, solutions for stress and displacement are proposed in line with the improved numerical method and numerical stepwise procedure. The proposed approach can be reduced to Fahimifar and Soroush’s (Tunn Undergr Space Technol 20:333–343, 2005) solutions for special cases. The proposed method was validated by field monitoring data and FLAC results of Yanzidong tunnel. Examples under the M–C and generalized H–B failure criteria for rock mass are generated through MATLAB programming. Moreover, parametric studies are conducted to highlight the influence of rockbolts effectiveness in combination with seepage force on the stress and displacement of very good, average, and very poor surrounding rock. Results show that in this case, stress confinement is higher and tunnel convergences are lower than the corresponding stresses and displacements obtained in non-reinforced tunnels. Displacement and plastic radius are also higher than those without considering seepage force.     

分岔隧道模型试验与数值模拟超载安全度研究

超载试验能得到隧道的超载安全度,通过大型地质力学模型对分岔隧道进行了超载试验,模拟了分岔隧道在不同侧压系数下围岩的变形、应力分布和破坏情况。同时,应用三维数值分析软件对模拟区域进行了模拟。模型试验和数值模拟结果分析表明,随着侧压系数K的增加,分岔隧道的侧向位移增加,拱顶位移由向下变为向上;当侧压系数为K=3.5时,应力达到极限;当侧压系数K≥4.0时,位移突变,最终最大位移达到100 mm;塑性区骤增,隧道拱顶围岩开始开裂,且有块体掉落。分岔隧道的拱顶和两帮是最易破坏的区域,隧道超载安全度为3.5。     

Anchoring Parameters Optimization of Tunnel Surrounding Rock Based on Particle Swarm Optimization

In the highway tunnel project, due to the uncertainty and complexity of geotechnical parameters, it is difficult to design and optimize the anchorage parameters. In order to solve this problem, based on the Zhenfengling tunnel project as the research object, 3D tunnel model was established by ANSYS software, the model was imported into FLAC^3D software for numerical analysis and calculation for the displacement and stress of surrounding rock during construction, using orthogonal experiment methods to analyze factors affecting the stability of surrounding rock. The influence of anchor length, anchor spacing, anchor diameter, the thickness and elastic modulus of spray layer on the displacement of arch waist, arch crown and arch bottom of the tunnel was obtained by using range and variance analysis. The regression model of the relationship between arch surrounding rock displacements and anchorage parameters was determined by fitting regression. The particle swarm optimization algorithm was used to optimize the anchorage parameters in combination with the tunnel section cost formula, and the parameters were compared with those not optimized. Finally, the anchor length is designed as 3 m, the anchor spacing is designed as 1.4 m, the anchor diameter is designed as 21 mm, the thickness of spray layer is designed as 24 cm, and the elastic modulus of spray layer is designed as 24 GPa. The stability requirements can be met, and the economic efficiency is also greatly improved. The cost of support with optimized parameters is 19.4% lower than that of the original design parameters.

     

大型地下洞室考虑开挖卸荷效应的位移反分析

基于现场监测资料的位移反分析是地下工程动态监控、信息化施工的重要组成部分。以乌江彭水水电站大型地下厂房（开挖跨度为30 m,高度为78.5 m）为例,从围岩实测位移出发,建立了基于均匀设计－神经网络－遗传算法的围岩力学参数的系统反分析方法,反演考虑开挖卸荷效应的围岩力学参数。根据数值分析结果形成训练样本,利用BP人工神经网络映射围岩的变形与力学参数的关系,同时针对传统人工神经网络存在初始权值难以确定的问题,应用遗传算法优化神经网络的初始权值;利用现场监测的增量变形反演了围岩的力学参数;最后利用反演出的参数,进行地下厂房开挖预测分析。结果表明,预测位移与现场监测位移较为接近,进行统计检验结果为优,说明该参数反演方法是正确合理的。     

Application of extended Kalman filter to back analysis of the natural stress state accounting for measuring uncertainties

In this work, we present a numerical procedure for determining the nature stress state in the rock mass around a tunnel. A finite element method is applied for analyzing the direct problems of tunneling during the back analysis of parameter estimation, in which a no‐tension elastic–plastic model is used to simulate the elastic–tensile and elastic–plastic‐tensile failure states which often occur in the cases of underground excavation in heavily jointed rock masses. By considering the natural stress state as random parameters of the tunneling system, the Kalman filter method is employed for feedback analysis to modify the parameter values in a statistical context, which uses the prior information in the process of estimation and employs a set of displacements obtained from field measurements. To verify the effectiveness of the proposed method of inverse analysis, the developed numerical procedure is applied to a synthetic example of deep tunnels in yielding rock masses. The relative importance of the a priori and updating information is investigated, as is the importance of their uncertainty. The results show great potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

考虑空间效应的地下洞室爆破开挖松动区参数场位移反分析

将地下洞室爆破开挖松动区视为一个随开挖过程演变的非均匀、非稳定三维扰动场,松动区内岩体力学参数则是一个具有时空演化特性的参数场。考虑爆破开挖扰动空间效应和岩体真实变形响应,提出了真实工作状态下开挖松动区岩体参数场辨识的位移反分析方法。基于局部监测变形空间插补得到的空间位移场,通过分析洞室爆破开挖围岩变形扰动机制,建立了开挖松动区岩体变形模量参数场数值演化模型,并进行了模型适用性和参数敏感性分析。在此基础上,以变形模量参数为例,结合围岩实测位移信息,提出了开挖松动区参数场位移反分析的动态实现过程。将该方法应用于溪洛渡地下洞室群施工期参数场反演和围岩稳定动态反馈评价及预测,结果表明,该方法合理有效,在大型地下洞群施工开挖与快速监测反馈方面具有显著的工程适用性及实用性。     

确定流变岩体的参数及地应力的位移反分析法

在隧道设计和施工中,工程师需要确定岩体的力学参数和地应力场。对于软弱地层,我们还将遇到流变问题。具体地说,我们在作工程设计前就需要确定地应力分量、岩体的弹性模量以及反映岩体流变特性的粘滞系数等重要参数。一般而言,这需要在野外作相应的岩体力学试验来确定。     

Progressive degradation of rock properties and time-dependent behavior of deep tunnels

Time-dependent response of deep tunnels is studied considering the progressive degradation of the mechanical properties of the rock mass. The constitutive model is based on a rock-aging law for the uniaxial strength of the rock and for the Young’s modulus. A semi-analytical solution is developed for the stresses and displacements around a deep circular tunnel taking into account the face advance. The evolution of the plastic and damage zones over time is determined. Numerical examples are presented for the case of Saint-Martin-La-Porte access adit in France of the Lyon–Turin Base Tunnel. The computed results which are compared with the field data in terms of the convergence of tunnel wall and of the displacements inside the rock mass monitored by multi-point extensometers show the efficiency of the approach to simulate the time-dependent deformation of a tunnel excavated in squeezing ground. Simple relationships are proposed to evaluate the parameters of the constitutive model directly from those of the empirical convergence law presented in previous work.     

马蹄形隧洞考虑支护滞后过程的应力分析

基于平面弹性复变函数中的保角变换方法,推导出带有衬砌的非圆形隧洞在原始地应力作用下的应力解析解。根据衬砌内边界的应力边界条件及围岩衬砌接触面上的应力和位移连续条件,获得求解围岩和衬砌解析函数的基本方程,计算了围岩和衬砌中的应力和位移。在求解过程中,考虑了支护滞后于开挖的力学过程,并认为围岩和衬砌之间紧密接触,不会相互分开和相对滑动。以马蹄形隧洞为例,获得了围岩开挖边界和衬砌内外边界的切向应力及围岩与衬砌接触面上的接触应力分布规律,并与ANSYS数值方法结果对比,算例表明两种方法的计算结果吻合很好。     

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。     

糯扎渡水电站1#导流隧洞三维非线性有限元开挖模拟分析

糯扎渡水电站1#导流隧洞开挖经过F3断层,开挖过程中,F3断层影响带附近的岩体力学参数直接控制着围岩的变形和应力分布。为了评判后续Ⅱ,Ⅲ层开挖围岩的稳定性,首先利用隧洞第Ⅰ层开挖的位移监测数据反演出F3断层附近围岩的岩体力学参数和初始地应力场;然后,利用反演得到的初始地应力场和岩体力学参数进行Ⅰ,Ⅱ,Ⅲ层开挖模拟分析,得到了F3断层附近围岩的应力变形情况。计算结果表明：随着开挖的不断进行,隧洞F3断层周围岩体的约束逐渐解除,围岩的应力逐渐增大,隧洞周边的位移也不断增大,并且隧洞周围应力变形在F3断层中心区域有明显的错动现象,说明F3断层对隧洞的开挖影响比较大,有必要对此区域后期变形加强观测和分析。     

厦门海底隧道顶板厚度选择及其开挖稳定性分析

在厦门海底隧道轴线的地质剖面图上,选取了4个典型的剖面,应用多裂隙岩体三维弹塑性本构关系和损伤演化方程进行数值分析研究,得到了应力分布、洞周位移、塑性区、损伤区等结果。通过对应力扰动区的分析,以及隧道轴线位置、轴线升高或降低后各剖面应力扰动范围与弱风化层厚度的对比,很容易确定厦门海底隧道的最小顶板厚度;根据应力分布、洞周位移、塑性区、损伤区结果,评价了海底隧道的开挖稳定性。二者的有机结合,说明了将设计方案的轴线位置提高4 m后隧道是稳定的。     

Empirical and numerical analyses of support requirements for a diversion tunnel at the Boztepe dam site, eastern Turkey

This paper presents the engineering geological properties and support design of a planned diversion tunnel at the Boztepe dam site that contains units of basalt and tuffites. Empirical, theoretical and numerical approaches were used and compared in this study focusing on tunnel design safety. Rock masses at the site were characterized using three empirical methods, namely rock mass rating (RMR), rock mass quality (Q) and geological strength index (GSI). The RMR, Q and GSI ratings were determined by using field data and the mechanical properties of intact rock samples were evaluated in the laboratory. Support requirements were proposed accordingly in terms of different rock mass classification systems. The convergence–confinement method was used as the theoretical approach. Support systems were also analyzed using a commercial software based on the finite element method (FEM). The parameters calculated by empirical methods were used as input parameters for the FEM analysis. The results from the two methods were compared with each other. This comparison suggests that a more reliable and safe design could be achieved by using a combination of empirical, analytical and numerical approaches.     

隧道开挖中围岩损伤演化分析及力学参数预测

数值方法所得出结论的可靠性很大程度上取决于岩体力学参数的选取,因此基于损伤演化分析,对损伤变量与围岩力学参数之间关系进行了研究。在各向同性损伤的假定下,通过分析开挖过程中围岩损伤演化,建立了采用损伤变量对弹性模量、泊松比、黏聚力、摩擦角等围岩材料参数进行估算的方法。采用弹性纵波波速定义初始损伤,根据壁城隧道现场监测资料建立ANSYS渐进性数值模型,反演典型断面开挖过程中围岩的宏观力学参数。分析结果表明,该方法可以有效地确定围岩力学参数的变化情况,与实际情况吻合较好。     

多失效模式下基于区间非概率的岩质隧道稳定可靠度分析

对于岩质隧道工程的稳定可靠度分析,一方面由于岩体参数的统计数据获取困难使得概率可靠度方法难以适用,另一方面其工程稳定与多种失效模式密切相关,须考虑隧道结构体系的可靠度问题。首先,基于区间理论,通过区间变量形式表征不确定性参数;然后,针对岩质隧道工程中多种失效模式并存的情况,引入结构体系可靠度理念,建立基于区间非概率的岩质隧道结构体系可靠度指标计算及其稳定性评价方法;在此基础上,通过工程实例验证了该方法的合理性;最后,定义不确定性参数的波动幅度,进一步分析各失效模式中不同参数对相应可靠度指标以及结构体系可靠度指标的影响。分析结果表明,各失效模式相应的非概率可靠度指标均随区间变量范围的增大而降低,且同一参数在不同失效模式中表现出不同的影响;另外,不确定性参数的变化还将导致影响岩质隧道结构体系稳定的主要失效模式发生相应的变化。     

锚杆支护圆形隧洞的等效强度参数及可靠性分析

通过采用均匀化方法,研究了圆形隧洞的锚杆支护特性,将高密度支护模式下的岩石和锚杆复合体考虑成均匀、连续、强度参数增强的等效材料,简化了岩石和锚杆间复杂的力学耦合问题。通过定义锚杆密度参数来反映不同支护模式的特性,建立锚杆密度参数与Mohr-Coulomb屈服准则中主要参数之间的关系,推导出等效弹性模量、等效黏聚力和等效内摩擦角的表达式,并分析比较了隧洞在支护前后的位移情况。结合可靠性理论,采用容许极限位移量作为失稳判据,分析了隧洞在支护前后的可靠性指标与破坏概率,结果表明,文中提出的方法简单可靠,锚杆支护对隧洞的位移限制效果明显,可显著提高隧洞的可靠性。     

节理岩体力学性能不确定性分析方法研究

基于连续介质损伤力学框架,通过损伤张量和有效应力来描述节理岩体的力学性能,自主研发了基于损伤力学模型的有限元程序（CD-FEM）,用于节理岩体等效力学性能研究。同时,采用Karhunen-Loeve（K-L）展开来分解随机输入场,用混沌多项式来表示随机输出场,采用概率配点法生成配点,再由连续损伤有限元分析系统CD-FEM求解确定性方程组,最终得到输出域的统计数据,从而提出了一种将随机分析与基于连续损伤力学模型的数值分析方法解耦进行节理岩体不确定性力学行为分析的方法。利用该方法,对一典型节理岩体在加载条件下的力学行为进行不确定性分析,并与蒙特卡罗方法进行对比,结果表明,所提方法的计算量大大减少,极大地提高了节理岩体力学性能不确定性分析的效率,可应用于对节理岩体在不同载荷条件下的不确定性进行分析。