Determination of the natural stress state in a Brazilian rock mass by back analysing excavation measurements: a case study

The Serra da Mesa Hydroelectric Power Plant, located in the Tocantins river, 210 km north of Brasilia, Brazil, has been completed and power (1200 MW) has been generated since 1998. This project includes one of the largest underground structures in Brazil, totalling 550,000 m³ of underground excavations in rock for the hydraulic circuit which was excavated in very high quality granite. Geotechnical investigations, laboratory tests and geological mapping showed that the rock mass could be considered as a continuous, homogeneous, isotropic and linearly elastic (CHILE) material.

In situ tests, for obtaining the natural stress tensor, namely hydraulic fracturing and small flat jack tests (SFJ), were executed. The hydraulic fracturing tests were performed in two boreholes, at the planned position of the future underground structures. SFJ were executed in a test gallery especially constructed for the purpose. These latter tests confirmed the in situ rock stress data obtained from the hydraulic fracturing tests.

This paper presents a new technique for interpretation of the SFJ results. This is achieved by inputting the SFJ measurements into a 3D program that compiles the influence matrix of the excavated rock mass domain and then, via the least square technique, the determination of the stress tensor. All the equations are fully developed and the methodology is presented in its entirety. The successful application of the methodology is also presented, with comparisons between the results obtained and the in situ stress tensor determined by other methods.     

Tunnel stability and arching effects during tunneling in soft clayey soil

A series of centrifuge model tests and numerical simulations of these tests were carried out to investigate the surface settlement troughs, excess pore water pressure generation, tunnel stability and arching effects that develop during tunneling in soft clayey soil. The two methods were found to provide consistent results of the surface settlement troughs, excess pore water generation, and the overload factors at collapse for both single and parallel tunneling. The arching ratio describes the evolution of the arching effects on the soil mass surrounding tunnels and can be derived from the numerical analysis. The boundaries of the arching zones for both single tunneling and parallel tunneling were determined. In addition, the boundaries of the positive and negative arching zones were also proposed.     

Artificial Ground Freezing to excavate a tunnel in sandy soil. Measurements and back analysis

The paper is dedicated to the case history of a 13 m wide, 17 m high and 40 m long service tunnel at Toledo Station, previously constructed in a deep open shaft and belonging to the Line 1 of the Napoli underground network. The existing Line 1 has been recently extended with a new stretch consisting of five new stations connected by twin rail tunnels for a total length of about 5 km. Toledo Station main shaft is located by a side of the line and it is connected to the pedestrian platforms by the above mentioned large size service tunnel. The station is situated in the historical center of the city of Napoli, under a deeply urbanized area. In Fig. 1 a longitudinal section of the main shaft of the station and of the large service tunnel with the above and surrounding buildings is sketched. The focus of this paper is on the settlement caused by the tunnel excavation and on the use of the Artificial Ground Freezing (AGF) technique to allow the safe excavation of the large crown of the service tunnel, located about one half in a silty sand layer and one half in yellow tuff, well below the groundwater table.     

Challenges associated with numerical back analysis in rock mechanics

Numerical back analysis is a valuable tool available to rock mechanics researchers and practitioners. Recent studies related to back analysis methods focused primarily on applications of increasingly sophisticated optimization algorithms (primarily machine learning algorithms) to rock mechanics problems. These methods have typically been applied to relatively simple problems; however, more complex back analyses continue to be conducted primarily through ad hoc manual trial-and-error processes. This paper provides a review of the basic concepts and recent developments in the field of numerical back analysis for rock mechanics, as well as some discussion of the relationship between back analysis and more broadly established frameworks for numerical modelling. The challenges of flexible constraints, non-uniqueness, material model limitations, and disparate data sources are considered, and representative case studies are presented to illustrate their impacts on back analyses. The role of back analysis (or “model calibration”) in bonded particle modelling (BPM), bonded block modelling (BBM), and synthetic rock mass (SRM) modelling is also considered, and suggestions are made for further studies on this topic.     

Numerical analyses in the design of umbrella arch systems

Due to advances in numerical modelling, it is possible to capture complex support-ground interaction intwo dimensions and three dimensions for mechanical analysis of complex tunnel support systems,although such analysis may still be too complex for routine design calculations. One such system is theforepole element, installed within the umbrella arch temporary support system for tunnels, whichwarrants such support measures. A review of engineering literature illustrates that a lack of designstandards exists regarding the use of forepole elements. Therefore, when designing such support, designersmust employ complex numerical models combined with engineering judgement. With referenceto past developments by others and new investigations conducted by the authors on the Driskos tunnelin Greece and the Istanbul metro, this paper illustrates how advanced numerical modelling tools canfacilitate understanding of the influences of design parameters associated with the use of forepole elements.In addition, this paper highlights the complexity of the ground-support interaction whensimulated with two-dimensional （2D） finite element software using a homogenous reinforced region,and three-dimensional （3D） finite difference software using structural elements. This paper further illustratessequential optimisation of two design parameters （spacing and overlap） using numericalmodelling. With regard to capturing system behaviour in the region between forepoles for the purpose ofdimensioning spacing, this paper employs three distinctive advanced numerical models： particle codes,continuous finite element models with joint set and Voronoi blocks. Finally, to capture the behaviour/failure ahead of the tunnel face （overlap parameter）, 2D axisymmetric models are employed. Finally,conclusions of 2D and 3D numerical assessment on the Driskos tunnel are drawn. The data enriched casestudy is examined to determine an optimum design, based on the proposed optimisation of designparameters, of forepole elements related to the si     

临近地铁隧道基坑开挖的数值模拟分析

临近地铁隧道的基坑开挖必定会对隧道产生影响,同样隧道的存在对基坑的变形也有一定作用。通过对上海某基坑工程应用FLAC3d软件进行数值模拟分析,研究发现,基坑开挖卸载后,地表发生沉降,基坑内土体发生隆起,其中靠近隧道区域隆起值最大;隧道开始整体向基坑方向侧移,但是上下、左右特征点位移量并不一致,隧道产生不均匀应力,特别是上下方向可能存在拉应力。     

Numerical Simulation of the Howard Street Tunnel Fire

The paper presents numerical simulations of a fire in the Howard Street Tunnel, Baltimore, Maryland, following the derailment of a freight train in July, 2001. The model was validated for this application using temperature data collected during a series of fire experiments conducted in a decommissioned highway tunnel in West Virginia. The peak predicted temperatures within the Howard Street Tunnel were approximately 1,000°C (1,800°F) within the flaming regions, and approximately 500°C (900°F) averaged over a length of the tunnel equal to about four rail cars.     

盾构隧道近距离下穿既有隧道的数值分析

通过对武汉市轨道交通3号线盾构隧道下穿2号线既有隧道工程实例的分析,结合类似地层工程经验提出了盾构隧道近距离下穿既有隧道的工程措施,并运用数值分析的方法,得到了盾构下穿过程中既有隧道的竖向位移与盾构机顶推力、土层加固、盾构机掘进位置的关系,验证了工程措施的可行性,提出了相关建议。     

Numerical investigation of underlying tunnel heave during a new tunnel construction

This paper presents a case study of protecting existing tunnels during the construction of a new cut-and-cover tunnel above in Nanjing, China. Various construction measures, including sequential excavation, jet grouting, and a pile-slab retaining system were performed to control the heave of existing tunnels. Furthermore, a numerical analysis using a finite difference program, FLAC3D, was conducted to investigate the influence of different construction schemes on the tunnel heave. Finally, a comparison between numerical results and field measurements were carried out to study the influence on the tunnel heave from various factors, such as the ground reinforcement depth, excavation sequence, and the skew angle between new tunnel and existing tunnels. The results show that when the excavation volume is small, the uplift values of existing tunnels increase nonlinearly with the increasing excavation width of each step. The pile-slab retaining system combining with ground treatment method can control the tunnel heave within the required limits. The optimum ground treatment scope is about 1.5 times of the excavation depth in this project. Compared to other construction schemes, the tunnel heave will be the smallest under a staggered segmentation excavation method starting from the sides to the center.     

浅埋铁路隧道CRD法施工对地表变形影响的数值分析

针对龙厦铁路石桥头隧道工程围岩软弱,埋深浅的特点,应用数值分析手段,分析了浅埋铁路隧道在CRD法下施工,对地表沉降变形的影响。结果表明:CRD法下隧道各部施工对地表沉降均有影响,掌子面上部开挖产生的地表沉降明显大于下部,纵向地表沉降随隧道开挖过程分为三个阶段。结合分析结果,文章指出了施工过程中应采取的相应措施。     

Back analysis of geomechanical parameters by optimisation of a 3D model of an underground structure

One of the major difficulties for geotechnical engineers during project phase is to estimate the geomechanical parameters values of the adopted constitutive model in a reliable way. In project phase, they are normally evaluated by laboratory and in situ tests and, in the specific case of rock masses, by the application of empirical classification systems. However, all methodologies lead to uncertainties due to factors like local heterogeneities, representativeness of the tests, etc. In order to reduce these uncertainties, geotechnical engineers can use inverse analysis during construction, using monitoring data to identify the parameters of the involved formations. This paper shows the back analysis of geomechanical parameters by the optimisation of a 3D numerical model of the hydroelectric powerhouse cavern of Venda Nova II built in Portugal. For this purpose, two optimisation techniques were considered: one classical optimisation algorithm and an evolutionary optimisation algorithm. In the optimisation process, displacements measured by extensometers during excavation were used to identify rock mass parameters, namely the deformability modulus (E) and the stress ratio (K₀). Efficiency of both algorithms is evaluated and compared. Both approaches allowed obtaining the optimal set of parameters and provided a better insight about the involved rock formation properties.     

Bolt length requirement in underground openings

A parametric study has been carried out using the numerical analysis code FLAC^3D to obtain the influence of various shapes of underground openings on the maximum induced boundary stress. Five shapes—viz. circular, horseshoe, rectangular, elongated D-shape and elliptical—have been considered. For each shape, four tunnel depths and five horizontal in situ stress models have been taken for the study of induced boundary stresses.The values of maximum and minimum induced boundary stresses in the roof and wall have been obtained from the analyses. This data has subsequently been used to develop correlations to estimate the normalized maximum and minimum boundary stresses, which have been subsequently compared with the strength of the rock mass obtained from the Sheorey's non-linear failure criterion for three rock masses represented by three values of Bieniawski's RMR and three values of crushing strength of intact rock material. The values of minimum factor of safety at the roof and the wall have been collected from all the plots. Using these data sets, different correlations have been developed to estimate the minimum factor of safety (f_min) in the roof and wall.Since the bolt length should be normalized with the opening size, some more computer models have been run with varying tunnel width of 5 and 20 m besides the earlier 10 m size to obtain the correlations for estimating the bolt length. The depth of factor of safety contour of 1.5 from the opening periphery has been picked up from all these models and the correlations have been developed for estimating the roof and wall bolt length for the five shapes of underground openings. The correlations for bolt length show that in addition to the shape of underground openings and in situ stress, the bolt length also varies with the rock mass type. These correlations have been verified for field cases of elongated D-shape openings.     

Intelligent back analysis of displacements using precedent type analysis for tunneling

Based on comprehensive monitored data obtained from typical tunnel projects, and by using engineering experiences of experts together with numerical modeling results, the precedent type analysis (PTA) technique developed was for back-analyzing in situ stress and elastic modulus of rock masses surrounding tunnels. Then, the PTA is used as a supporting technique in the method of intelligent back analysis (IBA). The IBA method can integrate the mechanism analysis with experimental identification. Such integration is based on ‘certainty factors’, and is implemented with the computer program BMP90 with a global inference engine. The program BMP90 can solve a series of back analysis problems—such as identifying potential problems to be encountered during back analysis, assessing the strategy to be adopted, selecting criteria for back analysis, and ensuring convergence of back analysis results. Based on the engineering applications to approximately 100 tunnel projects in China, it is found that the IBA method supported by the PTA technique can be successfully applied to tunnel projects, i.e. back-analyzing the lateral in situ stress factor (λ), and the elastic modulus (E) of rock masses. The method of IBA supported by PTA and its application to a tunnel project are presented in this paper.     

基坑开挖对下卧运营盾构隧道影响的数值模拟研究

上海外滩修建地下通道——外滩通道,通道南段采用明挖法施工,在延安东路路口与已建的延安东路隧道产生交叉跨越问题。外滩通道基坑坑底与延安东路南、北线隧道拱顶距离仅为7.1m与5.4m,基坑开挖必然使下卧运营隧道产生附加变形以及附加内力。为了研究外滩通道开挖对下卧延安东路隧道的影响,以及评价不同隧道保护措施的效果,通过三维有限元软件PLAXIS-GiD进行四组模拟,包括无隧道保护措施的工况、采取土体加固措施的工况、基坑开挖过程中在坑底进行堆载的工况以及同时进行土体加固和堆载的工况。实际工程中同时采用土体加固和堆载这两种措施来保护隧道,现场监测数据与对应的数值模拟结果具有较好的一致性。分析表明:基坑开挖将对下卧隧道产生很大的影响,且影响范围较大,约为6倍基坑宽度,施工中采取合理的隧道保护措施是十分必要的。     

单层导洞暗挖车站桩基差异沉降对结构内力影响分析

为研究单层导洞暗挖车站桩基差异沉降对结构内力的影响,以北京地铁16号线万泉河桥站工程为背景,通过建立车站平面有限元模型,分析桩基差异沉降加载方式和不同施工工况下桩基差异沉降值对车站结构内力影响.研究表明:两种不同的桩基差异沉降加载方式对结构内力影响差别不大,随着桩基差异沉降值的增加,车站结构内力不断增大.桩基差异沉降对...     

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design. The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design. The posterior distributions are often complex, multidimensional functions whose analysis requires the use of Markov chain Monte Carlo (MCMC) methods. These procedures are used to draw representative samples of the parameters investigated, providing information on their best estimate values, variability and correlations. The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method (FORM). The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety (FS) is calculated with a surrogate model from the more likely values of the input parameters. The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure. In this case, the condition FS = 1 is treated as a data point that is compared with the model prediction of FS. The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters. The parameters are updated according to their uncertainty, which is determined by the amount of data supporting them. The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength. The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.     

黄土基坑复合型土钉支护计算和施工分析

由于黄土具有与其他基坑不同的特性,结合案例分析了黄土基坑复合土钉支护的工作原理和计算方法,提出了合理的有限元模型,并将计算结果与工程实测数据进行了对比分析,以推广土钉支护技术在工程中的应用。     

坑中坑对软土基坑变形影响的有限元分析

以福州某设有坑中坑的软土深基坑工程为研究对象,采用土工有限元分析技术,考虑桩土相互作用,建立基坑开挖模型,土体采用HS模型模拟,分析围护桩水平位移变化特性,研究坑中坑开挖对外坑基坑变形的影响。通过与实际监测资料的对比分析,表明了坑中坑的存在对外坑围护结构的变形有很大影响,数值模拟计算方法在坑中坑工程中有良好适用性,对于类似工程具有指导意义。     

岩土工程数值分析中反分析方法探讨

通过查阅大量关于岩土工程方面的反分析文献资料,简要叙述了岩土工程反分析的概念,主要方法,并且介绍了目前具有代表性的反分析模型及各自的特点和适用性,同时阐述了在岩土工程非确定性反分析研究的发展方向,以期解决复杂岩土问题。     

Numerical modelling of in situ stress calculation using borehole slotter test

Accurate determination of in situ stress magnitude and orientation is an essential element of the design process of all underground openings. A stress calculation method was proposed for the new stress measurement technique using the borehole slotter device. Two major objectives were the focus of this research work. The first goal was to simulate the slotter test process numerically and delve into the mechanisms involved in this test. A precise 3D numerical model of a typical slotter test condition was constructed using the FLAC3D code. The effects of variations in rock mass deformation modulus on the strain/stress relieve, and thus borehole slotter test results, were investigated numerically. The second objective of the work was to employ 3D modelling in the interpretation of slotter field tests conducted at Bakhtiari dam site. These tests were aimed at determining the stress magnitude and orientation to be used in the design of underground chambers and tunnels associated with Bakhtiari dam. The stress regimes measured in field were applied as boundary condition on the constructed 3D model and a backward analysis was conducted. For each case the actual strain field measured was compared against strain field calculated numerically. Accordingly, the boundary condition (stress magnitude and orientation) associated with the model results that provided the best fit to the measured data was determined as the governing stress regime. A good agreement was achieved between numerical and field test results. The obtained numerical results provided valuable insights in selecting the governing in situ stress condition from a set of recorded field data.