Longitudinal Displacement Profile Research Articles

Determination of the Ground Reaction Curve for an Elasto-Plasto-Fractured Rock Mass

Polish National Standards for underground excavation support design outline the deformational pressure model for assessing loads acting on the support systems of deep underground excavations. They distinguish two different rock mass models, highlighting the pivotal role of the critical longitudinal strain of the rock mass in appropriate model selection. A comparison between the design method given by Polish Standards and the widely recognized convergence–confinement method, consisting of a ground reaction curve (GRC), longitudinal displacement profile (LDP), and support characteristics curve (SCC), reveals the advantages of the latter in capturing the three-dimensional nature of underground excavations. The following study presents a method for establishing a GRC curve for the elasto-plasto-fractured rock mass model, featured in Polish Standards, demonstrating its applicability through analyses of a typical circular roadway under varying rock mass conditions. Practical implications are discussed, including the design of yielding steel arches as the primary support system and the calculation of safety factors for both the support system and the surrounding rock mass, considered as a natural support component. Overall, the study contributes to a deeper understanding of the actions of rock masses in the vicinity of excavations located at great depths. Furthermore, it provides practical insights for engineering applications.

Analysis of interaction between tunnel support system and surrounding rock for underwater mined tunnels considering the combined effect of blasting damage and seepage pressure

When an underwater tunnel is constructed using the drill-and-blast method, the rock mass around the tunnel undergoes significant blasting damage. Quantifying the combined effect of blasting damage and seepage pressure on the support–surrounding rock interaction is critical for an underwater mined tunnel. An analytical model is proposed to analyze the entire process of support-surrounding rock interaction in an underwater mined tunnel considering the combined effect of blasting damage and seepage pressure. First, the ground reaction curves are derived considering the combined effect of blasting damage and seepage pressure. Four configurations according to the distribution of plastic zone in the damaged and undamaged zones are distinguished and solved. Subsequently, the fictitious pressure, which is introduced to quantify the spatial effect of tunnel face, is also solved. Thereafter, combining Hoek’s longitudinal displacement profile expression and the proposed ground reaction curve solution, an analytical algorithm for the support–surrounding rock interaction is proposed. The tunnel displacement and support pressure during the entire process of support–surrounding rock interaction are obtained, which are in agreement with the 3D numerical simulations and field monitoring results. Compared with the conventional convergence-confinement method, the performance and advantages of the proposed method are demonstrated. The proposed method is feasible with higher confidence for the preliminary design of underwater mined tunnel, particularly for tunnels excavated in weak zones.

Deformation Prediction of Tunnel-Surrounding Rock Considering the Time Effect of the Viscosity Coefficient: A Case of an NATM-Excavated Tunnel

Considering engineering problems such as complicated stress and the difficulty in controlling large deformation while a tunnel passes through a soft rock stratum, a theoretical prediction model of convergence deformation of tunnel-surrounding rock is proposed. Based on the longitudinal displacement profile curve reflecting the “space effect” of the excavation surface, the Hoek formula with better applicability was introduced to analyze and theoretically deduct the “time–space effect comprehensively.” By taking the influence of the “time effect” coefficient into account, an improved Nishihara model was established to derive the analytical equation of the viscoelastic–viscoplastic convergence of surrounding rock. Taking the Dingxi Tunnel of Wujing Expressway in Hunan Province, the physical and mechanical parameters of surrounding rock in the tunnel were firstly determined then they were used to calculate and predict the vault down of three typical sections with the scoping equation of surrounding rock deformation. Based on the calculation results, the causes of the differences between the measured and theoretical values were analyzed; moreover, it is indicated that the minimum root-mean-square error is 1.68, the minimum average error is 1.3%, and the correlation coefficient is 0.99. The comparison shows that the theoretical prediction results agree well with the corresponding field test results. The improved Nishihara model can accurately predict the final deformation of the surrounding rock. Simultaneously, it is also proved that the relevant parameters and the hypothesis and correlation of the nonlinear viscosity coefficient equation are reasonable, with particular effectiveness and applicability in practical engineering. This study is significant for further studying the tunnel-surrounding rock’s stability and accumulating theoretical and practical experience to develop rheological theory.

Physical model simulation of rock-support interaction for the tunnel in squeezing ground

The existence of squeezing ground conditions can lead to significant challenges in designing an adequate support system for tunnels. Numerous empirical, observational and analytical methods have been suggested over the years to design support systems in squeezing ground conditions, but all of them have some limitations. In this study, a novel experimental setup having physical model for simulating the tunnel boring machine (TBM) excavation and support installation process in squeezing clay-rich rocks is developed. The observations are made to understand better the interaction between the support and the squeezing ground. The physical model included a large true-triaxial cell, a miniature TBM, laboratory-prepared synthetic test specimen with properties similar to natural mudstone, and an instrumented cylindrical aluminum support system. Experiments were conducted at realistic in situ stress levels to study the time-dependent three-dimensional tunnel support convergence. The tunnel was excavated using the miniature TBM in the cubical rock specimen loaded in the true-triaxial cell, after which the support was installed. The confining stress was then increased in stages to values greater than the rock's unconfined compressive strength. A model for the time-dependent longitudinal displacement profile (LDP) for the supported tunnel was proposed using the tunnel convergence measurements at different times and stress levels. The LDP formulation was then compared with the unsupported model to calculate the squeezing amount carried by the support. The increase in thrust in the support was back-calculated from an analytical solution with the assumption of linear elastic support. Based on the test results and case studies, a recommendation to optimize the support requirement for tunnels in squeezing ground is proposed.

Displacement process analysis of deep tunnels with grouted rockbolts considering bolt installation time and bolt length

This study investigates the interaction process between grouted bolts and tunnel surrounding rock, and establishes an analytical model for deep tunnels reinforced with active grouted rockbolts of the convergence-confinement type. The rock mass is assumed to be elastic-perfectly plastic, obeying the Hoek–Brown criterion. The longitudinal displacement profile is introduced to represent the space effect of the tunnel face, based on which the fictitious pressure along the tunnel axis is determined. Because of delayed installation and limited length of the rockbolts, a rock mass may behave elastically or plastically at bolt installation with the rockbolts anchored in different zones. Six different evolution paths possibly encountered on the basis of the relative magnitude between the anchorage and plastic zones are proposed. The tunnel displacement, plastic radii, and stresses are determined. The analytical results are validated by comparing with those obtained from numerical simulations and an existing model. A parametric analysis shows that doubling bolt length from 2 to 4 m in a 14-m-diameter tunnel reduces the tunnel wall displacement up to 20%. Installing rockbolts close to the tunnel face (less than 1 m) can reduce tunnel wall displacement up to 51%. Doubling the pretension load can reduce tunnel wall displacement up to about 20%. Increasing the support density can reduce the tunnel wall displacement by up to about 50%. The analysis shows that the proposed model outperforms Fahimifar’s model, which deals with infinite rockbolts, in solving tunnel responses under grouted rockbolts, particularly in the case of large cross-sectional tunnels excavated in poor geological conditions.

Time-Dependent Behavior of the Tunnels in Squeezing Ground: An Experimental Study

The presence of squeezing ground conditions often poses significant challenges in predicting tunnel response over time and to the design of an adequate support system to stabilize the tunnel. Many analytical, empirical, observational, and numerical models have been proposed over the years for the design of tunnels in squeezing ground conditions, but they all have some limitations. The study presented in this paper focused on improving the understanding of tunnel squeezing via a unique physical model test that simulated tunnel boring machine (TBM) excavation in squeezing clay-rich rocks. The physical model included a large true-triaxial cell, a miniature TBM, a laboratory-prepared synthetic test specimen having properties similar to natural mudstone, and instrumentations to monitor deformations around the tunnel boundary during and after the excavation. Experiments were conducted at realistic in-situ stress levels to study time-dependent tunnel convergence in three-dimensions. A tunnel was excavated using the miniature TBM in a cubical rock specimen loaded in the true-triaxial cell; then the confining stress was increased in stages to values above the rock unconfined compressive strength. Strain gauges embedded in the rock specimen and a digital borehole caliper monitored tunnel wall deformations with time. The degree of tunnel squeezing was characterized using a classification system based on tunnel radial strain. A model for time-dependent tunnel longitudinal displacement profile (LDP) was proposed using measurements of the tunnel convergence at different times and different stress levels.

A procedure for interaction between rock mass and liner for deep circular tunnel based on new solution of longitudinal displacement profile

A new solution for the longitudinal displacement profile (LDP) is proposed based on three-dimensional finite-difference method. The improved convergence-confinement method (CCM) is divided into two stages. In the first stage, the fictitious support pressure can be derived, representing the support pressure acting on the periphery of the tunnel by the rock mass itself. In the second stage, the fictitious support pressure transforms to the pressure on liner, and this progress reflects the interaction between rock mass and liner. According to two-stage analysis, a computing procedure is proposed for calculating pressure and deformation of rock and liner. By comparing with the results of other approaches, the procedure is proved to be correct. The influences of elasticity modulus, thickness of liner, and supporting time are discussed individually. The results indicate that the final pressure on liner can be reduced by reducing stiffness of liner and postponing supporting time. To prevent the liner from yielding, the prior measure is to postpone supporting time, and meanwhile, the liner with lower elasticity modulus and smaller thickness can be selected. In final, a practical example is performed by utilising this procedure, confirming it can provide reference to tunnel engineering design.

A 3D Discrete-Continuum Coupling Approach for Investigating the Deformation and Failure Mechanism of Tunnels across an Active Fault: A Case Study of Xianglushan Tunnel

For water transmission tunnels constructed in high-risk seismic regions of western China, active faults pose threats of serious ruptures to the tunnels. To overcome this issue, a 3D discrete-continuum coupling approach is introduced into the study. By this approach, spherical discrete-element-method (DEM) particles are used to represent the surrounding rock mass, and the tunnel is considered to be the continuous finite-difference-method (FDM) zone. In this way, a 3D coupling model was established to study the longitudinal displacement profile and stress response of the tunnel lining under various fault dislocations. The failure pattern of the surrounding rock mass was investigated from a micro perspective. Meanwhile, the design strategy of flexible joint was investigated with the present numerical model. The results from a parametric study show that the smaller segment length, wider width and weaker strength of the flexible joints are beneficial to the anti-dislocation performance of the tunnel. Moreover, an orthogonal array test technique was utilized to investigate the influence level of the main design parameters of the flexible joint on the lining internal stress. With the obtained knowledge, the optimal combination for flexible joint design was presented. Findings may provide references for the anti-dislocation issue of tunnels across active faults.

Improved Longitudinal Displacement Profile and Initial Support for Tunnel Excavation

The ground support system has a significant impact on tunnel safety while the installation time of initial support is commonly designed by empirical method. The three dimensional numerical model, based on the engineering practice, is analyzed by FLAC3D. In this paper, an improved LDP (longitudinal displacement profile) equation is proposed, which is more accurate in describing the convergence of tunnel before excavation face reaching. Then, a methodology is presented to determine the installation location of initial support in a more efficient and effective way. By simulating the process of excavation load releasing, the appropriate time for installing initial support is when the evolution of surrounding rock displacement has a tendency to increase rapidly, namely that the stability of rock mass arrives at the critical state. The mathematical relationship between the convergence of tunnel and the relative location to tunnel face can be established by fitting monitoring data with the improved LDP equation. Substituting the critical tunnel convergence into the LDP relationship, the corresponding installation location of initial support will be calculated. Meanwhile, several schemes with diverse geological conditions are carried out to validate the improved LDP and the methodology.

Favorable driving direction of double shield TBM in deep mixed rock strata: numerical investigations to reduce shield entrapment

In deep mixed rock strata, a double shield TBM (DS-TBM) is easy to be entrapped by a large force during tunneling. In order to reduce the probability of the entrapment, we need to investigate a favorable driving direction, either driving with or against dip, which mainly associates with the angle between the tunneling axis and strike, theta, as well as the dip angle of rock strata, a. We, therefore, establish a 3DEC model to show the changes of displacements and contact forces in mixed rock strata through LDP (longitudinal displacement profile) and LFP (longitudinal contact force profile) curves at four characteristic points on the surrounding rock. This is followed by a series of numerical models to investigate the favorable driving direction. The computational results indicate driving with dip is the favorable tunneling direction to reduce the probability of DS-TBM entrapment, irrespective of theta and a, which is not in full agreement with the guidelines proposed in RMR. From the favorable driving direction (i.e., driving with dip), the smallest contact force is found when theta is equal to 90o.The present study is therefore beneficial for route selection and construction design in TBM tunneling.

Validation of longitudinal displacement profiles by measurement at the Brenner Base Tunnel

AbstractLongitudinal displacement profiles describe the displacement history during tunnel excavation, including that occurring ahead of the tunnel face. These deformations have an influence on the structural design of tunnel support. Theoretical approaches are used to estimate these deformations. However, as the approaches are based on assumptions, they should be applied with caution, particularly in case of deep tunnels. Therefore, experimentally determined longitudinal displacement profiles provide a valuable data basis for validation of the approaches. This study compares 40 m long horizontal chain inclinometer measurements in two lithologies in the exploration tunnel of the Brenner Base Tunnel with theoretically calculated profiles. The chain inclinometers were installed above the tunnel before the start of tunnelling. A measured radial displacement profile was created for each round, the statistical mean value curve was calculated and finally compared with the theoretical approaches. The measurement results show good qualitative agreement ahead of the tunnel face.

Effect of transient coupled hydro-mechanical response on the longitudinal displacement profile of deep tunnels in saturated ground

An advancing tunnel in deep saturated ground induces coupled interactions between transient fluid flow and deformation that affect the hydro-mechanical (H-M) response of the ground surrounding the excavation. The use of the convergence-confinement method (CCM) to simplify this three-dimensional (3-D) coupled problem into a 2-D plane strain model must then account for this transient coupling effect. Similarly, the induced radial displacement of the tunnel, commonly represented as the longitudinal displacement profile (LDP), will also be influenced by this time-dependent coupled interaction. This study investigates the effect of the transient H-M interaction on the practical implementation of the CCM and the LDP of an advancing tunnel in deep saturated ground. The tunnel is represented by a 2-D axisymmetric coupled H-M model that is built into the computer program Fast Lagrangian Analysis of Continua (FLAC) and is subjected to an isotropic in situ stress field. First, the study analyzes the induced pore pressure and deformation behavior during the excavation and standstill periods. Second, to account for the transient coupling effect, this study proposes: (1) nonlinear unloading factors for estimating excavation-induced pore pressure changes in CCM and (2) new LDP equations for predicting transient radial displacements along the axis of the tunnel. The resulting relationships from the two propositions are normalized, and thus, they should be applicable to other tunnel depths as well.

Improvement to the Convergence-Confinement Method: Inclusion of Support Installation Proximity and Stiffness

The convergence-confinement method (CCM) is a method that has been introduced in tunnel construction that considers the ground response to the advancing tunnel face and the interaction with installed support. One limitation of the CCM is due to the numerically or empirically driven nature of the longitudinal displacement profile and the incomplete consideration of the longitudinal arching effect that occurs during tunnelling operations as part of the face effect. In this paper, the authors address the issue associated with when the CCM is used within squeezing ground conditions at depth. Based on numerical analysis, the authors have proposed a methodology and solution to improving the CCM in order to allow for more accurate results for squeezing ground conditions for three different excavation cases involving various excavation-support increments and distances from the face to the supported front. The tunnelling methods of consideration include: tunnel boring machine, mechanical (conventional), and drill and blast.

Analysis of time-dependent deformation in tunnels using the Convergence-Confinement Method

During the excavation of a tunnel the accumulated wall displacement and the loading of tunnel support is the result of both the tunnel advance (round length and cycle time) and the time-dependent behaviour of the surrounding rock mass. The current approach to analyze the tunnel wall displacement increase is based on the Convergence-Confinement Method (CCM) performed with either analytical (closed form solutions) or the usage of the Longitudinal Displacement Profiles. This approach neglects the influence of time-dependency resulting in delayed deformation that may manifest even minutes or hours after excavation. Failure to consider the added displacements in the preliminary design can result in false selecting the time of installation and the type of support system causing safety issues to the working personnel, leading to cost overruns and project delivery delays. This study focuses on investigating and analyzing the total displacements around a circular tunnel in a visco-elastic medium by performing an isotropic axisymmetric finite difference modelling, proposing a new yet simplified approach that practitioners can use taking into account the effect of time.

Back Analysis of Rock Mass Displacements Around a Deep Shaft Using Two- and Three-Dimensional Continuum Modeling

An instrumented section of a 10-m-diameter circular shaft located at a depth of 1.2 km in an average quality rock mass was back analyzed to establish the rock mass behavior. Extensometers were installed radially at four locations and provided the primary data for the back analyses. Three- and two-dimensional continuum models were analyzed using the numerical codes FLAC3Dand Phase2 to assess the rock mass behavior. An initial set of mechanical parameters obtained from empirical relationships were found to give a reasonable match to the measured response of extensometers 2 and 4, when using a Mohr–Coulomb strain softening model. A different set of parameters were needed for FLAC3D when trying to match the significantly higher displacements recorded by only one of the extensometer. It was noted that regardless of the material model and corresponding parameters, the three-dimensional models were not able to give reasonable match to the results of all extensometers. It was shown that for the given problem, there is a theoretical limit for ratio of displacements predicted for different extensometers using a continuum isotropic material model. The two-dimensional models in Phase2, however, gave an apparently better overall match to all the extensometers. Comparison of the results of three-dimensional models with the assumed longitudinal displacement profile for the two-dimensional model indicated that the three-dimensional effects were not adequately captured in the two-dimensional model.

Computational modelling of the mechanised excavation of deep tunnels in weak rock

Tunnel Boring Machine (TBM) tunnelling in weak rock associated with high overburden is very demanding due to the difficulties in predicting the complex interactions between the rock mass, the tunnel machine, its system components, and the tunnel support during excavation/construction. These factors affect the performance and even the feasibility of a TBM drive (sticking of the cutterhead and jamming of the shield may occur). In this respect, several computational models such as the Convergence–Confinement Method (CCM), axially symmetric model and three-dimensional (3D) simulation have been developed in the literature. Among these models, this paper presents three modelling techniques (i.e., a 3D simulator using the Finite Element Method (FEM), an axisymmetric model using the Finite Difference Method (FDM) and an LDP (Longitudinal Displacement Profile) approach based on the CCM), and applies them to the Headrace Tunnel from the Kishanganga Hydroelectric Project in India. The three approaches are not considered to be alternatives but rather complementary to each other, depending on the real situation. The LDP approach is a simplified analytical method but is still efficient to provide a conceptual framework for evaluating the ground-shield interplay during mechanised excavation. The FDM axisymmetric model represents a powerful tool (i.e., with a large deformation scheme available) for the simulation of ground behaviour and its interaction with the machine components, especially in the case of weak rocks with high deformability. However, when the conditions violate the important assumptions underlying these two approaches, true 3D numerical analyses are necessary, which consider all the TBM components. Finally, the paper highlights the potentials of the 3D simulator to model the basic features (i.e., stepwise conicity of the shield, backfilling layer and anisotropic in-situ stress state) of a shield-driven deep tunnel, which determine the tunnel’s behaviour and its response to TBM advancement. The obtained results show that the 3D nature of the complex interactions and the in-situ state of stress, including the nonlinear behaviour can be better reproduced in a 3D simulation than in the other two methods.

Designing Tunnel Support in Jointed Rock Masses Via the DEM

A systematic approach of using the distinct element method (DEM) to provide useful insights for tunnel support in moderately jointed rock masses is illustrated. This is preceded by a systematic study of common failure patterns for unsupported openings in a rock mass intersected by three independent sets of joints. The results of our simulations show that a qualitative description of the failure patterns using specific descriptors is unattainable. Then, it is shown that DEM analyses can be employed in the preliminary design phase of tunnel supports to determine the main parameters of a support consisting of rock bolts or one lining or a combination of both. A comprehensive parametric analysis investigating the effect of bolt bonded length, bolt spacing, bolt length, bolt pretension, bolt stiffness and lining thickness on the tunnel convergence is illustrated. The highlight of the proposed approach of preliminary support design is the use of a rock bolt and lining interaction diagram to evaluate the relative effectiveness of rock bolts and lining thickness in the design of the tunnel support. The concept of interaction diagram can be used to assist the engineer in making preliminary design decisions given a target maximum allowable convergence. In addition, DEM simulations were validated against available elastic solutions. To the authors’ knowledge, this is the first verification of DEM calculations for supported openings against elastic solutions. The methodologies presented in this article are illustrated through 2-D plane strain analyses for the preliminary design stage. More rigorous analyses incorporating 3-D effects have not been attempted in this article because the longitudinal displacement profile is highly sensitive to the joint orientations with respect to the tunnel axis, and cannot be established accurately in 2-D. The methodologies and concepts discussed in this article, however, have the potential to be extended to 3-D analyses.

Advance numerical simulation of tunneling by using a double shield TBM

Double shield TBMs are amongst the most technically sophisticated excavation machines in use by tunneling industry. However, using the shielded machine limits access to the walls for observation of ground conditions and presence of shield makes the machine susceptible to entrapment or seizure in weak rocks under high stresses which results in high convergence. To realistically evaluate the possibility of machine seizure in such grounds, the interaction between the rock mass and shields, lining and backfilling need to be understood. This study explains the application of numerical analysis for 3D simulation of mechanized tunneling by using a double shield TBM. For this purpose, a comprehensive numerical simulation is developed to systematically evaluate the potential of excessive ground convergence. Simulation results at five reference points on the tunnel circumference along the tunnel have been examined. The results are including longitudinal displacement profile (LDP) as well as contact force profiles (LFP) on both front and rear shields, frictional forces and required thrust to move the machine, stress history of ground, and estimated loading of the segments. The results also proved that numerical analyses can successfully be used for prediction of loads on the shield during excavation to assess risks of machine entrapment.

Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.

3D finite difference model for simulation of double shield TBM tunneling in squeezing grounds

One of the main concerns in using a shielded machine in deep rock tunnels is the possibility of the shield seizure in squeezing ground. To realistically evaluate the possibility of machine seizure in such grounds, the interaction between the rock mass and shield, lining and backfilling need to be understood. This paper will explain the background theories and the application of numerical analysis for 3D modeling of mechanized tunneling by using a double shield TBM in squeezing ground. The discussions will include the effects of advance rate during excavation cycle of a shielded TBM to observe the impact of tunneling rate on the possibility of machine jamming in the squeezing grounds. Simulation results at five reference points on the tunnel circumference along the tunnel or longitudinal displacement profile (LDP) as well as longitudinal contact force profiles (LFP) on both front and rear shields have been examined. Also, maximum thrust force required to overcome friction and drive TBM forward is calculated. This exercise allows for evaluation of the effects of various parameters on convergence and contact forces between the rock and shield, which in turn determines the required propel forces and can define the possibility of machine entrapment.