Rectangular Tunnel Research Articles

Experimental simulation study of spalling in deep rectangular tunnel with plastic fine grain marble

Following the excavation of the rectangular tunnel faces with deep harder rock, spalling often occurs on both sidewalls of the tunnel, which affects the tunnel support and stability. To investigate the spalling phenomenon of the harder rock under the deep initial three-dimensional (3D) stress conditions, true triaxial loading tests of different depths (250, 500, 750, and 1000 m) and different stress combinations (four different horizontal stresses at the same depth 1000 m) were designed on plastic fine grain marble. The overall failure process of the surrounding rock was monitored and recorded by a wireless micro-camera. The results show that, under the shallow stress condition (250 and 500 m), the V-shaped bands will appear on the both sidewall due to the overall shear failure of the specimen. Under the deep stress condition (750 and 1000 m), the obvious spalling was observed on the hole sidewalls of all marble specimens. Moreover, at the time of hole sidewall spalling, the vertical stress is the maximum principal stress. The spalling process of the hole sidewall can be divided into four stages: the microcrack initiation, the appearance of thin rock slabs, the formation of arc-shaped notches, and the expansion to V-shaped notches. If the excavation depth remains the same (1000 m) when the maximum principal stress is perpendicular to the tunnel axis, excavation along the minimum principal stress direction is beneficial to reducing the spalling damage degree. Compared to the brittle granite specimens with rectangular holes under the same 3D stress conditions, the influence of brittleness and plasticity of rock materials on spalling failure was analysed. (1) Spalling failure mode of hole sidewalls: the plastic-marble is static failure without fine particle ejection, while the brittle granite will break dynamically with fine particle ejection. (2) Spalling failure process and zones of sidewall: the cracks on the plastic marble sidewalls develop parallel to the axial direction, and run through the whole hole sidewall along the axis, while the cracks on the brittle granite hole sidewalls propagate perpendicular to the axial direction, and the sidewalls first break locally and then break through the whole hole. Failure zones on both sidewalls of the two kinds of rock specimens will transit from arc-shaped notch to V-shape notch. Those failure notches are symmetrical and finally penetrate the sidewalls. (3) Microscopic failure mode: scanning electron microscope (SEM) shows that the plastic and brittle rock materials are tensile failure during the spalling under 3D stress conditions. The plastic marble is characterized by fracture tension failure, while the brittle granite is characterized by layered tension failure. Some suggestions are given finally, under the condition that the vertical stress is the maximum principal stress, when the tunnel is excavated along the horizontal direction, the resistant ability of the tunnel sidewall in the plastic and brittle surrounding rock should be strengthened by supporting the sidewall, which can effectively reduce the degree of spalling damage.

Simulation test of spalling failure of surrounding rock in rectangular tunnels with different height-to-width ratios

Spalling (Slabbing) is a typical failure phenomenon, which often occurs after excavation of rectangular tunnel. It has a serious impact on the construction, support and stability of the tunnel. To investigate the characteristics and mechanism of spalling-failure in rectangular tunnel, a series of tests were carried out on granite rectangular tunnel with different height-to-width ratios (H/Ws) (1/2, 3/4, 1/1, 4/3 and 2/1) by using true triaxial system. The whole process of spalling was monitored and recorded by wireless micro camera. According to the test results, the failure mode and failure characteristics of the sidewall spalling were summarized, and the influence of the H/Ws of the rectangular hole on the failure characteristics and stability of the tunnel were discussed in detail. The test results indicate that when the vertical principal stress is the maximum principal stress, the sidewalls of the specimens experience spalling failure. When the spalling occurs, the crack occurs at the shoulder corner of the sidewall and propagates along the axis, resulting in the spalling damage gradually developing from the local area to the whole sidewall along the axis, and forming the thin rock slab parallel to the sidewall. In addition, rectangular tunnels with different H/Ws clearly influence spalling failure. When the height was the same, the degree of spalling damage decreases with the decrease of its width. On the contrary, when the width was the same, the degree of spalling damage does not decrease with the increase in the height. When the height was equal to the width, the damage degree of the tunnel spalling is the largest, which seriously affects the safety of the tunnel. In the case of the same cross-section area of the tunnel, the stability of the tunnel can be improved by selecting the layout mode with the height greater than the width. It is necessary to strengthen the monitoring of the cracks at the shoulder corner of the tunnel, which can reduce the safety risk of the tunnel. These conclusions are helpful to the design of the tunnel, the prevention of spalling and the improvement of the stability of the tunnel.

Simulation and experimental study on the airflow distribution in rectangular cross-section tunnels

Ventilation is quite important for mine safety. The airflow behavior and the influence of the ventilation parameters on the airflow distribution in rectangular tunnels were investigated by experimental and simulation methods. Then the relationship between the distribution feature of the average velocity and the parameters of tunnel cross-section was analyzed quantitatively by mathematical method. The results showed that the average velocity points show a continuous circular distribution and the simulation results were in accordance with the experimental results. The shape of cross-section is the critical factor influencing airflow behaviour, and the ventilation velocity had little influence on the distribution of the average velocity points. In the region where the velocity was larger than the average velocity, the velocity gradient was small, and as the distance to the wall increased, the velocity increased slowly. While in the region where the velocity was smaller than the average velocity, the velocity gradient was large, and the velocity changed more quickly. Based on the simulation and experimental data, a group of the characteristic equations were developed and the location of the average velocity can be obtained conveniently while the dimension of the tunnel was known.

Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking

Combining multiple tunnels into a single tunnel complex while keeping the surrounding area compact is a complicated procedure. The condition becomes more complex when soft soil is present and the area is prone to seismic activity. Seismic vibrations produce sudden ground shaking, which causes a sharp decrease in the shear strength and bearing capacity of the soil. This results in larger ground displacements and deformation of structures located at the surface and within the soil mass. The deformations are more pronounced at shallower depths and near the ground surface. Tunnels located in that area are also affected and can undergo excessive distortions and uplift. The condition becomes worse if the tunnel area is larger, and, thus, the respective tunnel complex needs to be properly evaluated. In this research, a novel triple tunnel complex formed by combining three closely spaced tunnels is numerically analyzed using Plaxis 2D software under variable dynamic loadings. The effect of variations in lining thickness, the inner supporting structure, embedment depth on the produced ground displacements, tunnel deformations, resisting bending moments, and the developed thrusts are studied in detail. The triple tunnel complex is also compared with the rectangular and equivalent horizontal twin tunnel complexes in terms of generated thrusts and resisted seismic-induced bending moments. From the results, it is concluded that increased thickness of the lining, inner structure, and greater embedment depth results in decreased ground displacements, tunnel deformations, and increased resistance to seismic-induced bending moments. The comparison of shapes revealed that the triple tunnel complex has better resistance against moments with the least amount of thrust and surface heave produced.

Assessment of the Stability of an Unlined Rectangular Tunnel with an Overload on the Ground Surface

City tunnels are often constructed at shallow depths, and tunnel failure may be initiated by overloads resulting from surrounding buildings, structures, heavy‐haul trailers, and other installations. Although several works have been reported on tunnel stability, stability numbers have mainly been obtained for cases with fully cohesive soils. Moreover, little information has been presented about the influence of overloads on the failure patterns for unlined rectangular tunnels. This paper uses upper‐bound finite element methods to assess the stability of an unlined rectangular tunnel in cohesive‐frictional soils with an overload acting on the ground surface. A complete set of dimensionless parameters covering the tunnel size and shallow tunnel depth and Mohr‐Coulomb material parameters are determined to obtain the dimensionless overload. In addition, failure modes that are similar to slip line fields are acquired. A failure mechanism that may cause base heave is proposed in this paper to improve the accuracy of the results. These failure patterns are more complex for cases with larger dimensionless depth, larger internal friction angle, and smaller dimensionless unit weight. Compared with the rigid‐block mechanisms from the upper‐bound rigid‐block analysis method, these computed failure mechanisms are better suited for rectangular tunnel stability analysis.

Research on Fire Smoke Controlling Effect of Submarine Road Tunnel Based on FDS

Taking submarine road tunnel as the research objective, numerical calculation model of fire smoke controlling in rectangular underwater tunnel was established by FDS. The adaptability of lateral concentrated exhaust mode in tunnels of variable widths is obtained according to analysis of smoke distribution and smoke exhausting efficiency under different working conditions. The results are as follows: The increase of width results in the decrease of smoke exhausting efficiency. In the four-lane dual-directional tunnel, the smoke exhausting efficiency is 83.4%; while that of twelve-lane dual-directional tunnel is only 55.2%. The wind velocity is higher in the area near the lateral exhaust valves; and which is lower in the area far from the exhaust valves. The influence of wind velocity for lateral exhaust valves is limited. With the increase of width, the wind velocity of cross-section decreases dramatically. In a four-lane dual-directional tunnel, the wind velocity of the right wall decreases by 32%, and that in twelve-lane dual-directional tunnel decreases by 59.6%. For large-span rectangular tunnels of eight-lane dual-directional or even wider ones, the lateral centralized exhaust mode shows poor fire smoke controlling effect.

Study on the critical velocity for smoke control in a subway tunnel cross-passage

The critical velocity of subway tunnel cross-passage was investigated since the smoke control mode is different from that of road tunnel and larger blockage effect of train need to be given priority. In order to ensure an effective smoke control and safe evacuation, numerical simulation and experimental study were conducted to investigate the critical velocity of subway cross-passage. On the basis of exiting critical Froude model, the influence of tunnel shape, fire location and train blocking on critical condition were analyzed. The results indicate that the blockage of train has a great influence on the critical velocity. With the shorter distance between train and cross-passage, the ventilation velocity through cross-passage dramatically increases. In addition, critical velocity with rectangular tunnel is obvious larger than that with shield tunnel. As the fire source location is closer to the cross-passage, the critical velocity would be greater and the corresponding Froude number would become smaller.

Numerical Study of Fire Smoke Exhausting in an Eight-lane Dual-Directional Rectangular Tunnel

In order to obtain the smoke exhausting characteristics of large-span cross section rectangular tunnel under lateral exhaust model, fire numerical simulation calculation was conducted by FDS to analyse the influence of different factors on smoke exhausting efficiency, including the layout, area, and spacing of smoke exhausting valves in immersed tunnels, and the applicability of the different tunnel width under the model of lateral exhaust was studied. The results are as follows: The smoke exhausting efficiency of individual exhausting valve decreases with more exhausting valves opened, but the total smoke exhausting efficiency of immersed tunnel increases. When three smoke exhausting valves are arranged in a group, the increase of distance between groups is conducive to smoke exhausting. The Smoke exhausting efficiency of evenly arranged valves is higher than the ones where three valves are in a group. When the number of exhausting valves opened remains the same, the increase of opening area can increase the total smoke exhausting efficiency because the ventilation resistance reduces. In lateral exhaust model, the increase of the width of immersed tunnel can result in the sharp decrease of smoke exhausting efficiency. In a two-lane, uni-directional immersed tunnel, the smoke exhausting efficiency is 93.7%, and that of a four-lane one is only 45.94%. For the poor applicability of lateral exhaust model in the large-span cross section immersed tunnel fire, it is suggested that additional smoke exhausting measures should be adopted to increase the efficiency of smoke exhausting.

Arching Effect between the Pipes of a Pipe Umbrella Support System in a Shallow-Buried Tunnel

The pipe umbrella is one of the most commonly used prereinforcement techniques in tunnel construction. Current theoretical analyses of the pipe umbrella support mechanism are primarily based on the elastic foundation beam principle, whereby only a single pipe is concerned, and the interactions among pipes are ignored. In this study, a double-parameter elastic foundation beam theory-based model was established with consideration of the arching effect between two pipes. The model can simulate the support mechanism of the pipe umbrella system in shallow-buried tunnels. The support mechanisms of a pipe umbrella system installed in a rectangular tunnel and an arched tunnel were investigated. In the two cases, the arching effect and a single pipe were considered. The results indicate that the arching effect leads to larger pipe deflection and internal forces than considering a single pipe. The influences of the diameter of a single pipe, the distance between two pipes and the shear parameters of the surrounding rock on the pipe deflection and the arching effect are discussed. In addition, the proposed model was validated by the in situ monitoring results.

Chronological Changes in Anterior Knee Stability after Anatomical Anterior Cruciate Ligament Reconstruction Using Bone-Patellar Tendon-Bone and Hamstring Grafts.

The clinical outcomes of anterior cruciate ligament (ACL) reconstruction are typically evaluated at specific time points only. This study aimed to characterize the chronological changes in anterior knee stability after anatomical ACL reconstruction and to compare the anterior knee stability achieved with bone-patellar tendon-bone (BPTB) and hamstring tendon (HT) grafts. A total of 59 patients underwent anatomical rectangular tunnel ACL reconstruction using the BPTB graft and 23 patients underwent anatomical double-bundle ACL reconstruction using the HT graft. Anterior knee stability was quantitatively assessed using the KneeLax 3 arthrometer at 6 months, 1 year, and 2 years after surgery using side-to-side differences. The values for anterior knee stability using the BPTB graft were 0.3 mm after 6 months, 0.2 mm after 1 year, and 0.2 mm after 2 years, and no significant differences were observed during the postoperative study period. Meanwhile, the values for anterior knee stability using the HT graft were -0.3 mm after 6 months, 0.5 mm after 1 year, and 1.2 mm after 2 years, and anterior knee stability decreased chronologically from 6 months up to 2 years. Regarding anterior stability, the HT graft showed significant laxity compared with the BPTB graft only after 2 years. No chronological changes in anterior stability were observed from 6 months up to 2 years after ACL reconstruction using the BPTB graft, whereas anterior laxity developed during the same period after ACL reconstruction using the HT graft. This is a Level IV, therapeutic case series study.

Development of small propeller test bench system

A set of performance analysis was performed on Master Airscrew 10X7 Electric propeller. The airfoil geometry was extracted by cutting and scanning a number of blade cross-sections. Experimentally, the test was performed at Institut Teknologi Bandung using 40 cm x 40 cm rectangular test section wind tunnel. The experimental rig was built using 3 load cells designed to measure thrust and torque. For data comparison, theoretical and numerical analysis were also done using Momentum-Blade Element method and Computational Fluid Dynamics. Compared with the previous study, the experimental data shows good agreement with most of the reference data. The theoretical data overestimated the thrust value by around 20% and underestimated the torque value by 30% at max, but the performance curve follows the similar trend with the experimental data. Both the thrust and torque value of the numerical data shows better agreement when fitted to experimental data by around 10%. While it may need more propeller samples analyzed to draw general conclusion, the three methods performed in this research showed analogous results and could be used for a particular stage of research depending on the level of accuracy needed.

Experimental simulation and investigation of spalling failure of rectangular tunnel under different three-dimensional stress states

Spalling (or slabbing) in the sidewalls of deep rectangular tunnels is a type of rock failure phenomenon under the three-dimensional stress environment, which often occurs on the surrounding rocks after the tunnel face excavation is completed and has a significant impact on the safety of construction and support. In order to investigate the spalling process in deep rectangular excavated tunnels under three-dimensional stress, a granite material was firstly processed into cubic specimens (100 mm × 100 mm × 100 mm) with prefabricated rectangular holes (40 mm × 40 mm). Simulation experiments were performed using a rock true-triaxial electro-hydraulic servo mutagenesis testing system under four different initial stress states. Meanwhile, a wireless micro-camera was used to record and monitor the damage process on the sidewalls of the rectangular tunnel in real time. The results showed that under the four stress conditions, an evident spalling failure occurred on the entire sidewalls of the rectangular hole. It was observed that the spalling-damaged zone gradually developed toward the deep part of the hole in a horizontal direction. Finally, it formed a penetrating symmetric arc-shaped groove along the axial direction, whereas the roof and bottom slab remained stable. The spalling failure process of the sidewalls had four stages: the calm period, particle ejection at the upper and lower shoulders, sidewall crack propagation, and crack penetration spalling failure. Compared with the dynamic failure (rockburst) of a circular tunnel under the same three-dimensional high stress conditions, the spalling failure of the rectangular tunnel sidewalls was of the static failure mode. Under the three-dimensional stress condition, the radial stress had a greater effect on the spalling failure than the axial stress, by increasing the radial stress can be significantly reduced the degree of spalling failure and effectively improved the stability of the surroundings.

Upper bound limit analysis of unsymmetrical progressive collapse of shallow tunnels in inclined rock stratum

In order to provide more reasonable support design for shallow tunnels in inclined stratum, it is necessary to investigate the collapse of shallow tunnels in inclined stratum. A new collapse mechanism of shallow rectangular and circular tunnels in inclined rock stratum is constructed, which includes four curves. On the basis of the upper bound theorem of limit analysis and the nonlinear Hoek-Brown yield criterion, obtaining the precise expressions of four curves by means of the variational principle, and deriving the equations of the range and total gravity of the potential collapsing block of rectangular and circular tunnels can be solved respectively. The results are consistent with those published and numerical simulation, which confirms the rationality of this research. The parametric sensitivity analysis of the collapse of rectangular and circular tunnels is carried out, which shows that rock mechanics parameters and geometric parameters have a significant impact on the range and total gravity of the potential collapsing block is obvious. Especially, the dip angle of rock stratum plays a key role in the symmetry of tunnel collapse and the progressive collapsing block is unsymmetrical unless the rock strata are horizontal.

Analytical analysis of stress and displacement for surrounding rock of deep-buried rectangular tunnel in layered strata

This study presents a theoretical solution on stress and displacement of the deep-buried tunnel surrounding rock in layered strata. Based on theory of Покровский equivalent layer method, we convert layered strata into homogeneous ones and then map the rectangular tunnel in the coordinate plane z to the unit circle of complex plane ζ, through using a complex variable method and calculating the analytic functions Φ(ζ) and Ψ(ζ) with Matlab, the study obtains that the stress of the surrounding rock of deep-buried rectangular tunnel in layered strata. Subsequently, we derive the strain and displacement of the surrounding rock. Finally, we study the effects of lateral pressure coefficient and grade of surrounding rock and height-to-width ratio of the tunnel on the stress of tunnel surrounding rock. Based on our analysis, we formulate valuable rules.

Minimal tibial tunnel enlargement after anatomic rectangular tunnel anterior cruciate ligament reconstruction with bone-patellar tendon-bone graft

BackgroundThe purpose of this study was to evaluate the tibial tunnel enlargement after the anatomical rectangular tunnel (ART) anterior cruciate ligament reconstruction (ACLR) with a bone-patellar tendon-bone (BTB) graft and to elucidate the correlation between the enlargement and length of the tendinous portion inside the tibial tunnel. In addition, we aimed to analyze the correlation between patient characteristics and tibial tunnel enlargement. MethodsThis study included 50 patients who underwent ART ACLR. Lateral radiographs at the time of surgery and at 2 years were compared to evaluate the tibial tunnel enlargement. Subsequently, correlations between the tunnel enlargement and (1) length of tendinous portion inside the tibial tunnel or (2) characteristics of the patients, including anterior knee laxity measured by KT-1000 arthrometer, age, sex, height, body weight, and Tegner activity level scale, were analyzed. ResultsThe tibial tunnel was enlarged by 2.6 ± 4.2% 2 years postoperatively. The length of the tendinous portion inside the tibial tunnel was 7.8 ± 4.9 mm. There was no significant correlation between tunnel enlargement and length of tendinous portion inside the tunnel. None of the patient characteristics were detected as a risk factor for tibial tunnel enlargement. Conclusions(1) The postoperative tibial tunnel enlargement was minimum after ART ACLR with a BTB graft. (2) There was no correlation between tibial tunnel enlargement and length of tendinous portion of BTB graft inside the tunnel. (3) None of the patient characteristics were detected as a risk factor of the tibial tunnel enlargement.

Limit Analysis of Progressive Asymmetrical Collapse Failure of Tunnels in Inclined Rock Stratum

Tunnels commonly pass through inclined rock stratum, but research on the collapse of the rock surrounding the tunnels in inclined rock strata is currently underdeveloped. The purpose of this study was to predict the progressive asymmetrical collapse failure of deep-buried tunnels in inclined rock strata to decrease the risk of collapse during tunnel construction. We constructed a new two-dimensional progressive asymmetrical collapse failure mechanism for deep-buried tunnels in inclined rock layers to analyze their collapse failure characteristics with the help of the nonlinear Hoek–Brown yield criterion and the limit analysis theorem. The calculation equations of the range and total weight of the asymmetrical collapsing block in rectangular and circular tunnels were obtained via theoretical derivation. The validity of the proposed method in this work was verified by comparison with existing research. To discuss the impact of different parameters on the range and total weight of an asymmetrical collapsing block of the surrounding rock in inclined rock stratum, the range and total weight of the asymmetrical collapsing block of the most common rectangular and circular tunnels under the varied parameters are provided. The results of this study can provide useful support for practical tunnel construction and design.

Limit variation analysis of shallow rectangular tunnels collapsing with double-layer rock mass based on a three-dimensional failure mechanism

In the framework of upper bound theorem of limit analysis, the progressive collapse of shallow rectangular tunnels with double-layer rock mass has been theoretically analyzed based on the three-dimensional (3D) velocity discontinuity surfaces. According to the virtual work principle, the difference theorem and the variation method, the collapse surface of double-layer rock mass is determined based on the Hoek-Brown failure criterion. The formula can be degenerated to a single-layer rock collapsing problem when the rock mass is homogeneous. To estimate the validity of the result, the numerical simulation software PLAXIS 3D is used to simulate the collapse of shallow tunnels with double-layer rock mass, and the comparative analysis shows that numerical results are in good agreement with upper-bound solutions. According to the results of parametric analysis, the potential range of collapse of a double-layer rock mass above a shallow cavity decreases with a decrease in A1/A2, σci1/σci2 and σtm1/σtm2 and an increase in B1/B2, γ1/γ2. The range will decrease with a decrease in support pressure q and increase with a decrease in surface overload σ;s. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

Prediction of roof supporting pressure for shallow tunnels in layered soils incorporating the effect of pore water pressure

In this study, we propose a method for predicting the supporting pressure required for shallow tunnels in layered soils, based on a curved roof collapse mechanism with multi-failure surfaces. In this method, the effect of the number and thickness of soil layers, pore water pressure, arbitrary roof profile, and ground additional load is considered simultaneously. A nonlinear power-law failure criterion is employed to describe the failure characteristics of the roof soils. The internal energy dissipation rate and the work rates produced by external forces are obtained based on the associated flow rule and plasticity potential theory. The analytical expressions of the required supporting pressure and roof collapse surfaces are obtained with the upper bound method. Furtherly, a shallow rectangular tunnel in two soil layers is selected for parametric investigation. The change laws of the required supporting pressure and collapse curves under varying parameters are obtained. Furthermore, the corresponding engineering recommendations are given, which may potentially provide references for the support design and construction of shallow tunnels in layered strata.

The effect of cross-sectional shape on the dynamic response of tunnels under train induced vibration loads

This paper presents an experimental study of the influence of cross-sectional shape on the dynamic response of a tunnel and the surrounding soil. 1/20 scaled tunnel models with three different cross-sectional shapes (circle, rectangle and horseshoe) were tested. Two types of dynamic loads, sweep loads and train loads, were applied inside the model tunnels. The dynamic response of the tunnels and the soil were measured and both time and frequency domain analyses were performed. The experimental results show that the cross-sectional shape of tunnels can have a significant influence on the dynamic behavior of the tunnel. A clear amplification of the dynamic response of the rectangular tunnel was found, especially at tunnel invert. The distribution of the bending moment can also be changed due to variation of the tunnel cross-sectional shape. However, the test results demonstrate that the cross-sectional shape effects on the tunnel response are mainly in the near field and the influence decreases with increased distance from the excitation source. A limited effect of the cross-sectional shapes on soil response was also found.

A 3D Non-Stationary Channel Model with Moving Mobile Station in Rectangular Tunnel

This paper presents a three-dimensional (3D) geometry-based stochastic model (GBSM) for capturing the non-stationarity of radio channel at 1.8 GHz in a rectangular tunnel. A time-variant (TV) complex channel gain is derived for obtaining the statistical properties in time, frequency, and spatial domains such as the time-variant autocorrelation function (TV-ACF), the time-variant Doppler power spectral density (TV-DPSD), and the time-variant spatial cross-correlation function (TV-CCF), respectively. Then the TV channel statistical properties at different time instants can be extracted and the non-stationary channel characteristics caused by the TV scattering environment are thoroughly discussed. Furthermore, three cases including “approach”, “arrival”, and “away” are set to allow a comprehensive study on how the DPSD behaves with the relative position between transmitter and receiver. The reliability of proposed 3D GBSM is highlighted by a good agreement with the measured result in terms of the correlation function.