Nondestructive testing(NDT)is an advanced and commonly used technique in tunnel engineering quality inspection.To achieve good application of nondestructive testing technology,its main application in tunnel engineerin...Nondestructive testing(NDT)is an advanced and commonly used technique in tunnel engineering quality inspection.To achieve good application of nondestructive testing technology,its main application in tunnel engineering quality inspection strategy is analyzed,including the significance of applying nondestructive testing technology in tunnel engineering quality inspection,the main nondestructive testing technology applied in tunnel engineering quality test analysis,and the analysis of nondestructive testing technology of tunnel engineering quality inspection strategy.The analyses in this paper are done in hopes of providing scientific reference for the utilization of NDT technology and the improvement of tunnel engineering quality.展开更多
The control of large deformation problems in layered soft rock tunnels needs to solve urgently.The roof problem is particularly severe among the deformation issues in tunnels.This study first analyzes the asymmetric d...The control of large deformation problems in layered soft rock tunnels needs to solve urgently.The roof problem is particularly severe among the deformation issues in tunnels.This study first analyzes the asymmetric deformation modes in layered soft rock tunnels with large deformations.Subsequently,we construct a mechanical model under ideal conditions for controlling the roof of layered soft rock tunnels through high preload with the support of NPR anchor cables.The prominent roles of long and short NPR anchor cables in the support system are also analyzed.The results indicate the significance of high preload in controlling the roof of layered soft rock tunnels.The short NPR anchor cables effectively improve the integrity of the stratified soft rock layers,while the long NPR anchor cables effectively mobilize the self-bearing capacity of deep-stable rock layers.Finally,the high-preload support method with NPR anchor cables is validated to have a good effect on controlling large deformations in layered soft rock tunnels through field monitoring data.展开更多
The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-e...The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.展开更多
The lag in quantitative methods and detection techniques for geologic information has resulted in time-consuming and human-experienced geologic analysis in tunnels.Geochemical indicators of rocks can be used to identi...The lag in quantitative methods and detection techniques for geologic information has resulted in time-consuming and human-experienced geologic analysis in tunnels.Geochemical indicators of rocks can be used to identify adverse geology and to explain the intrinsic causes of damage to normal rocks.This study proposes a method to identify adverse geology by extracting and imaging the indicator elements.The mapping relationship between rock components and geologic bodies is quickly determined by indicator element extraction based on factor analysis,and then the data are gridded for image output.The location and size of the target adverse geology are visually identified through the distribution images of the indicator elements,thus reducing data dimensions and analysis time.A non-destructive,in-situ and fast element detection technique in tunnels was adopted to speed up the process of geology identification.The accuracy of the detection was validated by comparing field and laboratory test results.This study further confirms and refines the previous research,and the results provide references for geological,mining and underground projects.展开更多
The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone u...The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.展开更多
Sprayed concrete lining is a commonly employed support measure in tunnel engineering,which plays an important role in construction safety.Compressive strength is a key performance indicator of sprayed concrete lining,...Sprayed concrete lining is a commonly employed support measure in tunnel engineering,which plays an important role in construction safety.Compressive strength is a key performance indicator of sprayed concrete lining,and the traditional measuring method is time-consuming and laborious.This paper proposes various hybrid machine learning algorithms to accomplish the advanced prediction of compressive strength of sprayed concrete lining based on the mixture design.Two hundred and five sets of experimental data were collected from a water conveyance tunnel in northwestern China for model construction,and each set of data was made up of six basic input variables(i.e.,water,cement,mineral powder,superplasticizer,coarse aggregate,and fine aggregate)and one output variable(i.e.,compressive strength).In order to eliminate the correlation between input variables,a new composite indicator(i.e.,the water-binder ratio)was introduced to achieve dimensionality reduction.After that,four hybrid models in total were built,namely BPNN-QPSO,SVR-QPSO,ELM-QPSO,and RF-QPSO,where the hyper-parameters of BPNN,SVR,ELM,and RF were auto-tuned by QPSO.Engineering application results indicated that RF-QPSO achieved the lowest mean absolute percentage error(MAPE)of 3.47% and root mean square error(RMSE)of 1.30 and the highest determination coefficient(R^(2))of 0.93 in the four hybrid models.Moreover,RFQPSO had the shortest running time of 0.15 s,followed by SVR-QPSO(0.18 s),ELM-QPSO(1.19 s),and BPNN-QPSO(1.58 s).Compared with BPNN-QPSO,SVR-QPSO,and ELM-QPSO,RF-QPSO performed the most superior performance in terms of both prediction accuracy and running speed.Finally,the importance of input variables on the model performance was quantitatively evaluated,further enhancing the interpretability of RF-QPSO.展开更多
To explore the cumulative deformation effect of the dynamic response of a tunnel crossing the hauling sliding surface under earthquakes,the shaking table test was conducted in this study.Combined with the numerical ca...To explore the cumulative deformation effect of the dynamic response of a tunnel crossing the hauling sliding surface under earthquakes,the shaking table test was conducted in this study.Combined with the numerical calculations,this study proposed magnification of the Arias intensity(MIa)to characterize the overall local deformation damage of the tunnel lining in terms of the deformation characteristics,frequency domain,and energy.Using the time‐domain analysis method,the plastic effect coefficient(PEC)was proposed to characterize the degree of plastic deformation,and the applicability of the seismic cumulative failure effect(SCFE)was discussed.The results show that the low‐frequency component(f1 and f2≤10 Hz)and the high‐frequency component(f3 and f4>10 Hz)acceleration mainly cause global and local deformation of the tunnel lining.The local deformation caused by the high‐frequency wave has an important effect on the seismic damage of the lining.The physical meaning of PEC is more clearly defined than that of the residual strain,and the SCFE of the tunnel lining can also be defined.The SCFE of the tunnel lining includes the elastic deformation effect stage(<0.15g),the elastic–plastic deformation effect stage(0.15g–0.30g),and the plastic deformation effect stage(0.30g–0.40g).This study can provide valuable theoretical and technical support for the construction of traffic tunnels in high‐intensity earthquake areas.展开更多
The tunnel support system is composed of lining,bolt,and steel frame.It is of great significance to effectively control the deformation of the surrounding rock of the tunnel,make full use of the characteristics of dif...The tunnel support system is composed of lining,bolt,and steel frame.It is of great significance to effectively control the deformation of the surrounding rock of the tunnel,make full use of the characteristics of different support methods,and formulate an economical and effective support plan to ensure the safe operation of the tunnel structure.This paper clarifies the synergistic relationship between the support structure and the surrounding rock based on their fundamental characteristics and functions.Various support structures and components are also discussed in this paper.Additionally,the paper presents an optimized design of the tunnel support structure system.展开更多
Excavation and control of tunneling responses in swelling soft-rock tunnels of Sichuan-Tibet railway under seepage conditions were studied.For this,a fractional viscoplastic(FVP)model for swelling soft rocks was estab...Excavation and control of tunneling responses in swelling soft-rock tunnels of Sichuan-Tibet railway under seepage conditions were studied.For this,a fractional viscoplastic(FVP)model for swelling soft rocks was established by introducing Abel dashpot and unsteady viscosity coefficient,considering additional swelling deformation and damage of rock caused by humidity effect.In view of the FVP model,the viscoplastic deformation solutions for rock mass surrounding tunnel under seepage conditions were derived and long-term mechanical responses of swelling rocks upon tunnel excavation were analyzed.Next,a stress release coefficient considering seepage and creep was proposed,based on which control responses considering stress release and failure mechanism of stress release measures were analyzed.The results showed that:(i)The one-dimensional(1D)FVP model has a good application for swelling rock and the three-dimensional(3D)FVP model could well describe the whole creep process of rock mass despite a much higher creep attenuation rate in the first stage of creep;and(ii)An appropriate stress release and deformation of surrounding rocks could effectively reduce the supporting resistance.However,upon a large stress release,the radius of plastic region could increase significantly,and the strength of the surrounding rock mass decreases greatly.The proposed solution could provide a theoretical framework for capturing the excavation and support responses for tunneling in swelling rock mass in consideration of time effect.展开更多
Graduation project(thesis)is an important practice part in undergraduate education,which forms an organic whole with theoretical teaching link,and it is the continuation,deepening and examination of the theoretical te...Graduation project(thesis)is an important practice part in undergraduate education,which forms an organic whole with theoretical teaching link,and it is the continuation,deepening and examination of the theoretical teaching part.This paper focuses on the constitution that the lack of quality standards for undergraduate graduation design,resulting in different depth and breadth standards;the graduation design materials are scattered and lack of standardization,which leads to the lack of systematic reference materials for students,taking the tunnel and underground engineering major as an example,this paper carries out the practice research on the standardization of the graduation design of tunnel and underground engineering through investigation and combining the teaching resources accumulated in the past decades.Through the study of practice,the content of undergraduate graduation design of tunnel and underground engineering is standardized,the breadth and depth of graduation design is defined,and the“Guide for undergraduate graduation design of tunnel and underground engineering”is organized and compiled,which can provide reference for the standardization and guidance of undergraduate graduation design of tunnel and underground engineering.展开更多
In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the lar...In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.展开更多
The Muzhailing extra-long highway tunnel and corresponding inclined shafts in Lanzhou,Gansu Province,China passes through structurally complex carbonaceous slate that is under high ground stress.Rationally-designed an...The Muzhailing extra-long highway tunnel and corresponding inclined shafts in Lanzhou,Gansu Province,China passes through structurally complex carbonaceous slate that is under high ground stress.Rationally-designed and effective support is of high importance for achieving safe and efficient tunnel construction.The No.2 inclined shaft of Muzhailing Tunnel was taken as the engineering background prototype,for which,a similar model test was conducted to evaluate the effect of highly pretightened constant resistance(NPR,Negative Poisson’s Ratio)anchor cable support provision to the geologically complex carbonaceous slate at different depths.Two schemes were proposed during testing:one scheme was without support and the second was with asymmetric support from highly pre-tightened constant resistance anchor cable.Digital speckle displacement analysis system and micro-groundstress sensors were employed to measure the deformation and shear stress distribution of the tunnel.The results demonstrated that through the second support scheme,the deformation of the surrounding rock could be effectively ameliorated,while this support scheme was applied on the project site of the No.2 inclined shaft,to explore the rationality of the scheme through field engineering tests.On-site monitoring indicated that the deformation of the surrounding rock was within the reasonable design range and the problem of severe tunnel deformation was effectively controlled.The research methods and related conclusions can be used as a reference for the treatment of large deformation problems in deep-buried soft rock tunnels.展开更多
For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initi...For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.展开更多
Grouting is a major method used to prevent water and mud inrush in tunnels and underground engineering. In this paper, the current situation of control and prevention of water and mud inrush is summarized and recent a...Grouting is a major method used to prevent water and mud inrush in tunnels and underground engineering. In this paper, the current situation of control and prevention of water and mud inrush is summarized and recent advances in relevant theories, grout/equipment, and critical techniques are introduced. The time-variant equations of grout viscosity at different volumetric ratios were obtained based on the constitutive relation of typical fast curing grouts. A large-scale dynamic grouting model testing system （4000 mm × 2000 mm × 5 mm） was developed, and the diffusions of cement and fast curing grouts in dynamic water grouting were investigated. The results reveal that the diffusions of cement grouts and fast curing grouts are U-shaped and asymmetric elliptical, respectively. A multi-parameter real-time monitoring system （＆#981; = 1.5 m, h = 1.2 m） was developed for the grouting process to study the diffusion and reinforcement mechanism of grouting in water-rich faulted zone. A high early strength cream-type reinforcing/plugging grout, a high permeability nano-scale silica gel grout, and a high-expansion filling grout were proposed for the control of water hazards in weak water-rich faulted zone rocks, water inrush in karst passages, and micro-crack water inrush, respectively. Complement technologies and equipment for industrial applications were also proposed. Additionally, a novel full-life periodic dynamic water grouting with the critical grouting borehole as the core was proposed. The key techniques for the control of water inrush in water-rich faulted zone, jointed fissures and karst passages, and micro-crack water inrush were developed.展开更多
The Jianpudong No. 4 tunnel is a shallow tunnel, which belongs to Shaoshan County scenic highway in Hunan province, China and whose surrounding rock is weak. According to its characteristics, the field monitoring test...The Jianpudong No. 4 tunnel is a shallow tunnel, which belongs to Shaoshan County scenic highway in Hunan province, China and whose surrounding rock is weak. According to its characteristics, the field monitoring tests and numerical analysis were done. The mechanical characteristics of shallow tunnels under weak surrounding rock and the stress-strain rule of surrounding rock and support were analyzed. The numerical analysis results show that the settlement caused by upper bench excavating accounts for 44% of the total settlement, and the settlement caused by tunnel upper bench supporting accounts for 56% of the total settlement. The maximum axial force of shotcrete lining is 177.2 k N, which locates in hance under the secondary lining. The maximum moment of shotcrete lining is 5.08 k N·m, which locates in the arch foot. The stress curve of steel arch has three obvious stages during the tunnel construction. The maximum axial force of steel arch is 297.4 k N, which locates in tunnel vault. The axial forces of steel arch are respectively 23.5 k N and-21.8 k N, which is influenced by eccentric compression of shallow tunnel and locates in hance. The results show that there is larger earth pressure in tunnel vault which is most unfavorable position of steel arch. Therefore, the advance support should be strengthened in tunnel vault during construction process.展开更多
Active faults are a common adverse geological phenomenon that can occur during tunnel excavation and has a very negative impact on the construction and operation of the tunnel.In this paper,the grade IV rock surroundi...Active faults are a common adverse geological phenomenon that can occur during tunnel excavation and has a very negative impact on the construction and operation of the tunnel.In this paper,the grade IV rock surrounding the cross-fault tunnel with poor geological conditions has been chosen for the study.The support capacity of 2^(nd) Generation-Negative Poisson’s Ratio(2G-NPR)bolt in an active fault tunnel has been carried out on the basis of relevant results obtained from the geomechanical model test and numerical investigations of failure model for existing unsupported fault tunnel.The investigation shows that surrounding rock of the tunnel is prone to shear deformation and crack formation along the fault,as a result,the rock mass on the upper part of the fault slips as a whole.Furthermore,small-scale deformation and loss of blocks are observed around the tunnel;however,the 2G-NPR bolt support is found to be helpful in keeping the overall tunnel intact without any damage and instability.Due to the blocking effect of fault,the stress of the surrounding rock on the upper and lower parts of the fault is significantly different,and the stress at the left shoulder of the tunnel is greater than that at the right shoulder.The asymmetrical arrangement of 2G-NPR bolts can effectively control the asymmetric deformation and instability of the surrounding rock.The present numerical scheme is in good agreement with the model test results,and can reasonably reflect the stress and displacement characteristics of the surrounding rock of the tunnel.In comparison to unsupported and ordinary PR(Poisson’s Ratio)bolt support,2G-NPR bolt can effectively limit the fault slip and control the stability of the surrounding rock of the fault tunnel.The research findings may serve as a guideline for the use of 2G-NPR bolts in fault tunnel support engineering.展开更多
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 enginee...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.展开更多
Water inrush and mud gushing are one of the biggest hazards in tunnel construction. Unfavorable geological sections can be observed in almost all railway tunnels under construction or to be constructed, and vary in ex...Water inrush and mud gushing are one of the biggest hazards in tunnel construction. Unfavorable geological sections can be observed in almost all railway tunnels under construction or to be constructed, and vary in extent. Furthermore, due to the different heights of mountains and the lengths of tunnels, the locations of the unfavorable geological sections cannot be fully determined before construction, which increases the risk of water inrush and mud gushing. Based on numerous cases of water inrush and mud gushing in railway tunnels, the paper tries to classify water inrush and mud gushing in railway tunnels in view of the conditions of the surrounding rocks and meteorological factors associated with tunnel excavation. In addition, the causes of water inrush and mud gushing in combination of macroand micromechanisms are summarized, and site-specifc treatment method is put forward. The treatment methods include choosing a method of advance geological forecast according to risk degrees of different sections in the tunnel, determining the items of predictions, and choosing the appropriate methods, i.e. draining-oriented method, blocking-oriented method or draining-and-blocking method. The treatment technologies of railway water inrush and mud gushing are also summarized, including energy relief and pressure relief technology, advance grouting technology, and advance jet grouting technology associated with their key technical features and applicable conditions. The results in terms of treatment methods can provide reference to the prevention and treatment of tunnel water inrush and mud gushing.展开更多
Gas disasters always restrict the tunnel constructions in mountain area, which becomes a major geological barrier against the development of underground engineering. China is rich in coal resources and has a large amo...Gas disasters always restrict the tunnel constructions in mountain area, which becomes a major geological barrier against the development of underground engineering. China is rich in coal resources and has a large amount of gas with a wide range of distribution. However, China experienced not only adverse effects on coal mining but also gas disasters in underground engineering construction, such as tunnels and chambers. With the increased number of tunnels passing through coal-bearing strata, the incidence of gas accidents is also rising. Therefore, the significance of preventing and mitigating gas disasters should be emphasized, and an effective risk assessment method for gas disasters should be established. On the basis of research on over 100 gas tunnels in China, a relatively ideal gas disaster risk assessment method and system for tunnels are established through the following measures. Firstly, geo-environmental conditions and gas situations were analyzed during construction. Secondly, qualitative analysis was combined with quantitative analysis. Finally, the influencing factors of gas disasters, including geological conditions, gas,and human factors, were investigated. The gas tunnel risk assessment system includes three levels:(1) the grading assessment of a gas tunnel during the planning stage,(2) the risk assessment of gas tunnel construction during the design and construction stages,(3) the gas tunnel outburst risk assessment during the coal uncovering stage. This system was applied to the dynamic assessment of gas disaster during the construction of the Zipingpu tunnel of Dujiangyan–Wenchuan Highway(in Sichuan, Southwest China). The assessment results were consistent with the actual excavation, which verified the rationality and feasibility of the system. The developed system was believed to be back-up and applied for risk assessment of gas disaster in the underground engineering construction.展开更多
To explore the water table and water inflow after tunnel excavation in a vertically stratified phreatic aquifer,approximate analytical solutions for the steady-state water table and water inflow of a drained tunnel in...To explore the water table and water inflow after tunnel excavation in a vertically stratified phreatic aquifer,approximate analytical solutions for the steady-state water table and water inflow of a drained tunnel in a vertically stratified phreatic aquifer were obtained based on the Dupuit assumptions and the integral method.By comparing the approximate analytical solutions with numerical solutions,it was found that the relative error of the approximate analytical solution for the water table elevation is less than 10%,and the relative error of the approximate analytical solution for the water inflow is approximately 25%.The sources of the above errors are as follows:(1)At the lateral boundary of water replenishment,the water surface should be tangent to the horizontal line,but the water surface for the approximate analytical solutions has a gradient.(2)At the vertical boundaries near the tunnel,the total head is variable,but the total head for the approximate analytical solutions is assumed to be constant.(3)The Dupuit assumptions are applied in the flow domain near the tunnel.Although the relative errors of the approximate analytical solutions for the water table elevation and water inflow are evident,the lowered water table is reflected in the approximate analytical solutions.展开更多
文摘Nondestructive testing(NDT)is an advanced and commonly used technique in tunnel engineering quality inspection.To achieve good application of nondestructive testing technology,its main application in tunnel engineering quality inspection strategy is analyzed,including the significance of applying nondestructive testing technology in tunnel engineering quality inspection,the main nondestructive testing technology applied in tunnel engineering quality test analysis,and the analysis of nondestructive testing technology of tunnel engineering quality inspection strategy.The analyses in this paper are done in hopes of providing scientific reference for the utilization of NDT technology and the improvement of tunnel engineering quality.
基金financial support from the Second Tibetan Plateau Scientific Expedition and Research Program(STEP)(No.2019QZKK0708)the National Natural Science Foundation of China(No.41941018)the Special Fund of Yueqi Scholars(No.800015Z1207).
文摘The control of large deformation problems in layered soft rock tunnels needs to solve urgently.The roof problem is particularly severe among the deformation issues in tunnels.This study first analyzes the asymmetric deformation modes in layered soft rock tunnels with large deformations.Subsequently,we construct a mechanical model under ideal conditions for controlling the roof of layered soft rock tunnels through high preload with the support of NPR anchor cables.The prominent roles of long and short NPR anchor cables in the support system are also analyzed.The results indicate the significance of high preload in controlling the roof of layered soft rock tunnels.The short NPR anchor cables effectively improve the integrity of the stratified soft rock layers,while the long NPR anchor cables effectively mobilize the self-bearing capacity of deep-stable rock layers.Finally,the high-preload support method with NPR anchor cables is validated to have a good effect on controlling large deformations in layered soft rock tunnels through field monitoring data.
基金Projects(52378411,52208404)supported by the National Natural Science Foundation of China。
文摘The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively.
基金This research was supported by the National Natural Science Foundation of China(Nos.52022053 and 52279103)the Natural Science Foundation of Shandong Province,China(Nos.ZR201910270116 and ZR2023YQ049).
文摘The lag in quantitative methods and detection techniques for geologic information has resulted in time-consuming and human-experienced geologic analysis in tunnels.Geochemical indicators of rocks can be used to identify adverse geology and to explain the intrinsic causes of damage to normal rocks.This study proposes a method to identify adverse geology by extracting and imaging the indicator elements.The mapping relationship between rock components and geologic bodies is quickly determined by indicator element extraction based on factor analysis,and then the data are gridded for image output.The location and size of the target adverse geology are visually identified through the distribution images of the indicator elements,thus reducing data dimensions and analysis time.A non-destructive,in-situ and fast element detection technique in tunnels was adopted to speed up the process of geology identification.The accuracy of the detection was validated by comparing field and laboratory test results.This study further confirms and refines the previous research,and the results provide references for geological,mining and underground projects.
基金National Science and Technology Major Project,Grant/Award Number:2017YFC1503102National Natural Science Foundation of China,Grant/Award Number:51704144。
文摘The creep characteristics of rock under high crustal stress are of important influence on the long‐term stability of deep rock engineering.To study the creep characteristics and engineering application of sandstone under high crustal stress,this study constructed nonlinear creep damage(NCD)constitutive mode based on the triaxial graded loading‒unloading creep test of sandstone in the Yuezhishan Tunnel.A numerical NCD constitutive model and a breakable lining(BL)model were developed based on FLAC3D and then applied to the stability analysis of the Yuezhishan Tunnel.Based on the creep test results of sandstone,a power function of creep rate and stress level was constructed,by which the long‐term strength was solved.The results show that the long‐term strength of the red sandstone based on the related function of the steady‐state creep rate and stress level is close to the measured stress value in engineering.The NCD model considering damage factors reflects the instantaneous and viscoelastic plasticity deformation characteristics of the red sandstone.The numerical NCD constitutive model and the BL model can reflect surrounding rock deformation characteristics and lining failure characteristics in practical engineering.The research results provide theoretical references for long‐term stability analysis of rock engineering and the deformation control of surrounding rock under high crustal stress.
基金supported by the National Natural Science Foundation of China[Grant numbers 41941018,52074258,42177140,and 41807250]the Key Research and Development Project of Hubei Province[Grant number 2021BCA133].
文摘Sprayed concrete lining is a commonly employed support measure in tunnel engineering,which plays an important role in construction safety.Compressive strength is a key performance indicator of sprayed concrete lining,and the traditional measuring method is time-consuming and laborious.This paper proposes various hybrid machine learning algorithms to accomplish the advanced prediction of compressive strength of sprayed concrete lining based on the mixture design.Two hundred and five sets of experimental data were collected from a water conveyance tunnel in northwestern China for model construction,and each set of data was made up of six basic input variables(i.e.,water,cement,mineral powder,superplasticizer,coarse aggregate,and fine aggregate)and one output variable(i.e.,compressive strength).In order to eliminate the correlation between input variables,a new composite indicator(i.e.,the water-binder ratio)was introduced to achieve dimensionality reduction.After that,four hybrid models in total were built,namely BPNN-QPSO,SVR-QPSO,ELM-QPSO,and RF-QPSO,where the hyper-parameters of BPNN,SVR,ELM,and RF were auto-tuned by QPSO.Engineering application results indicated that RF-QPSO achieved the lowest mean absolute percentage error(MAPE)of 3.47% and root mean square error(RMSE)of 1.30 and the highest determination coefficient(R^(2))of 0.93 in the four hybrid models.Moreover,RFQPSO had the shortest running time of 0.15 s,followed by SVR-QPSO(0.18 s),ELM-QPSO(1.19 s),and BPNN-QPSO(1.58 s).Compared with BPNN-QPSO,SVR-QPSO,and ELM-QPSO,RF-QPSO performed the most superior performance in terms of both prediction accuracy and running speed.Finally,the importance of input variables on the model performance was quantitatively evaluated,further enhancing the interpretability of RF-QPSO.
基金National Key R&D Program of China,Grant/Award Number:2018YFC1504901Science and technology program of Gansu Province,Grant/Award Numbers:21JR7RA738,21JR7RA739+1 种基金Science and Technology Development Project of China Railway Research Institute Co.Ltd,Grant/Award Number:2017‐KJ008‐Z008‐XBNatural Science Foundation of Gansu Province,Grant/Award Number:145RJZA068。
文摘To explore the cumulative deformation effect of the dynamic response of a tunnel crossing the hauling sliding surface under earthquakes,the shaking table test was conducted in this study.Combined with the numerical calculations,this study proposed magnification of the Arias intensity(MIa)to characterize the overall local deformation damage of the tunnel lining in terms of the deformation characteristics,frequency domain,and energy.Using the time‐domain analysis method,the plastic effect coefficient(PEC)was proposed to characterize the degree of plastic deformation,and the applicability of the seismic cumulative failure effect(SCFE)was discussed.The results show that the low‐frequency component(f1 and f2≤10 Hz)and the high‐frequency component(f3 and f4>10 Hz)acceleration mainly cause global and local deformation of the tunnel lining.The local deformation caused by the high‐frequency wave has an important effect on the seismic damage of the lining.The physical meaning of PEC is more clearly defined than that of the residual strain,and the SCFE of the tunnel lining can also be defined.The SCFE of the tunnel lining includes the elastic deformation effect stage(<0.15g),the elastic–plastic deformation effect stage(0.15g–0.30g),and the plastic deformation effect stage(0.30g–0.40g).This study can provide valuable theoretical and technical support for the construction of traffic tunnels in high‐intensity earthquake areas.
文摘The tunnel support system is composed of lining,bolt,and steel frame.It is of great significance to effectively control the deformation of the surrounding rock of the tunnel,make full use of the characteristics of different support methods,and formulate an economical and effective support plan to ensure the safe operation of the tunnel structure.This paper clarifies the synergistic relationship between the support structure and the surrounding rock based on their fundamental characteristics and functions.Various support structures and components are also discussed in this paper.Additionally,the paper presents an optimized design of the tunnel support structure system.
基金Authors are thankful to Dr.Chen Xu of Ningbo University for his instructive discussions.The authors are also grateful for the support provided by the National Natural Science Foundation of China(Grant Nos.41972274 and 42207176)Ningbo Natural Science Foundation(Grant No.2022J116)for this research work.
文摘Excavation and control of tunneling responses in swelling soft-rock tunnels of Sichuan-Tibet railway under seepage conditions were studied.For this,a fractional viscoplastic(FVP)model for swelling soft rocks was established by introducing Abel dashpot and unsteady viscosity coefficient,considering additional swelling deformation and damage of rock caused by humidity effect.In view of the FVP model,the viscoplastic deformation solutions for rock mass surrounding tunnel under seepage conditions were derived and long-term mechanical responses of swelling rocks upon tunnel excavation were analyzed.Next,a stress release coefficient considering seepage and creep was proposed,based on which control responses considering stress release and failure mechanism of stress release measures were analyzed.The results showed that:(i)The one-dimensional(1D)FVP model has a good application for swelling rock and the three-dimensional(3D)FVP model could well describe the whole creep process of rock mass despite a much higher creep attenuation rate in the first stage of creep;and(ii)An appropriate stress release and deformation of surrounding rocks could effectively reduce the supporting resistance.However,upon a large stress release,the radius of plastic region could increase significantly,and the strength of the surrounding rock mass decreases greatly.The proposed solution could provide a theoretical framework for capturing the excavation and support responses for tunneling in swelling rock mass in consideration of time effect.
文摘Graduation project(thesis)is an important practice part in undergraduate education,which forms an organic whole with theoretical teaching link,and it is the continuation,deepening and examination of the theoretical teaching part.This paper focuses on the constitution that the lack of quality standards for undergraduate graduation design,resulting in different depth and breadth standards;the graduation design materials are scattered and lack of standardization,which leads to the lack of systematic reference materials for students,taking the tunnel and underground engineering major as an example,this paper carries out the practice research on the standardization of the graduation design of tunnel and underground engineering through investigation and combining the teaching resources accumulated in the past decades.Through the study of practice,the content of undergraduate graduation design of tunnel and underground engineering is standardized,the breadth and depth of graduation design is defined,and the“Guide for undergraduate graduation design of tunnel and underground engineering”is organized and compiled,which can provide reference for the standardization and guidance of undergraduate graduation design of tunnel and underground engineering.
基金The authors would like to acknowledge the financial support from the Key Special Project of the National Natural Science Foundation of China(No.41941018)the Special Fund of Yueqi Scholars(No.800015Z1207).
文摘In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.
基金supported by the National Key Research and Development Program of China(No.2016YFC0600901)the Fundamental Research Funds for the Central Universities(No.2015QB02)。
文摘The Muzhailing extra-long highway tunnel and corresponding inclined shafts in Lanzhou,Gansu Province,China passes through structurally complex carbonaceous slate that is under high ground stress.Rationally-designed and effective support is of high importance for achieving safe and efficient tunnel construction.The No.2 inclined shaft of Muzhailing Tunnel was taken as the engineering background prototype,for which,a similar model test was conducted to evaluate the effect of highly pretightened constant resistance(NPR,Negative Poisson’s Ratio)anchor cable support provision to the geologically complex carbonaceous slate at different depths.Two schemes were proposed during testing:one scheme was without support and the second was with asymmetric support from highly pre-tightened constant resistance anchor cable.Digital speckle displacement analysis system and micro-groundstress sensors were employed to measure the deformation and shear stress distribution of the tunnel.The results demonstrated that through the second support scheme,the deformation of the surrounding rock could be effectively ameliorated,while this support scheme was applied on the project site of the No.2 inclined shaft,to explore the rationality of the scheme through field engineering tests.On-site monitoring indicated that the deformation of the surrounding rock was within the reasonable design range and the problem of severe tunnel deformation was effectively controlled.The research methods and related conclusions can be used as a reference for the treatment of large deformation problems in deep-buried soft rock tunnels.
基金Project(2021JLM-49) supported by Natural Science Basic Research Program of Shaanxi-Joint Fund of Hanjiang to Weihe River Valley Water Diversion Project,ChinaProject(42077248) supported by the National Natural Science Foundation of China
文摘For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.
文摘Grouting is a major method used to prevent water and mud inrush in tunnels and underground engineering. In this paper, the current situation of control and prevention of water and mud inrush is summarized and recent advances in relevant theories, grout/equipment, and critical techniques are introduced. The time-variant equations of grout viscosity at different volumetric ratios were obtained based on the constitutive relation of typical fast curing grouts. A large-scale dynamic grouting model testing system （4000 mm × 2000 mm × 5 mm） was developed, and the diffusions of cement and fast curing grouts in dynamic water grouting were investigated. The results reveal that the diffusions of cement grouts and fast curing grouts are U-shaped and asymmetric elliptical, respectively. A multi-parameter real-time monitoring system （＆#981; = 1.5 m, h = 1.2 m） was developed for the grouting process to study the diffusion and reinforcement mechanism of grouting in water-rich faulted zone. A high early strength cream-type reinforcing/plugging grout, a high permeability nano-scale silica gel grout, and a high-expansion filling grout were proposed for the control of water hazards in weak water-rich faulted zone rocks, water inrush in karst passages, and micro-crack water inrush, respectively. Complement technologies and equipment for industrial applications were also proposed. Additionally, a novel full-life periodic dynamic water grouting with the critical grouting borehole as the core was proposed. The key techniques for the control of water inrush in water-rich faulted zone, jointed fissures and karst passages, and micro-crack water inrush were developed.
基金Projects(51408060,51208063)supported by the National Natural Science Foundation of China
文摘The Jianpudong No. 4 tunnel is a shallow tunnel, which belongs to Shaoshan County scenic highway in Hunan province, China and whose surrounding rock is weak. According to its characteristics, the field monitoring tests and numerical analysis were done. The mechanical characteristics of shallow tunnels under weak surrounding rock and the stress-strain rule of surrounding rock and support were analyzed. The numerical analysis results show that the settlement caused by upper bench excavating accounts for 44% of the total settlement, and the settlement caused by tunnel upper bench supporting accounts for 56% of the total settlement. The maximum axial force of shotcrete lining is 177.2 k N, which locates in hance under the secondary lining. The maximum moment of shotcrete lining is 5.08 k N·m, which locates in the arch foot. The stress curve of steel arch has three obvious stages during the tunnel construction. The maximum axial force of steel arch is 297.4 k N, which locates in tunnel vault. The axial forces of steel arch are respectively 23.5 k N and-21.8 k N, which is influenced by eccentric compression of shallow tunnel and locates in hance. The results show that there is larger earth pressure in tunnel vault which is most unfavorable position of steel arch. Therefore, the advance support should be strengthened in tunnel vault during construction process.
基金supported by the National Natural Science Foundation of China(NSFC)(41941018)the Program of China Scholarship Council(202106430031)。
文摘Active faults are a common adverse geological phenomenon that can occur during tunnel excavation and has a very negative impact on the construction and operation of the tunnel.In this paper,the grade IV rock surrounding the cross-fault tunnel with poor geological conditions has been chosen for the study.The support capacity of 2^(nd) Generation-Negative Poisson’s Ratio(2G-NPR)bolt in an active fault tunnel has been carried out on the basis of relevant results obtained from the geomechanical model test and numerical investigations of failure model for existing unsupported fault tunnel.The investigation shows that surrounding rock of the tunnel is prone to shear deformation and crack formation along the fault,as a result,the rock mass on the upper part of the fault slips as a whole.Furthermore,small-scale deformation and loss of blocks are observed around the tunnel;however,the 2G-NPR bolt support is found to be helpful in keeping the overall tunnel intact without any damage and instability.Due to the blocking effect of fault,the stress of the surrounding rock on the upper and lower parts of the fault is significantly different,and the stress at the left shoulder of the tunnel is greater than that at the right shoulder.The asymmetrical arrangement of 2G-NPR bolts can effectively control the asymmetric deformation and instability of the surrounding rock.The present numerical scheme is in good agreement with the model test results,and can reasonably reflect the stress and displacement characteristics of the surrounding rock of the tunnel.In comparison to unsupported and ordinary PR(Poisson’s Ratio)bolt support,2G-NPR bolt can effectively limit the fault slip and control the stability of the surrounding rock of the fault tunnel.The research findings may serve as a guideline for the use of 2G-NPR bolts in fault tunnel support engineering.
基金support from the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z020006)the National Natural Science Foundation of China(Grant Nos.U1765206 and 51874119).
文摘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.
文摘Water inrush and mud gushing are one of the biggest hazards in tunnel construction. Unfavorable geological sections can be observed in almost all railway tunnels under construction or to be constructed, and vary in extent. Furthermore, due to the different heights of mountains and the lengths of tunnels, the locations of the unfavorable geological sections cannot be fully determined before construction, which increases the risk of water inrush and mud gushing. Based on numerous cases of water inrush and mud gushing in railway tunnels, the paper tries to classify water inrush and mud gushing in railway tunnels in view of the conditions of the surrounding rocks and meteorological factors associated with tunnel excavation. In addition, the causes of water inrush and mud gushing in combination of macroand micromechanisms are summarized, and site-specifc treatment method is put forward. The treatment methods include choosing a method of advance geological forecast according to risk degrees of different sections in the tunnel, determining the items of predictions, and choosing the appropriate methods, i.e. draining-oriented method, blocking-oriented method or draining-and-blocking method. The treatment technologies of railway water inrush and mud gushing are also summarized, including energy relief and pressure relief technology, advance grouting technology, and advance jet grouting technology associated with their key technical features and applicable conditions. The results in terms of treatment methods can provide reference to the prevention and treatment of tunnel water inrush and mud gushing.
基金support by the National Natural Science Foundation of China (Grant No. 41302244)
文摘Gas disasters always restrict the tunnel constructions in mountain area, which becomes a major geological barrier against the development of underground engineering. China is rich in coal resources and has a large amount of gas with a wide range of distribution. However, China experienced not only adverse effects on coal mining but also gas disasters in underground engineering construction, such as tunnels and chambers. With the increased number of tunnels passing through coal-bearing strata, the incidence of gas accidents is also rising. Therefore, the significance of preventing and mitigating gas disasters should be emphasized, and an effective risk assessment method for gas disasters should be established. On the basis of research on over 100 gas tunnels in China, a relatively ideal gas disaster risk assessment method and system for tunnels are established through the following measures. Firstly, geo-environmental conditions and gas situations were analyzed during construction. Secondly, qualitative analysis was combined with quantitative analysis. Finally, the influencing factors of gas disasters, including geological conditions, gas,and human factors, were investigated. The gas tunnel risk assessment system includes three levels:(1) the grading assessment of a gas tunnel during the planning stage,(2) the risk assessment of gas tunnel construction during the design and construction stages,(3) the gas tunnel outburst risk assessment during the coal uncovering stage. This system was applied to the dynamic assessment of gas disaster during the construction of the Zipingpu tunnel of Dujiangyan–Wenchuan Highway(in Sichuan, Southwest China). The assessment results were consistent with the actual excavation, which verified the rationality and feasibility of the system. The developed system was believed to be back-up and applied for risk assessment of gas disaster in the underground engineering construction.
基金supported by the High Speed Railway and Natural Science United Foundation of China(No.U1734205)the Fundamental Research Funds for the Central Universities of China(No.2682021CG002)+1 种基金the National Natural Science Foundation of China(No.51808459)the China State Railway Group Co.,Ltd.Science and Technology Research and Development Program Systematic Major Project(No.P2019G040)。
文摘To explore the water table and water inflow after tunnel excavation in a vertically stratified phreatic aquifer,approximate analytical solutions for the steady-state water table and water inflow of a drained tunnel in a vertically stratified phreatic aquifer were obtained based on the Dupuit assumptions and the integral method.By comparing the approximate analytical solutions with numerical solutions,it was found that the relative error of the approximate analytical solution for the water table elevation is less than 10%,and the relative error of the approximate analytical solution for the water inflow is approximately 25%.The sources of the above errors are as follows:(1)At the lateral boundary of water replenishment,the water surface should be tangent to the horizontal line,but the water surface for the approximate analytical solutions has a gradient.(2)At the vertical boundaries near the tunnel,the total head is variable,but the total head for the approximate analytical solutions is assumed to be constant.(3)The Dupuit assumptions are applied in the flow domain near the tunnel.Although the relative errors of the approximate analytical solutions for the water table elevation and water inflow are evident,the lowered water table is reflected in the approximate analytical solutions.
