Analytical solution to rock pressure acting on three shallow tunnels subjected to unsymmetrical loads

According to the interaction of three shallow tunnels with large section, the analytical solution to rock pressure has been derived and discussed. The load model is given when the bilateral tunnels are excavated. According to the model, the stresses of three tunnels and single tunnel are calculated and compared to analyze the distribution characteristics, where the stresses are influenced by controlling factors of clear distance, covering depth and inclination angle of ground surface. The results show that, in general, the bias distribution is more serious. Therefore, it is significant to settle down the load model of three shallow tunnels so as to determine the measure of reinforcement and design the structure of support. The model and results can be used as a theoretical basis in designation and further research of the three shallow tunnels.

Safe range analysis of clear distance of twin shallow tunnels based on limit analysis and reliability theory

A method of analyzing the stability of twin shallow tunnels was presented using both limit analysis with nonlinear failure criterion and reliability theory.In the condition of nonlinear failure criterion,the critical clear distancesof twin shallow tunnels were obtained by analyzing the change of surrounding pressure.A reliability model was established based on limit state equation,and the failure probability was solved by virtue of Monte Carlo method.Safety factor and corresponding clear distance of different safety levels were obtained by introducing a target reliability index.The scope of clear distance for different safety levels is described,which can be used as a supplement and improvement to the design codes of tunnels.

Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion

Based on nonlinear Mohr-Coulomb failure criterion, the analytical solutions of stability number and supporting force on twin shallow tunnels were derived using upper bound theorem of limit analysis. The optimized solutions were obtained by the technique of sequential quadratic programming. When nonlinear coefficient equals 1 and internal friction angle equals 0, the nonlinear Mohr-Coulomb failure criterion degenerates into linear failure criterion. The calculated results of stability number in this work were compared with previous results, and the agreement verifies the effectiveness of the present method. Under the condition of nonlinear Mohr-Coulomb failure criterion, the results show that the supporting force on twin shallow tunnels obviously increases when the nonlinear coefficient, burial depth, ground load or pore water pressure coefficients increase. When the clear distance is 0.5to 1.0 times the diameter of tunnel, the supporting force of twin shallow tunnels reaches its maximum value, which means that the tunnels are the easiest to collapse. While the clear distance increases to 3.5 times the diameter of tunnel, the calculation for twin shallow tunnels can be carried out by the method for independent single shallow tunnel. Therefore, 3.5 times the diameter of tunnel serves as a critical value to determine whether twin shallow tunnels influence each other. In designing twin shallow tunnels,appropriate clear distance value must be selected according to its change rules and actual topographic conditions, meanwhile, the influences of nonlinear failure criterion of soil materials and pore water must be completely considered. During the excavation process, supporting system should be intensified at the positions of larger burial depth or ground load to avoid collapses.

Upper bound solutions for supporting pressures of shallow tunnels with nonlinear failure criterion

Linear failure criterion is widely used in calculation of earth pressure acting on shallow tunnels. However, experimental evidence shows that nonlinear failure criterion is able to represent fairly well the failure of almost all types of rocks, A nonlinear Hock-Brown failure criterion is employed to estimate the supporting pressures of shallow tunnels in limit analysis framework. Two failure mechanisms are proposed for calculating the work rate of extemal force and the internal energy dissipation. A tangential line to the nonlinear failure criterion is used to formulate the supporting pressure problem as a nonlinear programming problem. The objective function formulated in this way is minimized with respect to the failure mechanism and the location of tangency point. In order to assess the validity, the supporting pressures for the proposed failure mechanisms are calculated and compared with each other, and the present results are compared with previously published solutions when the nonlinear criterion is reduced to linear criterion. The agreement supports the validity of the proposed failure mechanisms. An experiment is conducted to investigate the influences of the nonlinear criterion on collapse shape and supporting pressures of shallow tunnels.

Upper bound solutions of stability factor of shallow tunnels in saturated soil based on strength reduction technique

Based on the upper bound theorem of limit analysis,the factor of safety for shallow tunnel in saturated soil is calculated in conjunction with the strength reduction technique.To analyze the influence of the pore pressure on the factor of safety for shallow tunnel,the power of pore pressure is regarded as a power of external force in the energy calculation.Using the rigid multiple-block failure mechanism,the objective function for the factor of safety is constructed and the optimal solutions are derived by employing the sequential quadratic programming.According to the results of optimization calculation,the factor of safety of shallow tunnel for different pore pressure coefficients and variational groundwater tables are obtained.The parameter analysis shows that the pore pressure coefficient and the location of the groundwater table have significant influence on the factor of safety for shallow tunnel.

Catastrophe stability analysis for shallow tunnels considering settlement

Limit analysis of the stability of geomechanical projects is one of the most difficult problems.This work investigates the influences of different parameters in NL failure strength on possible collapsing block shapes of single and twin shallow tunnels with considering the effects of surface settlement.Upper bound solutions derived by functional catastrophe theory are used for describing the distinct characteristics of falling blocks of different parts in twin tunnels.Furthermore the analytical solutions of minimum supporting pressures in shallow tunnels are obtained by the help of the variational principle.Lastly,the comparisons are made both in collapsed mechanism and stability factor with different methods.According to the numerical results in this work,the influences of different parameters on the size of collapsing block are presented in the tables and the limit supporting loads are illustrated in the form graphs that account for the surface settlement.

Numerical analysis and field monitoring tests on shallow tunnels under weak surrounding rock

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.

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.

Upper bound limit analysis of roof collapse in shallow tunnels with arbitrary cross sections under condition of seepage force

The analytical solutions for predicting the exact shape of collapse mechanisms in shallow tunnels with arbitrary excavation profiles were obtained by virtue of the upper bound theorem of limit analysis and variation principle according to Hoek-Brown failure criterion. The seepage force was included in the upper bound limit analysis, and it was computed from the gradient of excess pore pressure distribution. The seepage was regarded as a work rate of external force. The numerical results of roof collapse in square and circular tunnels with different rock parameters were derived and discussed, which proves to be valid in comparison with the previous work. The influences of different parameters on the shape of collapsing blocks were also discussed.

Application of excavation compensation method for enhancing stability and efficiency in shallow large-span rock tunnels

Engineering shallow,large-span rock tunnels challenges deformation control and escalates construction costs.This study investigates the excavation compensation method(ECM)and its associated technologies to address these issues.Utilizing five key technologies,the ECM effectively modulates radial stress post-excavation,redistributes stress in the surrounding rock,and eliminates tensile stress at the excavation face.Pre-tensioning measures further enhance the rock’s residual strength,establishing a new stability equilibrium.Field tests corroborate the method’s effectiveness,demonstrating a crown settlement reduction of 3–8 mm,a nearly 50%decrease compared to conventional construction approaches.Additionally,material consumption and construction duration were reduced by approximately 30%–35%and 1.75 months per 100 m,respectively.Thus,the ECM represents a significant innovation in enhancing the stability and construction efficiency of large-span rock tunnels,marking a novel contribution to the engineering field.

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 σs. Therefore, reinforced supporting is beneficial to improve the stability of the cavity during actual construction.

Upper bound analytical solution for surrounding rock pressure of shallow unsymmetrical loading tunnels

By combining the results of laboratory model tests with relevant flow rules, the failure mode of shallow unsymmetrical loading tunnels and the corresponding velocity field were established. According to the principle of virtual power, the upper bound solution for surrounding rock pressure of shallow unsymmetrical loading tunnel was derived and verified by an example. The results indicate that the calculated results of the derived upper bound method for surrounding rock pressure of shallow unsymmetrical loading tunnels are relatively close to those of the existing "code method" and test results, which means that the proposed method is feasible. The current code method underestimates the unsymmetrical loading feature of surrounding rock pressure of shallow unsymmetrical loading tunnels, so it is unsafe; when the burial depth is less or greater than two times of the tunnel span and the unsymmetrical loading angle is less than 45°, the upper bound method or the average value of the results calculated by the upper bound method and code method respectively, is comparatively reasonable. When the burial depth is greater than two times of the tunnel span and the unsymmetrical loading angle is greater than 45°, the code method is more suitable.

Shallow Tunneling Method and Control Measure for Ground Surface Settlement

In order to ensure that the tunnel deformation and surface settlement are controlled within the allowable range during the construction process,the design unit has compiled technical measures and monitoring schemes for ground settlement control of this project.Based on the example of a shallow tunneling project on Subway line 8,this paper analyzes and discusses the shallow tunneling method in detail and puts forward corresponding technical measures for ground settlement control.

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.

Deformation mechanism and collapse treatment of the rock surrounding a shallow tunnel based on on-site monitoring

When tunnels are constructed at shallow depths in areas with poor geological conditions,such as portal sections,valleys and hillsides in regions with granitic bedrock,considerable excavation-induced deformation of the surrounding rock may occur,potentially resulting in tunnel collapses.The main reason for these problems is the lack of understanding of the deformation mechanism and evolution of the soft granitic rock surrounding the tunnel and the adoption of inappropriate construction technology and methods.This article analyzes the deformation mechanism of the rock surrounding a shallow tunnel based on in situ monitoring data as a case study and suggests that certain measures should be taken to effectively control the deformation of the surrounding rock and to minimize the potential for tunnel collapse.The results show that the deformation of the granitic soil surrounding the tunnel can be divided into three stages:the rapid deformation stage,the slow deformation stage and the stabilization stage.Appropriate construction methods should be carefully selected to ensure safety during tunnel excavation in the first stage.To avoid secondary disasters caused by tunnel collapses,three treatment measures may be implemented as part of safety management:enhancing the monitoring of the surrounding rock deformation,adjusting the construction methods and optimizing the support systems.In particular,accurate monitoring data and timely information feedback play a vital role in tunnel construction.Therefore,engineers with considerable engineering experience and professional knowledge are needed to analyze the monitoring data and make accurate predictions of tunnel deformation to ensure that reasonable measures are taken in the process of shallow tunnel excavation.

Test and damage assessment of shallow buried RC tunnel under explosion

As a major element of the transportation network,tunnels are unavoidably threatened by accidental loads such as vehicle bombs and tank truck explosions.The goal of this research is to explore the dynamic characteristics and damage assessment of tunnel structures under contact blast loads.First,three scaled-down reinforced concrete tunnel models were made,and the explosion test and static loading test were carried out successively to evaluate the axial residual bearing capacity,axial displacement and failure mechanism of the tunnel.Secondly,the finite element model is built by utilizing LS-DYNA,and the reliability of the finite element method is confirmed by comparing the data of the explosion test with the static loading test.At the same time,the calculation method for damage coefficient and the classification criteria for damage grade based on axial residual bearing capacity are presented.Then,based on the finite element method,the propagation process of the explosion shock wave in the tunnel and the damage mechanism of the tunnel are investigated.Finally,seven explosion scenarios are developed,the damage degree of these seven tunnels under the blast load is quantitatively analyzed,and further anti-blast design ideas are put forth.The study in this article may give an intended reference for the damage assessment,anti-explosion design and strengthening work of reinforced concrete tunnels.

Control of rock joint parameters on deformation of tunnel opening

In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method（BEM）. The existing fullplane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.

Calculation of maximum surface settlement induced by EPB shield tunnelling and introducing most effective parameter

This study aims to predict ground surface settlement due to shallow tunneling and introduce the most affecting parameters on this phenomenon.Based on data collected from Shanghai LRT Line 2 project undertaken by TBM-EPB method,this research has considered the tunnel's geometric,strength,and operational factors as the dependent variables.At first,multiple regression(MR) method was used to propose equations based on various parameters.The results indicated the dependency of surface settlement on many parameters so that the interactions among different parameters make it impossible to use MR method as it leads to equations of poor accuracy.As such,adaptive neuro-fuzzy inference system(ANFIS),was used to evaluate its capabilities in terms of predicting surface settlement.Among generated ANFIS models,the model with all input parameters considered produced the best prediction,so as its associated R^2 in the test phase was obtained to be 0.957.The equations and models in which operational factors were taken into consideration gave better prediction results indicating larger relative effect of such factors.For sensitivity analysis of ANFIS model,cosine amplitude method(CAM) was employed; among other dependent variables,fill factor of grouting(n) and grouting pressure(P) were identified as the most affecting parameters.

Novel hybrid method to predict the ground-displacement field caused by shallow tunnel excavation

Based on machine-learning(ML) and analytical methods, a hybrid method is developed herein to predict the ground-displacement field(GDF) caused by tunneling. The extreme learning machine(ELM), as a single hidden layer feedforward neural network, is used as an ML model to predict maximum settlement smaxof the ground surface. The particle swarm optimization(PSO) algorithm is applied to optimize the parameters for the ELM method, namely, weight and bias values from the input layer to the hidden layer. The mean square error of the k-fold cross validation sets is considered the fitness function of the PSO algorithm. For 38 data samples from published papers, 30 samples are used as the training set, and 8 samples are used as the test set. For the test samples, the error of five samples ranges between-5 and 5 mm. The error of only one sample is slightly greater than 10 mm. The proposed PSO-ELM method demonstrates good prediction performance of smax. A deformation parameter of the nonuniform displacement mode for the tunnel cross-section is calibrated based on predicted smax. When the determined nonuniform displacement mode is used as the boundary condition of the tunnel cross-section, the GDF of a shallow circular tunnel is analytically predicted based on the complex-variable method prior to tunnel excavation. For a specific engineering case,i.e., the Heathrow Express tunnel, the proposed PSO-ELM-analytical method can well predict the surface-settlement trough curve, horizontal displacements at different depths, and vertical displacements above the tunnel.

Study of the Pavement Settlement Standard Induced by Tunnel to Under-traverse Highway in Close Quarter

Now the surface settlement induced by shallow buried tunnel to under-traverse highway,mostly adopt the empirical value,3 cm,acquired from Beijing or Shenzhen metro,which is regarded as the controlling standard.But to more project,tunnel under-traverse highway,we must decide the controlling standard flexibly,which should base on the pavement service function and the pavement condition.The thesis,based on the pavement evenness and running comfort ability in the view of completing the pavement service function,supposes the longitudinal pavement settlement cross section as a quadratic parabola,and gets the maximal settlement value in the range of longitudinal pavement influence when the tunnel is under-traverse highway perpendicularly.Then the controlling standard is decided.As Wenxiang Tunnel under-traverse Lianhuo Freeway on Zhengzhou-Xi'an Passenger Dedicated Railway Line for an example,the settlement controlling standard is acquired,and we hope it has an direction and reference value to similar tunnel construction.