Experimental and numerical simulation of the attenuation effect of blast shock waves in tunnels at different altitudes

Traffic engineering such as tunnels in various altitudinal gradient zone are at risk of accidental explosion,which can damage personnel and equipment.Accurate prediction of the distribution pattern of explosive loads and shock wave propagation process in semi-enclosed structures at various altitude environment is key research focus in the fields of explosion shock and fluid dynamics.The effect of altitude on the propagation of shock waves in tunnels was investigated by conducting explosion test and numerical simulation.Based on the experimental and numerical simulation results,a prediction model for the attenuation of the peak overpressure of tunnel shock waves at different altitudes was established.The results showed that the peak overpressure decreased at the same measurement points in the tunnel entrance under the high altitude condition.In contrast,an increase in altitude accelerated the propagation speed of the shock wave in the tunnel.The average error between the peak shock wave overpressure obtained using the overpressure prediction formula and the measured test data was less than15%,the average error between the propagation velocity of shock waves predicted values and the test data is less than 10%.The method can effectively predict the overpressure attenuation of blast wave in tunnel at various altitudes.

Analysis of the interaction between bolt-reinforced rock and surface support in tunnels based on convergence-confinement method

To investigate the interaction of the bolt-reinforced rock and the surface support,an analytical model of the convergence-confinement type is proposed,considering the sequential installation of the fully grouted rockbolts and the surface support.The rock mass is assumed to be elastic-brittle-plastic material,obeying the linear Mohr-Coulomb criterion or the non-linear Hoek-Brown criterion.According to the strain states of the tunnel wall at bolt and surface support installation and the relative magnitude between the bolt length and the plastic depth during the whole process,six cases are categorized upon solving the problem.Each case is divided into three stages due to the different effects of the active rockbolts and the passive surface support.The fictitious pressure is introduced to quantify the threedimensional(3D)effect of the tunnel face,and thus,the actual physical location along the tunnel axis of the analytical section can be considered.By using the bolt-rock strain compatibility and the rocksurface support displacement compatibility conditions,the solutions of longitudinal tunnel displacement and the reaction pressure of surface support along the tunnel axis are obtained.The proposed analytical solutions are validated by a series of 3D numerical simulations.Extensive parametric studies are conducted to examine the effect of the typical parameters of rockbolts and surface support on the tunnel displacement and the reaction pressure of the surface support under different rock conditions.The results show that the rockbolts are more effective in controlling the tunnel displacement than the surface support,which should be installed as soon as possible with a suitable length.For tunnels excavated in weak rocks or with restricted displacement control requirements,the surface support should also be installed or closed timely with a certain stiffness.The proposed method provides a convenient alternative approach for the optimization of rockbolts and surface support at the preliminary stage of tunnel design.

Mechanism of high-preload support based on the NPR anchor cable in layered soft rock tunnels

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.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

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.

Assessing foundation behaviour under complex loading near tunnels

The stability of strip footings subjected to eccentrically inclined loads is critical for reliable foundation design.This study investigates the effect of a circular unlined tunnel in a rock mass on the ultimate bearing capacity(UBC)of a foundation with width B under inclined and eccentric loads.Adaptive finite element limit analysis was employed to evaluate the reduction in UBC of the footing resting above a tunnel.The examined critical parameters include normalized load eccentricity(e/B),load inclination(β),and horizontal and vertical distances of the tunnel from the foundation(P/B and Q/B,respectively),along with rock mass properties.The results reveal that for e/B≥0.25 and β≤60°,the reduction coefficient,R_(c)≥0.90,suggesting that the presence of a tunnel has a minimal impact on the load-bearing capacity of the footing,with failure primarily governed by load eccentricity and inclination.Additionally,potential failure mechanisms are explored,showing that at lower e/B,higher β,and lower Q/B,the tunnel significantly affects footing's failure envelope.Conversely,at higher e/B and lower β,failure is due to rotational effects of footing,regardless of the tunnel's position.To predict the Rc more accurately,due to the time-consuming nature of direct calculations,both MLR and ANN models were developed.The MLR model provided a baseline for comparison,while the ANN model,with a coefficient of determination(R2)of 0.98,demonstrated superior accuracy compared to the R2=0.96 of MLR.Using both approaches ensured robust and efficient predictions of Rc.Since Rc does not directly provide the reduced UBC of footing due to presence of tunnel,the study introduced bearing capacity factor(Nc)to enable direct calculation of the reduced UBC of footing.These findings offer theoretical guidelines for preliminary design and provide practitioners with an effective tool for evaluating UBC reduction in complex loading scenarios involving tunnels.

Mechanical properties of steel mesh in anchor-mesh support for rocky tunnels

Underground geotechnical engineering encounters persistent challenges in ensuring the stability and safety of surrounding rock structures, particularly within rocky tunnels. Rock reinforcement techniques, including the use of steel mesh, are critical to achieving this goal. However, there exists a knowledge gap regarding the comprehensive understanding of the mechanical behavior and failure mechanisms exhibited by steel mesh under diverse loading conditions. This study thoroughly explored the steel mesh's performance throughout the entire loading-failure process, innovating with detailed analysis and modeling techniques. By integrating advanced numerical modeling with laboratory experiments, the study examines the influence of varying reinforcement levels and geometric parameters on the steel mesh strength and deformation characteristics. Sensitivity analysis, employing gray correlation theory, identifies the key factors affecting the mesh performance, while a BP (Backpropagation) neural network model predicts maximum vertical deformation with high accuracy. The findings underscore the critical role of steel diameter and mesh spacing in optimizing peak load capacity, displacement, and energy absorption, offering practical guidelines for design improvements. The use of a Bayesian Regularization (BR) algorithm further enhances the predictive accuracy compared to traditional methods. This research provides new insights into optimizing steel mesh design for underground applications, offering an innovative approach to enhancing structural safety in geotechnical projects.

Roof collapse mechanism of weak surrounding rock for deep-buried tunnels under high geostress conditions

High geostress,a typical attribute of tunnels located at significant depths,is crucial in causing stress-induced failure and influencing the stability of the tunnel crown.This study developed an analytical method for the failure mechanism that occurs in deep-buried tunnel roofs,taking into account the influence of geostress.The limit analysis theory was utilized for deriving analytical solutions about the geometry of the collapsing surface and the limit supporting pressure.The collapsing surface obtained by the analytical solution was validated by the findings of the physical model test,which shows a high level of agreement with the actual one.An extensive investigation was done to explore the effects of the lateral pressure coefficients,the tunnel buried depth,the geological conditions of the surrounding rock,the long-short axis ratio,and the size of the tunnel profile.The findings indicate that an increase in the lateral pressure coefficient from 0.5 to 1.5 results in a reduction in the height of the collapsing zone by 2.08 m and the width of the collapsing zone by 1.15 m,while simultaneously increases the limit supporting pressure by 18.9%.The proposed upper bound method accurately determines the limit supporting pressure and the geometry of the collapsing surface,which aligns well with the results acquired through numerical modelling and on-site monitoring in actual engineering applications.The proposed analytical method can serve as a reference for similar crown failure issues of deep-buried tunnels.

A Simplified Method for the Stress Analysis of Underground Transfer Structures Crossing Multiple Subway Tunnels

According to the design specifications,the construction of extended piles involves traversing the tunnel’s upper region and extending to the underlying rock layer.To address this challenge,a subterranean transfer structure spanning multiple subway tunnels was proposed.Deliberating on the function of piles in the transfer structure as springs with axial and bending stiffness,and taking into account the force balance and deformation coordination conditions of beams and plates within the transfer structure,we established a simplified mechanical model that incorporates soil stratification by combining it with the Winkler elastic foundation beam model.The resolved established simplifiedmechanicalmodel employed finite difference technology and the Newton-Simpsonmethod,elucidating the mechanical mechanism of the transfer structure.The research findings suggest that the load carried by the upper structural columns can be transferred to the pile foundation beneath the beams through the transfer structure,subsequently reaching the deep soil layer and ensuring minimal impact on adjacent tunnels.The established simplified analysis method can be used for stress analysis of the transfer structure,concurrently considering soil stratification,pile foundation behavior,and plate action.The pile length,pile section size,and beam section size within the transfer structure should account for the characteristics of the upper load,ensuring an even distribution of the beam bending moment.

Mechanical responses of underground carriageway structures due to construction of metro tunnels beneath the existing structure:A case study

To understand the mechanical response pattern of the existing structure and ground due to the construction of metro tunnels underneath,the finite difference method is adopted to study the torsional deformation and stress variation of the existing structure and the effect of underground carriageway structures on the surface subsidence.The curves of the maximum differential subsidence,torsion angle,and distortion of the cross-section of the existing structure show two peaks in succession during traversing of two metro tunnels beneath it.The torsion angle of the existing structure changes when the two tunnels traverse beneath it in opposite directions.The first traversing of the shield tunnel mainly induces the magnitude variation in torsional deformation of the existing structure,but the second traversing of the subsurface tunnel may cause a dynamic change in the magnitude and form of torsional deformation in the existing structure.The shielding effect can reduce the surface subsidence caused by metro tunnel excavation to a certain extent,and the development trend of subsidence becomes slower as the excavation continues.

Support design method for deep soft-rock tunnels in non-hydrostatic high in-situ stress field

Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.

Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position

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.

Dynamic performance assessment of shallow buried circular tunnels under explosion hazard

In recent years,the escalation in accidental explosions has emerged as a formidable threat to tunnel infrastructures.Therefore,it is of great significance to conduct a dynamic performance analysis of the tunnels,to improve the safety and maintain the functionality of underground transport hubs.To this end,this study proposes a dynamic performance assessment framework to assess the extent of damage of shallow buried circular tunnels under explosion hazards.First,the nonlinear dynamic finite element numerical model of soil-tunnel interaction system under explosion hazard was established and validated.Then,based on the validated numerical model,an explosion intensity(EI)considering both explosion equivalent and relative distance was used to further analyze the dynamic response characteristics under typical explosion conditions.Finally,this study further explored the influence of the integrity and strength of the surrounding soil,concrete strength,lining thickness,rebar strength,and rebar rate on the tunnel dynamic performance.Our results show that the dynamic performance assessment framework proposed for shallow circular tunnels fully integrates the coupling effects of explosion equivalent and distance,and is able to accurately measure the degree of damage sustained by these structures under different EI.This work contributes to designing and managing tunnels and underground transport networks based on dynamic performance,thereby facilitating decision-making and efficient allocation of resources by consultants,operators,and stakeholders.

The role of polyurethane foam compressible layer in the mechanical behaviour of multi-layer yielding supports for deep soft rock tunnels

The polyurethane foam(PU)compressible layer is a viable solution to the problem of damage to the secondary lining in squeezing tunnels.Nevertheless,the mechanical behaviour of the multi-layer yielding supports has not been thoroughly investigated.To fill this gap,large-scale model tests were conducted in this study.The synergistic load-bearing mechanics were analyzed using the convergenceconfinement method.Two types of multi-layer yielding supports with different thicknesses(2.5 cm,3.75 cm and 5 cm)of PU compressible layers were investigated respectively.Digital image correlation(DIC)analysis and acoustic emission(AE)techniques were used for detecting the deformation fields and damage evolution of the multi-layer yielding supports in real-time.Results indicated that the loaddisplacement relationship of the multi-layer yielding supports could be divided into the crack initiation,crack propagation,strain-hardening,and failure stages.Compared with those of the stiff support,the toughness,deformability and ultimate load of the yielding supports were increased by an average of 225%,61%and 32%,respectively.Additionally,the PU compressible layer is positioned between two primary linings to allow the yielding support to have greater mechanical properties.The analysis of the synergistic bearing effect suggested that the thickness of PU compressible layer and its location significantly affect the mechanical properties of the yielding supports.The use of yielding supports with a compressible layer positioned between the primary and secondary linings is recommended to mitigate the effects of high geo-stress in squeezing tunnels.

Optimal intensity measures for longitudinal seismic response of tunnels

To study the ground motion intensity measures(IMs)suitable for the design of seismic performance with a focus on longitudinal resistance in tunnel structures,21 different seismic intensity parameters are selected for nonlinear calculation and analysis of tunnel structures,in order to determine the optimal IM for the longitudinal seismic performance of tunnel structures under different site conditions.An improved nonlinear beam-spring model is developed to calculate the longitudinal seismic response of tunnels.The PQ-Fiber model is used to simulate the longitudinal nonlinear behavior of tunnel structures and the tangential interactions between the tunnel and the soil is realized by load in the form of moment.Five different site types are considered and 21 IMs is evaluated against four criteria:effectiveness,practicality,usefulness,and sufficiency.The results indicate that the optimal IMs are significantly influenced by the site conditions.Specifically,sustained maximum velocity(V_(SM))emerges as the optimal IM for circular tunnels in soft soil conditions(CaseⅠsites),peak ground velocity(V PG)is best suited for CaseⅡsites,sustained maximum acceleration(A_(SM))is ideal for both CaseⅢand CaseⅤsites,and peak ground acceleration(A PG)for CaseⅣsites.As site conditions transition from CaseⅠto CaseⅤ,from soft to hard,the applicability of acceleration-type intensity parameters gradually decreases,while the applicability of velocity-type intensity parameters gradually increases.

Case study of performance assessment of overlapping shield tunnels with a small curve radius

Due to the network planning of subways and their surrounding structures,increasingly more overlapping shields with a small curve radius have been constructed. A newly constructed upper tunnel partly overlaps a lower one, leading to the extremely complex uplift of the lower tunnel caused by the construction of a new tunnel. Based on the shield-driven project that runs from the Qinghe Xiaoyingqiao Station to the Qinghe Station in Beijing, which adopts the reinforcement measures of interlayer soil grouting and steel supports on site, in this study, the uplift pattern of the lower tunnel and the stress characteristics of steel supports were investigated through numerical simulations and on-site monitoring.The study results show that among all tunnel segments, the first segment of the shield witnesses a maximum uplift displacement that increases with the horizontal space between tunnels. On using either interlayer soil grouting or steel-ring bracing reinforcement, the uplift of the tunnel lining exceeds the control value;by contrast,when these two measures are jointly applied, the uplift of the tunnel lining does not exceed a maximum value of 4.87 mm, which can satisfy the requirements of deformation control. Under these two joint measures, the soil strength between two stacked shield tunnels can be enhanced and the uplift deformation can be restricted with the interlayer soil grouting. Also, the segmental deformation and overall stability of the existing tunnel can be controlled with the temporary steel supports.The deformation of circumferential supports and segments is closely related to each other, and the segmental uplift is controlled by H-shaped steel supports. With the increase in the horizontal space between twin shields, the effect of the construction would gradually weaken, accompanied by a gradual reduction of the stresses of steel supports. These findings provide a valuable reference for the engineering design and safe construction of overlapping shield tunnels with a small curve radius.

Waterproofing Technology of Underground Subway Tunnels

The waterproof construction of subway tunnels is a crucial and challenging aspect of subway tunnel engineering.Mastering excellent waterproof construction technology is essential to ensure that the construction meets design requirements and guarantees the safe operation of subway lines.This paper focuses on discussing waterproof construction technology for subway station tunnels.By analyzing the main methods and techniques of underground tunnel construction,as well as the key techniques and difficulties of waterproofing construction,this paper examines the waterproofing construction project of Guangzhou Metro Culture Park Station as a case study.It analyzes the methods,quality management practices,and safety management strategies applied in the project.This paper serves as a reference for tunnel engineering design and construction units in our country,offering insights into effective waterproof construction techniques for subway tunnels.

Research on visual differences of exits of different grades of tunnels based on machine learning

Tunnels are vital in connecting crucial transportation hubs as transportation infrastructure evolves.Variations in tunnel design standards and driving conditions across different levels directly impact driver visual perception and traffic safety.This study employs a Gaussian hybrid clustering machine learning model to explore driver gaze patterns in highway tunnels and exits.By utilizing contour coefficients,the optimal number of classification clusters is determined.Analysis of driver visual behavior across tunnel levels,focusing on gaze point distribution,gaze duration,and sweep speed,was conducted.Findings indicate freeway tunnel exits exhibit three distinct fixation point categories aligning with Gaussian distribution,while highway tunnels display four such characteristics.Notably,in both tunnel types,65%of driver gaze is concentrated on the near area ahead of their lane.Differences emerge in highway tunnels due to oncoming traffic,leading to 13.47%more fixation points and 0.9%increased fixation time in the right lane compared to regular highway tunnel conditions.Moreover,scanning speeds predominantly fall within the 0.25-0.3 range,accounting for 75.47%and 31.14%of the total sweep speed.

Rock engineering evaluation of existing and planned Salang Tunnels with high overburden through Hindukush Mountains,Afghanistan

The Kabul-Mazar Highway connects Kabul,the capital of Afghanistan,to northern provinces of the country,and further extends into Central Asian countries through the Hindukush mountains.The Salang Tunnel,which is 2600 m long,was designed by Soviet engineers in 1958 and constructed using conventional techniques in 1964.During its construction,the tunnel ranked the distinction of being the highest-altitude tunnel at 3400 m.The socioeconomic importance of the tunnel is exceptionally high,as the Hindukush Mountain range to the east and south of the country is crossed by it.Since 1964,there has been a significant increase in traffic volume.Due to the narrowness of the existing tunnel,the Ministry of Public Works(MOPW)of Afghanistan has planned the con-struction of new twin-tube tunnels.Although there have been rehabilitation and enlargement efforts for the existing tunnel,none of these renovation works have been proven effective,and challenges persist.In 2008,the MOPW initiated a pre-feasibility study for new tunnels,which was finalized in 2012,presenting various options.Subsequently,in early 2018,the MOPW commenced feasibility and detailed studies,leading to the proposal of new twin-tube tunnels,which are designated as the planned tunnels in this paper.In this study,the available geotechnical and environmental data are used to evaluate the rock engineering aspects of the tunnels,including an assessment of the in-situ stress state.A particular emphasis is placed on the reassessment and design of the support system for both the existing and planned tunnels according to RMQR and another system,respectively.The evaluation of the response and stability of the tunnels is concluded,and the implications are subsequently discussed.

Large-scale shaking table test on unlined tunnel in fault zone under threedimensional earthquake

A fault is a geological structure characterized by significant displacement of rock masses along a fault plane within the Earth's crust.The Yunnan Tabaiyi Tunnel intersects multiple fault zones,making tunnel construction in fault-prone areas particularly vulnerable to the effects of fault activity due to the complexities of the surrounding geological environment.To investigate the dynamic response characteristics of tunnel structures under varying surrounding rock conditions,a three-dimensional large-scale shaking table physical model test was conducted.This study also aimed to explore the damage mechanisms associated with the Tabaiyi Tunnel under seismic loading.The results demonstrate that poor quality surrounding rock enhances the seismic response of the tunnel.This effect is primarily attributed to the distribution characteristics of acceleration,dynamic strain,and dynamic soil pressure.A comparison between unidirectional and multi-directional(including vertical)seismic motions reveals that vertical seismic motion has a more significant impact on specific tunnel locations.Specifically,the maximum tensile stress is observed at the arch shoulder,with values ranging from 60 to 100 k Pa.Moreover,NPR(Non-Prestressed Reinforced)anchor cables exhibit a substantial constant resistance effect under low-amplitude seismic waves.However,when the input earthquake amplitude reaches 0.8g,local sliding occurs at the arch shoulder region of the NPR anchor cable.These findings underscore the importance of focusing on seismic mitigation measures in fault zones and reinforcing critical areas,such as the arch shoulders,in practical engineering applications.