Tunnelling and Underground Space Technology最新文献

{"title":"Study on static and dynamic mechanical properties of polyvinyl alcohol fiber EPP concrete as buffer layer of high geo-stress soft rock tunnel","authors":"Junfu Lu,&nbsp;Minrui Li,&nbsp;Kui Wang,&nbsp;Yunpeng Hu","doi":"10.1016/j.tust.2025.106763","DOIUrl":"10.1016/j.tust.2025.106763","url":null,"abstract":"<div><div>The study is based on the combined advantages of PVA fibers and EPP materials, a new PVA fiber EPP concrete was prepared as a filler material for tunnel buffer layers. 10 groups of specimens with different working conditions were designed and prepared. The failure pattern, physical and mechanical parameters and energy absorption index of the material were analyzed by static mechanical test and Hopkinson pressure bar (SHPB) dynamic compression test. The results indicate that E0 specimen showed brittle failure in static tests and SHPB tests. When PVA fiber and EPP beads were added to the specimen, the failure mode of the specimen changed from brittle failure to ductile failure, and the specimen shows typical core-remaining failure under impact load. The static test results reveal that EPP volume content significantly influences the axial compressive strength, elastic modulus, and confined compressive strength of PVA fiber EPP concrete, while fiber content has the most pronounced impact on splitting tensile strength, Poisson ratio, and dynamic compressive strength. the confined uniaxial compression ontological relationship of PVA fiber EPP concrete under confined compression was established by confined uniaxial compression test, and the formula fitting was carried out. The fitting results were in good agreement with the test data. Based on the stress–strain curve of confined compression, the static energy absorption performance of PVA fiber EPP concrete was discussed. The results show that the energy absorption effect of E60-P18-1.2 concrete is the best; The results of SHPB test showed that comparing the energy absorption value and dissipation rate of each group of specimens under 0.06 MPa air pressure, it was found that the concrete of E50-P12-0.7 had the best energy absorption effect under dynamic compression. These studies provide a valuable theoretical basis for optimizing the design of tunnel buffer layers.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106763"},"PeriodicalIF":6.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Visualizing the full-field stress and plastic zones in arch tunnel surrounding rocks embedded with roadway-scale discontinuities using 3D printed transparent models and stress freezing techniques","authors":"Yang Ju ,&nbsp;Dongyi Xing ,&nbsp;Shanyong Wang ,&nbsp;Zhangyu Ren ,&nbsp;Changbing Wan","doi":"10.1016/j.tust.2025.106772","DOIUrl":"10.1016/j.tust.2025.106772","url":null,"abstract":"<div><div>Embedded roadway-scale discontinuities present significant risks to the safety of underground tunnels. Their effects on the stress distribution, plastic zone development, and failure behavior must be systematically analyzed for optimizing the tunnel design and support systems. However, accurately quantifying the full-field stress and visualizing failure processes in 3D tunnels through laboratory experiments and numerical simulations remains challenging. This study proposes a novel experimental system that integrates 3D printing, stress-freezing, and digital photoelasticity techniques to address the challenges associated with the preparation of structurally complex tunnel models, quantitative analysis of stress and plastic zones, and visualization of failure behaviors. The 3D experimental results indicate that the embedded structural plane exhibits considerable stress localization and blocking effects. The stress concentration and plastic zones are primarily located at the structural plane ends and on regions far from the structural plane. Furthermore, the presence of the structural plane significantly alters the failure mode of the tunnel, presenting pronounced regional failure characteristics. The 3D experiments in this study consider the influence of the model thickness direction and structural plane effects, which are typically neglected in simplified 2D analyses. Consequently, more realistic insights into the distribution and evolution of stress, plastic zones, and failure behaviors within tunnels are obtained. The mechanisms and principles realized through these laboratory experiments present new perspectives for optimizing and further improving the tunnel design and support systems. Furthermore, they present a scientific basis and valuable reference for subsequent numerical simulations of engineering-scale, structurally complex tunnel systems.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106772"},"PeriodicalIF":6.7,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimization study on artificial ground freezing in elliptical tunnel construction: A comprehensive analysis of groundwater flow and thermodynamic parameters of soil","authors":"Gyu-Hyun Go ,&nbsp;Viet Dinh Le","doi":"10.1016/j.tust.2025.106774","DOIUrl":"10.1016/j.tust.2025.106774","url":null,"abstract":"<div><div>Recently, there has been a growing interest in the use of Artificial Ground Freezing (AGF) to temporarily stabilize unstable ground at tunnel construction sites. Recognizing that the effectiveness of this method is significantly influenced by groundwater flow, it is crucial to conduct a sophisticated thermal-hydraulic coupling analysis to assess the potential adverse effects of groundwater flow in the artificial ground freezing process. This study establishes a numerical analysis model to evaluate the efficiency of AGF and proposes a novel design approach for freeze pipe layouts in elliptical tunnel face under conditions of excessive groundwater flow. These design concepts are implemented using a Gravitational Search Algorithm (GSA) and the COMSOL Multiphysics platform integrated with MATLAB. Furthermore, the study employs a constructed simulation model to analyze and assess the sensitivity of thermodynamic parameters concerning the efficiency of AGF under groundwater flow conditions. The findings contribute valuable insights to the field of tunnel construction and ground stabilization.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106774"},"PeriodicalIF":6.7,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Study on effect of fibers reinforcement on sand soil liquefaction mitigation and shield tunnel stability under seismic conditions","authors":"Jun Shen ,&nbsp;Xiaohua Bao ,&nbsp;Xiangsheng Chen ,&nbsp;Zhizao Bao ,&nbsp;Hongzhi Cui","doi":"10.1016/j.tust.2025.106765","DOIUrl":"10.1016/j.tust.2025.106765","url":null,"abstract":"<div><div>Fiber reinforcement has been demonstrated to mitigate soil liquefaction, making it a promising approach for enhancing the seismic resilience of tunnels in liquefiable strata. This study investigates the seismic response of a tunnel embedded in a liquefiable foundation locally improved with carbon fibers (CFs). Consolidated undrained (CU), consolidated drained (CD), and undrained cyclic triaxial (UCT) tests were conducted to determine the optimal CFs parameters, identifying a fiber length of 10 mm and a volume content of 1 % as the most effective. A series of shake table tests were performed to evaluate the effects of CFs reinforcement on excess pore water pressure (<em>EPWP</em>), acceleration, displacement, and deformation characteristics of both the tunnel and surrounding soil. The results indicate that CFs reinforcement significantly alters soil-tunnel interaction dynamics. It effectively mitigates liquefaction by enhancing soil stability and slowing <em>EPWP</em> accumulation. Ground heave is reduced by 10 %, while tunnel uplift deformation decreases by 61 %, demonstrating the stabilizing effect of CFs on soil deformation. The fibers network interconnects soil particles, improving overall structural integrity. However, the increased shear strength and stiffness due to CFs reinforcement amplify acceleration responses and intensify soil-structure interaction, leading to more pronounced tunnel deformation compared to the unimproved case. Nevertheless, the maximum tunnel deformation remains within 3 mm (0.5 % of the tunnel diameter), posing no significant structural risk from the perspective of the experimental model. These findings provide valuable insights into the application of fibers reinforcement for improving tunnel stability in liquefiable foundations.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106765"},"PeriodicalIF":6.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The effect of ground improvement materials on the impact resistance and behavior of buried pipes: An experimental and numerical study","authors":"Mohammad Manzoor Nasery ,&nbsp;Elif Ağcakoca ,&nbsp;Sedat Sert ,&nbsp;Mohammad Saber Sadid ,&nbsp;Zeynep Yaman","doi":"10.1016/j.tust.2025.106761","DOIUrl":"10.1016/j.tust.2025.106761","url":null,"abstract":"<div><div>Buried pipes are subjected to static and dynamic loads depending on their areas of use. To mitigate the risk of damage caused by these effects, various materials and reinforcement methods are utilized. In this study, five buried uPVC pipes designed in accordance with ASTM D2321 standards were reinforced with three different ground improvement materials: Geocell, Geonet, and Geocomposite, and experimentally subjected to dynamic impact loading. Acceleration, velocity, and displacement values were obtained from the experiments. Subsequently, finite element analysis (FEA) was performed using the ABAQUS software to determine stress values and volumetric displacements in the pipes, and the model was validated with a 5–7% error margin. In the final stage of the study, a parametric analysis was conducted by modifying the soil cover height above the pipe and the Geocell thickness in the validated finite element model. The parametric study revealed that the displacement value in the pipe decreased by 78% with an increase in soil cover height, while a 16% reduction was observed with an increase in Geocell thickness. The results demonstrate that the soil improvement techniques examined in this study provide an effective solution for enhancing the impact resistance of buried pipeline systems.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106761"},"PeriodicalIF":6.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel pressure-resistant isolation layer for tunnels and performance analysis","authors":"Qingcheng Yang ,&nbsp;Ping Geng ,&nbsp;Yan Zhao ,&nbsp;Song Wang ,&nbsp;Changjian Chen ,&nbsp;Qi Wang","doi":"10.1016/j.tust.2025.106766","DOIUrl":"10.1016/j.tust.2025.106766","url":null,"abstract":"<div><div>After the installation of rubber isolation layer in tunnels, surrounding rock convergence may apply permanent pressure on the tunnel, compressing the isolation material. This can reduce its elasticity, impairing its recovery capacity and potentially leading to failure. Therefore, this paper proposes a new type of pressure-resistant isolation layer that embeds the compressive layer into the energy dissipation layer. Indoor testing of the material was carried out to obtain the test data, and parameters were fitted based on a phenomenological hyperelastic constitutive model, and the fitting effect was evaluated and verified. On the basis, a numerical model was established to investigate the static load-bearing capacity, seismic isolation, and energy dissipation performance of the compressive layer’s polyurethane material within the pressure-resistant isolation layer under varying aperture sizes and hardness. The results show that: compared with the rubber isolation layer, the pressure-resistant isolation layer reduces compression rates by 13.3% to 18.3% under static load. Under seismic action, the acceleration reduction rate is reduced by approximately 10%, while the stress reduction rate of the lining increases by around 20%, and the energy dissipation effect improves by 15%. This demonstrates that the pressure-resistant isolation layer effectively improves static load-bearing capacity, energy dissipation, and reduces lining stress. Additionally, its isolation performance is significantly influenced by parameters such as the aperture size and hardness of the compressive layer.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106766"},"PeriodicalIF":6.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic characteristics and energy absorption mechanism of prestressed anchorage support","authors":"Qi Wang,&nbsp;Mingzi Wang,&nbsp;Shuo Xu,&nbsp;Bei Jiang,&nbsp;Rugang Duan","doi":"10.1016/j.tust.2025.106759","DOIUrl":"10.1016/j.tust.2025.106759","url":null,"abstract":"<div><div>In deep underground engineering construction and resource exploitation, complex conditions such as high stress and strong disturbance are often encountered, and dynamic disasters such as rockburst and coal burst are prone to occur. As a common anchorage support form in deep underground engineering, bolts and cables are often applied with high prestress to improve the bearing capacity of surrounding rock. It is the key to the reasonable support design of deep underground engineering to clarify the dynamic characteristics of prestressed anchorage support. Therefore, the dynamic impact test system of prestressed anchorage support is developed. Taking the commonly used high-strength (HS) support and the self-developed constant resistance energy-absorbing (CREA) support as the research objects, the dynamic impact tests are carried out. The test results show that applying high prestress significantly weakens the impact resistance and energy absorption capacity of anchorage support. Compared with the non-prestressed condition, the average impact force of HS bolt with 100kN prestress and HS cable with 250kN prestress is reduced by 56.2% and 43.3%, with energy absorption reduced by 17.8% and 19.6%, respectively. The average impact force of CREA bolt with 160kN prestress and CREA cable with 250kN prestress is reduced by 64.3% and 79.5%, with energy absorption reduced by 25.4% and 22.9%, respectively. The linear relationship between the energy absorption reduction rate and the strength utilization rate is revealed. The design method of anchorage support based on the strength-energy comprehensive criterion is proposed. The field application is successfully carried out in deep underground engineering influenced by dynamic pressure.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106759"},"PeriodicalIF":6.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prediction on the degradation process of steel fiber-reinforced concrete lining of a ‘Deep Tunnel’ under sulfuric acid corrosion","authors":"Qihang Xu ,&nbsp;Xin Huang","doi":"10.1016/j.tust.2025.106764","DOIUrl":"10.1016/j.tust.2025.106764","url":null,"abstract":"<div><div>Sulfuric acid corrosion poses a significant threat to urban ‘deep tunnel’ systems, exacerbating flood disasters and causing economic losses. Therefore, it is crucial to predict the deterioration process of steel fiber-reinforced concrete under sulfuric acid corrosion. This study developed four predictive models for the degradation process of steel fiber-reinforced concrete of ‘deep tunnel’ lining during service characterized by the corrosion depth and strength loss under sulfuric acid corrosion. The database consisted of various numerical data obtained from a validated numerical model. Based on correlation and grey relational analysis, the concrete’s historical maximum load, initial corrosion depth, and load for 10 time points were selected as input data, while the output parameters are the corrosion depth and strength loss at these 10 time points. It was found that the Transformer-LSTM model not only exhibited the highest prediction accuracy but also demonstrated robust performance in the continuous prediction mode. Furthermore, after incorporating additional training data, the Transformer-LSTM model was able to predict the variation in corrosion depth and strength loss of steel fiber-reinforced concrete under sulfuric acid corrosion over a 120-year period under different loading conditions, which gives the maximum corrosion depth of 8.00 mm and strength loss of 15.06 MPa, with maximum prediction errors of 0.37 mm and 0.63 MPa, respectively. This prediction model can effectively capture the deterioration process of steel fiber-reinforced concrete under sulfuric acid corrosion during the service life of ‘deep tunnel’ structures, thereby, offering valuable guidance on scheduled maintenance and corrosion area repairs for the long-term serviceability of ‘deep tunnel’ structures.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106764"},"PeriodicalIF":6.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Identification of segment joint and automatic segmentation for shield tunnel based on LiDAR detection","authors":"Shui-Long Shen ,&nbsp;Jia-Xuan Zhang ,&nbsp;Yu-Lin Chen ,&nbsp;Annan Zhou","doi":"10.1016/j.tust.2025.106758","DOIUrl":"10.1016/j.tust.2025.106758","url":null,"abstract":"<div><div>This study presents a novel method for identifying joints and automatically segmenting shield tunnels using light detection and ranging (LiDAR). In cylindrical coordinates, the Hough transform is used to extract feature LiDAR data corresponding to ring joints at different azimuths. This feature extraction using LiDAR data facilitates the computation of ring joint feature coordinates and average ring joint width. Subsequently, the M−estimator Sample Consensus (MSAC) algorithm is used to fit the plane containing the ring joint, resulting in successful recognition and segmentation of ring joints within the tunnel LiDAR data. Following the segmentation of the LiDAR data into distinct ring LiDAR data, the three-sigma (3<em>σ</em>) criterion is used to extract coordinates of longitudinal joint endpoints. The average width of the longitudinal joints is then determined. In cases where extraction of the longitudinal joint points is challenging, the azimuth difference in the design model is leveraged to calculate the azimuths. This approach enables joint recognition within LiDAR data as well as the geometric segmentation of individual segments. The proposed method is validated using a case study from Luoyang Metro Line 2. The results indicate that the segmentation method can accurately extract the majority of the ring and longitudinal joints. Moreover, these results are useful for not only monitoring structural health but also developing a building information model (BIM) for the tunnel.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106758"},"PeriodicalIF":6.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extraction of image fractal characteristics of rock chips based on the Sandbox method and analysis of shield tunneling performance","authors":"Changbin Yan ,&nbsp;Yuxuan Shi ,&nbsp;Zihe Gao ,&nbsp;Weiwei Zhan","doi":"10.1016/j.tust.2025.106751","DOIUrl":"10.1016/j.tust.2025.106751","url":null,"abstract":"<div><div>The size distribution of rock chips can fully reflect the performance of shield machine, and existing size distribution indicators suffer from low efficiency and poor accuracy. Therefore, the aim is to find an accurate and rapid quantitative indicator to characterize the rock chips size distribution and address the engineering issues of shield machine rock-breaking efficiency analysis and tunneling parameter optimization. In this study, five groups of rock chips with different quality components and eight shooting heights were designed to explore the performance and applicability of the image fractal dimension (<em>D</em>), a quantitative indicator of rock chip size distribution based on the Sandbox fractal method, and also to compare it with the traditional Box-counting method. Additionally, an analysis of 136 groups of rock chips data from different surrounding rock grades was conducted to investigate the correlation between image fractal dimension and common shield performance indexes, such as the average single cutter thrust force (<em>F</em>_n), and penetration depth (<em>P</em>_rev). The results indicate that the experimental platform constructed in this study, with image data acquired at a shooting height of 120 cm, is well-suited for calculating image fractal dimension. Compared to the traditional Box-counting method, the Sandbox method demonstrates higher sensitivity to changes in the particle size distribution of rock chips and does not impose restrictions on input image size, making it more appropriate for quantitative analysis. The image fractal dimension decreases as the proportion of large-sized rock chips increases. Under the same surrounding rock conditions, the image fractal dimension of rock chips is positively correlated with the logarithm of specific energy (<em>SE</em>) and negatively correlated with the logarithm of coarseness index (<em>CI</em>), effectively reflecting shield rock-breaking efficiency. Based on the correlation between image fractal dimension and <em>SE</em>, the optimal ranges of <em>F</em>_n and <em>S</em>/<em>P</em>_rev under grade II, III, IV, and V surrounding rock conditions can be determined, thereby enabling the optimization of tunneling performance.</div></div>","PeriodicalId":49414,"journal":{"name":"Tunnelling and Underground Space Technology","volume":"163 ","pages":"Article 106751"},"PeriodicalIF":6.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144147429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}