Soil Dynamics and Earthquake Engineering最新文献

{"title":"A DPIM-GFDM-PML framework for the modelling of stochastic response of elastic wave propagation in viscoelastic media","authors":"Mingjuan Li ,&nbsp;Hanshu Chen ,&nbsp;Zhuochao Tang ,&nbsp;Xiaoying Zhuang ,&nbsp;Wenzhi Xu ,&nbsp;Zhuojia Fu","doi":"10.1016/j.soildyn.2025.109838","DOIUrl":"10.1016/j.soildyn.2025.109838","url":null,"abstract":"<div><div>The stochastic response analysis of elastic wave propagation in viscoelastic media is critical for applications in seismic engineering, geological exploration, coastal engineering and non-destructive testing of composite materials. Conventional studies predominantly rely on deterministic models, neglecting the spatial inhomogeneity and parameter randomness. This study proposes a non-intrusive stochastic framework, DPIM-GFDM-PML, integrating the Direct Probability Integral Method (DPIM), the Generalized Finite Difference Method (GFDM), and the Perfectly Matched Layer (PML) technique. Parameter uncertainties are modeled via Karhunen-Loève (K-L) expansion and embedding stochastic fields into frequency-domain governing equations using the GFDM discretization and the PML boundary treatment, establishing a mapping between stochastic inputs and physical responses. DPIM further decouples governing equations from probability density integration, enabling efficient computation of response probability density functions (PDFs) through Gaussian kernel smoothing. Three numerical examples, namely infinite-domain cavities, multi-cavity domain, and complex multilayered media, demonstrate that the proposed framework captures the stochastic characteristics of wave propagation accurately and efficiently. Compared to Monte Carlo simulation (MCS), the DPIM achieves consistent probabilistic results with three orders of magnitude fewer samples, thereby achieving high computational efficiency while maintaining accuracy. Key quantitative findings reveal that multi-parameter coupling amplifies displacement variance by nearly two orders of magnitude and significantly increases the coefficient of variation; whereas increasing the spatial correlation length reduces variance by 14–27 %. The results reveal that spatial randomness in material properties significantly affects wave behavior, with the combined effects of multiple stochastic parameters playing a dominant role. This framework provides a novel and effective tool for uncertainty quantification in viscoelastic wave dynamics.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109838"},"PeriodicalIF":4.6,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145181306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep learning for the localization of seismic sources based on synthetic full waveform and wavelet de-noising","authors":"Ju Ma ,&nbsp;Jiaolan Hou ,&nbsp;Boyang Fang ,&nbsp;Peicong Wang ,&nbsp;Shuang Wu ,&nbsp;Zhaojun Qi","doi":"10.1016/j.soildyn.2025.109832","DOIUrl":"10.1016/j.soildyn.2025.109832","url":null,"abstract":"<div><div>Seismic source localization is an essential technique for the study of earthquakes. Accurate seismic source localization is important in seismic risk assessment. Various machine learning-based methods for earthquake monitoring and source localization have been proposed, along with the development of source localization techniques. However, these methods require a large amount of historical data for training, and acquiring the required data using monitoring stations may take years or even decades. Moreover, the acquired data often contain various seismic noise types that can affect the calculation results. To address this problem, we combine wavelet de-noising with convolutional neural network (CNN) to achieve fast source localization without any historically cataloged events. The results show that adding the wavelet de-noising technique improves the proposed model. In addition, provided that the regional model is known a priori, the method has a wide range of applications. For example, it can be applied to scenarios such as rock bursts in mines, microseismic events generated by mining, or big earthquakes. Based on this approach, we also have the potential to build a picking-free, non-historical catalog, noise-robust, and fully automated location method.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109832"},"PeriodicalIF":4.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157694","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seismic isolation of railway bridges isolated with a novel multi-stage friction bearing","authors":"S. Zou ,&nbsp;H.L. Wang ,&nbsp;Z.P. Zhai ,&nbsp;H.S. Wenliuhan ,&nbsp;C.X. Qu ,&nbsp;C.B. Zhang","doi":"10.1016/j.soildyn.2025.109829","DOIUrl":"10.1016/j.soildyn.2025.109829","url":null,"abstract":"<div><div>Conventional bridges are highly vulnerable to strong and mega-earthquakes. To improve seismic performance and achieve controllable structural behavior under high-intensity ground motions, this study introduces a novel Multi-stage Friction Bearing (MSFB) featuring a multi-stage activation mechanism. The bearing provides three-stage functionality—“rigid connection → friction damping → potential energy-based displacement restriction”—through its composite horizontal and inclined sliding surfaces. The research methodology encompasses three key phases: First, the restoring force model of the MSFB across its distinct operational stages is derived through theoretical analysis. Subsequently, comprehensive mechanical performance tests validate the accuracy of this model. Finally, the effectiveness of the MSFB in controlling the seismic response is evaluated through numerical simulations of a realistic three-span simply supported girder bridge. The findings demonstrate that the MSFB successfully implements its three-stage mechanism, transitioning smoothly between stages based on seismic excitation intensity. Under moderate earthquakes, the MSFB functions as an effective isolator, elongating structural periods and dissipating seismic energy. During major earthquakes, it acts as an effective displacement-restriction device, mitigating seismic damage risks of by preventing girder unseating and superstructure collisions.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109829"},"PeriodicalIF":4.6,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Passive or active control of an actual building under earthquakes using rolling rim-type TMD: A comparative study","authors":"Ngoc-An Tran ,&nbsp;N.D. Anh ,&nbsp;Ngoc-Linh Nguyen ,&nbsp;Hai-Le Bui ,&nbsp;Huong Quoc Cao","doi":"10.1016/j.soildyn.2025.109828","DOIUrl":"10.1016/j.soildyn.2025.109828","url":null,"abstract":"<div><div>In this study, for the first time, a novel damper -rolling rim-type tuned mass damper (rolling rim-type TMD) - is developed to passively or actively control the dynamic response of buildings under earthquakes. First, the equations of motion for multi-floor building structures with an installed rolling rim-type TMD on the top floor are established. Next, the parameters of the damper are determined based on the passive control problem by optimizing with the objective function of minimizing the vibration amplitude of the main structure. The design variables include the stiffness and damping coefficient of the damper. Additionally, the damper's performance in the active control case is also investigated by supplementing it with a control force. The linear–quadratic regulator (LQR) is used to determine the rule for the active control force. The damping effectiveness of the traditional and rolling disk-type TMDs is also compared with the proposed damper. The numerical investigations show that the proposed damper has higher efficiency in reducing the main structure's dynamic responses and has a smaller displacement than the remaining dampers. Furthermore, it also demonstrates stability when the structure is subjected to different earthquakes and robustness when the stiffness of the structure changes. The advantages of the proposed damper in terms of damping effectiveness and operational space highlight its potential for application in structures under dynamic loads.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109828"},"PeriodicalIF":4.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 strain rate enhanced continuum damage model for rocks subjected to dynamic loading","authors":"Sachin Kumar,&nbsp;Arghya Das,&nbsp;Gaurav Tiwari","doi":"10.1016/j.soildyn.2025.109819","DOIUrl":"10.1016/j.soildyn.2025.109819","url":null,"abstract":"<div><div>Deformation and failure mechanisms of rocks are dependent on the imposed loading rate and its range, like quasi-static and dynamic. This study proposes a continuum damage model (CDM) to predict the rate-dependent deformation response of rocks subjected to dynamic compressive (impact) load. The model formulation considers the coupling of damage and plasticity in the dissipative stress space, while compressive damage alone governs the yielding in the true stress space. Strain rate effects under dynamic conditions are accounted for through a Perzyna-type viscoplastic formulation using an overstressed function of the yield equation of CDM. A fully implicit stress integration scheme is adopted for finite element (FE) implementation of the model as a user-defined material. Further, it is demonstrated that the proposed strain rate enhancement can regularise the model to overcome bifurcation instability and associated mesh sensitivity during numerical simulations. The FE model is validated against the experimental results of three types of rocks (rock-like material, marble and sandstone). The model predicts the impact loading response of rock, especially constitutive response, post-peak structural response, and energy dissipation at varying strain rates in agreement with the experimental results, requiring fewer parameters than similar classes of other existing CDMs. The model response indicates that localised damage evolution is strain rate sensitive, and its intensity and distribution across the sample increase with the increment in strain rates. Further, the analysis shows that the dynamic loading response is highly sensitive to the exponent used for defining the Perzyna overstressed function, while insensitive under quasistatic loading conditions.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109819"},"PeriodicalIF":4.6,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assessment of seismic ground motion incoherency induced by subsurface topography using dynamic centrifuge tests","authors":"Dong-Hyeong Choi ,&nbsp;Hak-Sung Kim ,&nbsp;Yonghee Lee ,&nbsp;Tae-Hyuk Kwon","doi":"10.1016/j.soildyn.2025.109834","DOIUrl":"10.1016/j.soildyn.2025.109834","url":null,"abstract":"<div><div>Seismic ground motion incoherency due to spatial variability has a significant impact on soil-foundation-structure systems, including vital infrastructures such as nuclear power plants, long-span bridges, and pipelines. For the first time, this study employs dynamic centrifuge tests to investigate ground motion coherency functions affected by subsurface topography. A fleet of earthquakes was excited to the soil models with flat and inclined layering, each, and the coherency functions at the ground surface were compared across different separation distances and frequency bands. The analysis reveals that topography significantly influences seismic coherency, with a greater incoherency observed in the inclined layering case. Additionally, a comparison of coherency at the surface and the deeper depth indicates that the greater surface-to-bedrock depth results in a more pronounced incoherency effect. This study demonstrates the feasibility of using well-controlled physical modelling to explore seismic ground motion incoherency caused by ray-path effect. The results are expected to elucidate how local conditions affect seismic coherency, thereby enhancing infrastructure stability solutions.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109834"},"PeriodicalIF":4.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semi-analytical solution for ground vibrations of a finite soil layer induced by symmetrical vertical distributed loads","authors":"Cheng Yue ,&nbsp;Qijian Liu","doi":"10.1016/j.soildyn.2025.109824","DOIUrl":"10.1016/j.soildyn.2025.109824","url":null,"abstract":"<div><div>This study presents a semi-analytical solution for ground vibrations of a three-dimensional elastic soil layer induced by vertically distributed loads based on the wave function expansion method and the Fourier–Bessel expansion method. The generating wave fields are constructed using the method of the separation of variables. General expressions for the displacement and stress components are derived based on Hooke’s law and the theory of small-strain elasticity. Wave potentials and the vertically distributed loads are transformed into Fourier–Bessel series with the given calculation range. A boundary value problem involves displacement-fixed boundary conditions at the rigid base and stress-given boundary conditions along the ground surface, resulting in a series of algebraic equations. Unknown coefficients are numerically solved by truncating the series numbers. Contour integrals, including branch points and poles in Lamb-type problems, are circumvented using Fourier–Bessel series expansion methods. A parametric study is conducted to investigate the ground vibrations of the soil layer under time-harmonic vertically distributed loads. Numerical results reveal that the soil damping ratio, slenderness ratio, and non-dimensional frequency of loading have a significant influence on the ground motions. Resonance occurs when the load frequency matches the first natural frequency of the soil layer. Higher load frequencies result in more concentrated dynamic effects but narrower vibration ranges.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109824"},"PeriodicalIF":4.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 seismic dynamic failure of tunnel-soil-frame structure system through shaking table test and numerical simulation","authors":"Xiaogang Wei ,&nbsp;Zhifan Qin ,&nbsp;Shiao Wang ,&nbsp;Shuaixin Ma ,&nbsp;Mengqing Shi ,&nbsp;Runze Zhang ,&nbsp;Junheng Guo ,&nbsp;Shasha Lu","doi":"10.1016/j.soildyn.2025.109825","DOIUrl":"10.1016/j.soildyn.2025.109825","url":null,"abstract":"<div><div>To investigate the dynamic response characteristics of an underground structure–soil–aboveground structure interaction system under seismic loading, a shaking table test based on a metro section in Zhengzhou was conducted. A three-dimensional numerical model including both aboveground and underground structures was developed in ABAQUS. Four typical working conditions and three representative seismic motions were selected. Key response parameters such as acceleration, shear force, bending moment, and inter-story drift angle of the tunnel and frame structures were systematically analyzed. Results reveal strong dynamic coupling between the aboveground and underground structures. The integrated system significantly alters seismic wave propagation and energy distribution, showing a “near-field attenuation and far-field amplification” pattern, with an influence range up to 33.3 times the structural width. The aboveground frame dissipates part of the seismic energy near the site center, reducing peak acceleration by 2.75 % and delaying amplification at around 86 m and 92 m. Meanwhile, the tunnel causes non-uniform far-field amplification. With aboveground structures, tunnel acceleration becomes more spatially uneven, with a 5 % increase in peak response at the center section, indicating stronger localized effects due to wave path disturbance. In terms of internal forces, without the aboveground frame, the tunnel shows pronounced nonlinear responses, with peak shear force and bending moment reaching ±4 × 10⁴ N and ±1 × 10⁵ N m, revealing potential weak zones. With the frame present, although peak shear increases to ±1.2 × 10⁵ N, force distribution becomes smoother and more delayed, reflecting an “energy storage–release” effect that buffers seismic impact. Inter-story drift angles in the aboveground structure are also affected by the tunnel; the maximum drift increases from 0.021 % to 0.030 %, following a “larger at the bottom, smaller at the top” pattern, indicating reduced stiffness in lower stories and an enhanced soft-story effect. Under RSN32 input, resonance with low-order modes causes a significant increase in bottom-story response and more variability across different input motions, highlighting increased sensitivity to seismic frequency. Overall, the dynamic coupling in such systems profoundly affects seismic response in dense urban areas, and seismic design should account for these interactions to enhance structural resilience.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109825"},"PeriodicalIF":4.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating annular baffle performance to enhance characteristics of isolated cylindrical TLD for improved mitigation of earthquake-induced vibrations in high-rise buildings","authors":"Shahin Farahmandpey,&nbsp;Seyed Mehrab Amiri","doi":"10.1016/j.soildyn.2025.109816","DOIUrl":"10.1016/j.soildyn.2025.109816","url":null,"abstract":"<div><div>This research explores the potential of an isolated cylindrical Tuned Liquid Damper (TLD) with an annular baffle to function as a multi-role system for high-rise buildings, simultaneously mitigating earthquake-induced vibrations and suppressing liquid sloshing. The inherent symmetric dynamic response of cylindrical TLDs offers advantages over rectangular designs; however, tuning steel cylindrical tanks to match the low natural frequencies typically found in high-rise buildings remains a considerable challenge. To overcome this tuning challenge for broad cylindrical TLDs, Laminated Rubber Bearings (LRB) are utilized. The study investigates how the annular baffle, traditionally known to increase base shear, can be strategically employed to enhance vibration damping in a 10-story building while also ensuring liquid stability under earthquake excitations. Employing Coupled Acoustic-Structure Interaction (CAS) analysis with a mid-mounted baffle, the results show that the annular baffle can provide significant improvements: a 17.7 % reduction in top-story maximum relative displacement (compared to 13.6 % without a baffle), a 5.5 % greater decrease in the standard deviation of relative displacement, and increased resistance forces. Notably, the average sloshing displacement is reduced by 20.6 %. The findings confirm that the annular-baffled, isolated cylindrical TLD offers superior performance in both vibration control and sloshing suppression, facilitating its dual use and enabling broader, architecturally and structurally viable tank designs.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109816"},"PeriodicalIF":4.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Comparative assessment of surface and body wave methods for shear wave velocity profiling in Almaty basin","authors":"Shynggys Abdialim ,&nbsp;Sung-Woo Moon ,&nbsp;Jong Kim ,&nbsp;Yeraly Shokbarov ,&nbsp;Vitaliy Khomyakov","doi":"10.1016/j.soildyn.2025.109765","DOIUrl":"10.1016/j.soildyn.2025.109765","url":null,"abstract":"<div><div>Almaty is located near seismically active faults, where periodic earthquakes pose a sig-nificant hazard. Although no large earthquakes have occurred in recent years, historical records indicate past events with substantial casualties. Accurate characterization of dy-namic soil properties is essential for appropriate seismic design, with shear wave velocity (<span><math><mrow><msub><mi>V</mi><mi>s</mi></msub></mrow></math></span>) being the most widely used parameter for site classification. In many practical cases, budget constraints limit site investigations to a single <span><math><mrow><msub><mi>V</mi><mi>s</mi></msub></mrow></math></span> estimation method, potentially introducing methodological bias. This study aims to evaluate and compare the performance of non-invasive surface wave techniques and body wave-based methods in estimating <span><math><mrow><msub><mi>V</mi><mi>s</mi></msub></mrow></math></span> pro-files across multiple sites in Almaty. Multichannel analysis of surface waves (MASW) and ellipticity curve inversion derived from horizontal-to-vertical spectral ratio (HVSR) measure-ments were employed at surface wave techniques. Their results were benchmarked against those obtained from seismic refraction and seismic dilatometer tests (SDMT), the latter being the only invasive method used. Among all techniques, SDMT – based on the true-interval approach – provided direct and high-resolution <span><math><mrow><msub><mi>V</mi><mi>s</mi></msub></mrow></math></span> measurements. However, surface wave methods demonstrated sufficient accuracy, with <span><math><mrow><msub><mi>V</mi><mrow><mi>s</mi><mn>30</mn></mrow></msub></mrow></math></span> values in good agreement with those from invasive methods. Given their cost-effectiveness and practical applicability, sur-face wave techniques are recommended as reliable alternatives for evaluating dynamic soil properties in urban environments such as Almaty.</div></div>","PeriodicalId":49502,"journal":{"name":"Soil Dynamics and Earthquake Engineering","volume":"200 ","pages":"Article 109765"},"PeriodicalIF":4.6,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}