{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:10:23Z","timestamp":1760159423567,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:00:00Z","timestamp":1759968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Large Strain-based Oil and Gas Pipe Safety Early Warning Technology","award":["GWHT20230013782","52475070"],"award-info":[{"award-number":["GWHT20230013782","52475070"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["GWHT20230013782","52475070"],"award-info":[{"award-number":["GWHT20230013782","52475070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Buried pipelines in permafrost areas are affected by harsh environments, especially those with defects and damages, which are prone to failure or even leakage accidents. However, current research is limited to single-factor analysis and fails to comprehensively consider the interaction relationships among temperature fields, moisture fields, and stress fields. Therefore, based on the thermodynamic equilibrium equation and the ice\u2013water phase transition theory, this paper constructs the temperature field equation including the latent heat of phase transition, the water field equation considering the migration of unfrozen water, and the elastoplastic stress field equation. A numerical model of the heat\u2013water\u2013force three-field coupling is established to systematically study the influence laws of key parameters such as burial depth, water content, pipe diameter, and wall thickness on the strain distribution of pipelines with defects. The numerical simulation results show that the moisture content has the most significant influence on the stress of pipelines. Pipelines with defects are more prone to damage under the action of freeze\u2013thaw cycles. Based on data analysis, the safety criteria for pipelines were designed, the strain response surface function of pipelines was constructed, and the simulation was verified through experiments. It was concluded that the response surface function has good predictability, with a prediction accuracy of over 90%.<\/jats:p>","DOI":"10.3390\/sym17101689","type":"journal-article","created":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T09:41:02Z","timestamp":1760002862000},"page":"1689","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on Safety of Pipelines with Defects in Frozen Soil Regions Based on PDE"],"prefix":"10.3390","volume":"17","author":[{"given":"Yuan","family":"Li","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Xi\u2019an Jiaotong University, Xi\u2019an 710049, China"},{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, XiaMen University, Xiamen 361000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyang","family":"Wang","sequence":"additional","affiliation":[{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Fan","sequence":"additional","affiliation":[{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wangqiang","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, XiaMen University, Xiamen 361000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanbin","family":"Li","sequence":"additional","affiliation":[{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayong","family":"Wu","sequence":"additional","affiliation":[{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Wang","sequence":"additional","affiliation":[{"name":"Construction Project Management Branch of National Petroleum and Natural Gas Pipe Network Group Co., Ltd., Langfang 065001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiqin","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, XiaMen University, Xiamen 361000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s40891-020-00228-9","article-title":"Numerical analysis of pipeline uplift resistance in frozen clay soil considering hybrid tensile-shear yield behaviors","volume":"6","author":"Akhtar","year":"2020","journal-title":"Int. J. Geosynth. Ground Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1139\/cgj-2020-0482","article-title":"Centrifuge modelling of gas pipelines undergoing freeze\u2013thaw cycles","volume":"59","author":"Dayarathne","year":"2022","journal-title":"Can. Geotech. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.geotexmem.2024.10.005","article-title":"Mitigating frost heave of a soil stabilized with sisal fiber exposed to freeze-thaw cycles","volume":"53","author":"Deng","year":"2025","journal-title":"Geotext. Geomembr."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.coldregions.2018.10.014","article-title":"Review of the state of the art: Interactions between a buried pipeline and frozen soil","volume":"157","author":"Li","year":"2019","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1007\/s11440-018-0710-1","article-title":"Centrifuge and numerical modeling of the frost heave mechanism of a cold-region canal","volume":"14","author":"Li","year":"2019","journal-title":"Acta Geotech."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103040","DOI":"10.1016\/j.coldregions.2020.103040","article-title":"Model test study on mechanical properties of pipe under the soil freeze-thaw condition","volume":"174","author":"Ma","year":"2020","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.enggeo.2019.03.013","article-title":"Pipeline\u2013permafrost interaction monitoring system along the China\u2013Russia crude oil pipeline","volume":"254","author":"Wang","year":"2019","journal-title":"Eng. Geol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1039\/tf9615701541","article-title":"The thermodynamics of frost damage to porous solids","volume":"57","author":"Everett","year":"1961","journal-title":"Trans. Faraday Soc."},{"key":"ref_9","first-page":"1","article-title":"Freezing and heaving of saturated and unsaturated soils","volume":"393","author":"Miller","year":"1972","journal-title":"Highw. Res. Rec."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108485","DOI":"10.1016\/j.oceaneng.2020.108485","article-title":"Numerical simulation of level ice\u2013structure interaction using damage-based erosion model","volume":"220","author":"Jeon","year":"2021","journal-title":"Ocean Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2136\/vzj2018.08.0157","article-title":"Simulation of soil freezing and thawing for different groundwater table depths","volume":"18","author":"Chen","year":"2019","journal-title":"Vadose Zone J."},{"key":"ref_12","first-page":"1078","article-title":"Numerical analysis of temperature fields around the buried gas pipeline in permafrost regions of Qinghai-Tibet Plateau","volume":"41","author":"Wei","year":"2019","journal-title":"J. Glaciol. Geocryol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106761","DOI":"10.1016\/j.tust.2025.106761","article-title":"The effect of ground improvement materials on the impact resistance and behavior of buried pipes: An experimental and numerical study","volume":"163","author":"Nasery","year":"2025","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2684","DOI":"10.3390\/w12102684","article-title":"The Modelling of Freezing Process in Saturated Soil Based on the Thermal-Hydro-Mechanical Multi-Physics Field Coupling Theory","volume":"12","author":"Lei","year":"2020","journal-title":"Water"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.coldregions.2018.07.008","article-title":"Numerical analysis of coupled liquid water, vapor, stress and heat transport in unsaturated freezing soil","volume":"155","author":"Yin","year":"2018","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"125603","DOI":"10.1016\/j.jhydrol.2020.125603","article-title":"Coupling analysis of the heat-water dynamics and frozen depth in a seasonally frozen zone","volume":"593","author":"Zhang","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103986","DOI":"10.1016\/j.coldregions.2023.103986","article-title":"The small-strain stiffness of frozen clay soils at different temperatures and initial water contents: Experimental study and predicted model","volume":"215","author":"Li","year":"2023","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_18","first-page":"1","article-title":"Safety assessment of corrosion-defective natural gas pipeline under ground overload based on FEM","volume":"37","author":"Zheng","year":"2021","journal-title":"M\u00e9todos Num\u00e9ricos Para C\u00e1lculo Y Dise\u00f1o En Ing. Rev. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"108965","DOI":"10.1016\/j.engfailanal.2024.108965","article-title":"Ground failure and soil erosion caused by bursting of buried water pipeline: Experimental and numerical investigations","volume":"167","author":"Chao","year":"2025","journal-title":"Eng. Fail. Anal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.undsp.2018.05.002","article-title":"Application of the finite element method for evaluating the stress distribution in buried damaged polyethylene gas pipes","volume":"4","year":"2019","journal-title":"Undergr. Space"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ijpvp.2013.03.009","article-title":"Elastic\u2013plastic fracture analyses for pipeline girth welds with 3D semi-elliptical surface cracks subjected to large plastic bending","volume":"105","author":"Zhang","year":"2013","journal-title":"Int. J. Press. Vessel. Pip."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.tafmec.2017.07.012","article-title":"Development of a strain based fracture assessment procedure for undermatched pipe girth welds subjected to bending","volume":"92","author":"Ruggieri","year":"2017","journal-title":"Theor. Appl. Fract. Mech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"106992","DOI":"10.1016\/j.oceaneng.2020.106992","article-title":"Strain-based fracture assessment for an interface crack in clad pipes under complicated loading conditions","volume":"198","author":"Zhao","year":"2020","journal-title":"Ocean Eng."},{"key":"ref_24","unstructured":"Fang, Z., Dong, S., and Duan, Y. (2025, January 24\u201326). Analysis of Remaining Strength and Failure of Submarine Pipeline with Double-Point Corrosion Defects. Proceedings of the International Petroleum and Petrochemical Technology Conference, Beijing, China."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1007\/s42452-020-2994-7","article-title":"Burst capacity analysis of pipeline with multiple longitudinally aligned interacting corrosion defects subjected to internal pressure and axial compressive stress","volume":"2","author":"Arumugam","year":"2020","journal-title":"SN Appl. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.coldregions.2009.12.007","article-title":"Modeling frost heave in freezing soils","volume":"61","author":"Bronfenbrener","year":"2010","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.coldregions.2010.01.009","article-title":"Thermal elasto-plastic computation model for a buried oil pipeline in frozen ground","volume":"64","author":"Wen","year":"2010","journal-title":"Cold Reg. Sci. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.engfracmech.2009.10.001","article-title":"J and CTOD estimation procedure for circumferential surface cracks in pipes under bending","volume":"77","author":"Chiodo","year":"2010","journal-title":"Eng. Fract. Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104944","DOI":"10.1016\/j.ijpvp.2023.104944","article-title":"Strain-based fracture analysis for internal surface cracks of X80 pipe girth welds","volume":"203","author":"Shen","year":"2023","journal-title":"Int. J. Press. Vessel. Pip."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Li, Y., Chen, S., Hou, Y., Xiao, W., Fan, L., Cai, Z., Wu, J., and Li, Y. (2025). Strain Response Analysis and Experimental Study of the Cross-Fault Buried Pipelines. Symmetry, 17.","DOI":"10.3390\/sym17040501"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"790","DOI":"10.1177\/09544089211049012","article-title":"Comparative prediction of surface roughness for MAFM finished aluminium\/silicon carbide\/aluminium trioxide\/rare earth oxides (Al\/SiC\/Al2O3)\/REOs) composites using a Levenberg\u2013Marquardt Algorithm and a Box\u2013Behnken Design","volume":"236","author":"Sharma","year":"2022","journal-title":"Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1689\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T04:39:32Z","timestamp":1760157572000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1689"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,9]]},"references-count":31,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["sym17101689"],"URL":"https:\/\/doi.org\/10.3390\/sym17101689","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,10,9]]}}}