Knowledge of the strength of faults in the continental upper crust is critical to our understanding of crustal stress states, coseismic faulting, and lithospheric deformation. In this paper, we investigate time- and displacement-dependent fault-zone weakening (softening) over geological time caused by the hydrothermal alteration of rock, the development of faulting-related structure and fabric, and changes in the relevant deformation mechanisms. In the shallow portion of the continental seismogenic zone (< 5 km), hydrothermal alteration induced by comminution and fluid flow along fault zones progressively enriches weak phyllosilicates. The development of phyllosilicate-aligned fabric with increasing shear strain leads to an effective weakening with increasing cumulative fault displacement. In the deep portion of the seismogenic zone (> 5 km), frictional–viscous flow occurs in combination with friction contributed by phyllosilicates and the dissolution–precipitation of clasts after the introduction of water, phyllosilicates and anastomosing fabrics all increasing with greater fault displacement. In addition, the water weakening of quartz and feldspar is an important softening process in the deeper portion of the seismogenic zone (> 10 km). The smoothing of fault-zone topography by the shearing of irregularities and asperities, as well as the thickening of the fault zone, leads to a reduction over time in the bulk frictional resistance of a fault as displacement increases. These time- and displacement-dependent weakening processes of fault zones give rise to diverse strength and stress states of the crust depending on its maturity and may provide clues to reconciling the stress–heat flow paradox of crustal faults.
"}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1420564276166470912","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"70615525"},{"@type":"NRID","@value":"1000070615525"},{"@type":"ORCID","@value":"0000-0002-0064-547X"},{"@type":"NRID","@value":"9000006340681"},{"@type":"NRID","@value":"9000006340468"},{"@type":"NRID","@value":"9000413472465"},{"@type":"NRID","@value":"9000410320296"},{"@type":"NRID","@value":"9000311498090"},{"@type":"NRID","@value":"9000405103754"},{"@type":"NRID","@value":"9000410320301"},{"@type":"NRID","@value":"9000410320268"},{"@type":"NRID","@value":"9000405103742"},{"@type":"NRID","@value":"9000410320339"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/oohashik"}],"foaf:name":[{"@language":"en","@value":"OOHASHI Kiyokazu"},{"@language":"ja","@value":"大橋 聖和"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"山口大学大学院創成科学研究科"},{"@language":"en","@value":"Graduate School of Sciences and Technology for Innovation, Yamaguchi University"}]},{"@id":"https://cir.nii.ac.jp/crid/1030003658299814022","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"30216882"},{"@type":"NRID","@value":"1000030216882"},{"@type":"NRID","@value":"9000397841485"},{"@type":"NRID","@value":"9000283729260"},{"@type":"NRID","@value":"9000014140186"},{"@type":"NRID","@value":"9000391404246"},{"@type":"NRID","@value":"9000410320297"},{"@type":"NRID","@value":"9000254586008"},{"@type":"NRID","@value":"9000254150860"},{"@type":"NRID","@value":"9000237782916"},{"@type":"NRID","@value":"9000254262814"},{"@type":"NRID","@value":"9000017396142"},{"@type":"NRID","@value":"9000277863286"},{"@type":"NRID","@value":"9000021238724"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0043143"}],"foaf:name":[{"@language":"en","@value":"TAKESHITA Toru"},{"@language":"ja","@value":"竹下 徹"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"北海道大学大学院理学研究院"},{"@language":"en","@value":"Graduate School of Science, Hokkaido University"}]},{"@id":"https://cir.nii.ac.jp/crid/1420282801205377664","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"10633290"},{"@type":"NRID","@value":"1000010633290"},{"@type":"ORCID","@value":"0000-0002-5318-4646"},{"@type":"NRID","@value":"9000267805706"},{"@type":"NRID","@value":"9000016926789"},{"@type":"NRID","@value":"9000240048250"},{"@type":"NRID","@value":"9000409997403"},{"@type":"NRID","@value":"9000004626162"},{"@type":"NRID","@value":"9000258414468"},{"@type":"NRID","@value":"9000410320298"},{"@type":"NRID","@value":"9000283726126"},{"@type":"NRID","@value":"9000016572325"},{"@type":"NRID","@value":"9000297496714"},{"@type":"NRID","@value":"9000409997066"},{"@type":"NRID","@value":"9000258415415"},{"@type":"NRID","@value":"9000409997664"},{"@type":"NRID","@value":"9000258416856"},{"@type":"NRID","@value":"9000258412481"},{"@type":"NRID","@value":"9000258414060"},{"@type":"NRID","@value":"9000017483656"},{"@type":"NRID","@value":"9000258412447"},{"@type":"NRID","@value":"9000413779492"},{"@type":"NRID","@value":"9000258434933"},{"@type":"NRID","@value":"9000332226137"},{"@type":"NRID","@value":"9000386338203"},{"@type":"NRID","@value":"9000258411187"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/7000011592"}],"foaf:name":[{"@language":"en","@value":"HIRAUCHI Ken-ichi"},{"@language":"ja","@value":"平内 健一"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"静岡大学理学部地球科学科"},{"@language":"en","@value":"Department of Geoscience, Faculty of Science, Shizuoka University"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"0022135X"},{"@type":"LISSN","@value":"0022135X"},{"@type":"EISSN","@value":"18840884"},{"@type":"NDL_BIB_ID","@value":"000000014613"},{"@type":"ISSN","@value":"0022135X"},{"@type":"NCID","@value":"AN00322536"}],"prism:publicationName":[{"@language":"en","@value":"Journal of Geography (Chigaku Zasshi)"},{"@language":"ja","@value":"地学雑誌"},{"@language":"ja","@value":"地學雜誌"},{"@language":"en","@value":"J. Geogr."},{"@language":"en","@value":"Jour. Geogr."},{"@language":"en","@value":"Journal of Geography"},{"@language":"ja","@value":"地学雑"},{"@language":"en","@value":"Journal of Geography (Chigaku Zasshi)"},{"@language":"en","@value":"Journal of Geography(Chigaku Zasshi)"},{"@language":"ja","@value":"地學雜誌"}],"dc:publisher":[{"@language":"en","@value":"Tokyo Geographical Society"},{"@language":"ja","@value":"公益社団法人 東京地学協会"}],"prism:publicationDate":"2020-08-25","prism:volume":"129","prism:number":"4","prism:startingPage":"473","prism:endingPage":"489"},"reviewed":"false","url":[{"@id":"http://id.ndl.go.jp/bib/030621674"},{"@id":"https://ndlsearch.ndl.go.jp/books/R000000004-I030621674"},{"@id":"https://www.jstage.jst.go.jp/article/jgeography/129/4/129_129.473/_pdf"}],"availableAt":"2020-08-25","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=crustal%20strength%20profile","dc:title":"crustal strength profile"},{"@id":"https://cir.nii.ac.jp/all?q=brittle-plastic%20transition%20zone","dc:title":"brittle-plastic transition zone"},{"@id":"https://cir.nii.ac.jp/all?q=phyllosilicate","dc:title":"phyllosilicate"},{"@id":"https://cir.nii.ac.jp/all?q=frictional%E2%80%93viscous%20flow","dc:title":"frictional–viscous flow"},{"@id":"https://cir.nii.ac.jp/all?q=water%20weakening","dc:title":"water weakening"},{"@id":"https://cir.nii.ac.jp/all?q=the%20heat-flow%20paradox","dc:title":"the heat-flow paradox"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%9C%B0%E6%AE%BB%E5%BC%B7%E5%BA%A6%E6%96%AD%E9%9D%A2","dc:title":"地殻強度断面"},{"@id":"https://cir.nii.ac.jp/all?q=%E8%84%86%E6%80%A7%E5%A1%91%E6%80%A7%E9%81%B7%E7%A7%BB%E5%B8%AF","dc:title":"脆性塑性遷移帯"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%B1%A4%E7%8A%B6%E7%8F%AA%E9%85%B8%E5%A1%A9%E9%89%B1%E7%89%A9","dc:title":"層状珪酸塩鉱物"},{"@id":"https://cir.nii.ac.jp/all?q=%E6%91%A9%E6%93%A6%E2%80%93%E7%B2%98%E6%80%A7%E6%B5%81%E5%8B%95","dc:title":"摩擦–粘性流動"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%8A%A0%E6%B0%B4%E8%BB%9F%E5%8C%96","dc:title":"加水軟化"},{"@id":"https://cir.nii.ac.jp/all?q=%E7%86%B1%E6%B5%81%E9%87%8F%E3%83%91%E3%83%A9%E3%83%89%E3%83%83%E3%82%AF%E3%82%B9","dc:title":"熱流量パラドックス"}],"project":[{"@id":"https://cir.nii.ac.jp/crid/1040000782017323776","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"19K04015"},{"@type":"JGN","@value":"JP19K04015"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19K04015/"}],"notation":[{"@language":"ja","@value":"海洋マントルの加水反応がプレート沈み込み開始に与える影響の解明"},{"@language":"en","@value":"Influence of upper mantle hydration on the initiation of oceanic plate subduction"}]},{"@id":"https://cir.nii.ac.jp/crid/1040282256991920384","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"19H04624"},{"@type":"JGN","@value":"JP19H04624"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PUBLICLY-19H04624/"}],"notation":[{"@language":"ja","@value":"マントルウェッジ蛇紋岩の準脆性流動と深部スロー地震の関連性"}]},{"@id":"https://cir.nii.ac.jp/crid/1040282256992236928","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"19H05449"},{"@type":"JGN","@value":"JP19H05449"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-WRAPUP-19H05449/"}],"notation":[{"@language":"ja","@value":"地殻ダイナミクス －東北沖地震後の内陸変動の統一的理解－"}]}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050282813846313984","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Reaction-induced rheological weakening enables oceanic plate subduction"}]},{"@id":"https://cir.nii.ac.jp/crid/1050285700281570048","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Depth dependence of the frictional behavior of montmorillonite fault gouge: Implications for seismicity along a décollement zone"}]},{"@id":"https://cir.nii.ac.jp/crid/1360002216709061888","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Estimates of stress and strain rate in mylonites based on the boundary between the fields of grain‐size sensitive and insensitive creep"}]},{"@id":"https://cir.nii.ac.jp/crid/1360002216798563072","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fault lubrication during earthquakes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011144094087552","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fault rocks and fault mechanisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011144139586816","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Comparative mineral chemistry and textures of SAFOD fault gouge and damage-zone rocks"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011144940269696","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Continental fault structure and the shallow earthquake source"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011145360607360","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Oscillating brittle and viscous behavior through the earthquake cycle in the Red River Shear Zone: Monitoring flips between reaction and textural softening and hardening"}]},{"@id":"https://cir.nii.ac.jp/crid/1360011145474388864","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Frictional and hydrologic properties of clay‐rich fault gouge"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292618491671680","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Strain hardening and strength of clay‐rich fault gouges"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292620095253376","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Internal structure and weakening mechanisms of the San Andreas Fault"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292620560594816","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fault zone fabric and fault weakness"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292620627088000","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Similarities between Shear Zones of Different Magnitudes"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292621336184704","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Clay gouge"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298345004985216","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Earthquake size as a function of fault slip rate"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574094968934144","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The nature and origin of off-fault damage surrounding strike-slip fault zones with a wide range of displacements: A field study from the Atacama fault system, northern Chile"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095210823296","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Creep cavitation can establish a dynamic granular fluid pump in ductile shear zones"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095688133632","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Frictional heating, fluid pressure, and the resistance to fault motion"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095928105856","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fault damage zones"}]},{"@id":"https://cir.nii.ac.jp/crid/1360846641638521984","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Plastic anisotropy and fabric evolution in sheared and recrystallized quartz single crystals"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569135439872","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Evolution in H2O contents during deformation of polycrystalline quartz: An experimental study"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855569344746112","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The solid‐state flow of polymineralic rocks"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855570005949568","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Effect of clay content and mineralogy on frictional sliding behavior of simulated gouges: Binary and ternary mixtures of quartz, illite, and montmorillonite"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855570571179520","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Slip localization on the southern Alpine Fault, New Zealand"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855570878253952","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Strength of the lithosphere: Constraints imposed by laboratory experiments"}]},{"@id":"https://cir.nii.ac.jp/crid/1360855571278492288","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Hydration-phase diagrams and friction of montmorillonite under laboratory and geologic conditions, with implications for shale compaction, slope stability, and strength of fault gouge"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137043576910720","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"How thick is a fault? Fault displacement-thickness scaling revisited"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137043776145408","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fabric induced weakness of tectonic faults"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137044241792128","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"11. Friction of the Smectite Clay Montmorillonite"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137044750276480","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The process zone: A microstructural view of fault growth"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137045329746944","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The effect of mineral bond strength and adsorbed water on fault gouge frictional strength"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137046374319104","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Chlorite-smectite clay minerals and fault behavior: New evidence from the San Andreas Fault Observatory at Depth (SAFOD) core"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418519379442688","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Basal slip and mechanical anisotropy of biotite"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418519446488960","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Geology of the earthquake source: an introduction"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418520944260864","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Chapter 18 Brace-Goetze Strength Profiles, The Partitioning of Strike-slip and Thrust Faulting at Zones of Oblique Convergence, and the Stress-Heat Flow Paradox of the San Andreas Fault"}]},{"@id":"https://cir.nii.ac.jp/crid/1361418521083688192","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Recent advances in the understanding of fault zone internal structure: a review"}]},{"@id":"https://cir.nii.ac.jp/crid/1361699994784210560","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Correlation between velocity dependence of friction and strain localization in large displacement experiments on feldspar, muscovite and biotite gouge"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981468461443456","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Determination of the stress conditions of the ductile-to-brittle regime along the Asuke Shear Zone, SW Japan"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981469685607040","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fault rocks from the SAFOD core samples: Implications for weakening at shallow depths along the San Andreas Fault, California"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981470214280704","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Fluid‐rock reaction weakening of fault zones"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981471050147200","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Earthquake Repeat Time and Average Stress Drop"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981471063776512","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Frictional strengths of talc-serpentine and talc-quartz mixtures"}]},{"@id":"https://cir.nii.ac.jp/crid/1361981471365049600","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Effects of clay content on the frictional strength and fluid transport property of faults"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262943463419264","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Effect of hydration state on the frictional properties of montmorillonite‐based fault gouge"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262943808399744","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Frictional behavior of materials in the 3D SAFOD volume"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262943984070144","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Definition and classification of fault damage zones: A review and a new methodological approach"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262944185596800","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Scaling of fault damage zones with displacement and the implications for fault growth processes"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262944467505152","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Frictional dependence of gouge mixtures of quartz and montmorillonite on velocity, composition and fabric"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262944782130048","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The strength profile for bimineralic shear zones: an insight from high-temperature shearing experiments on calcite–halite mixtures"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262945414008064","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Ductile fracture of fine-grained plagioclase in the brittle–plastic transition regime: implication for earthquake source nucleation"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262945740130304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Deformation at the frictional-viscous transition: Evidence for cycles of fluid-assisted embrittlement and ductile deformation in the granitoid crust"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262946024783360","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Talc-bearing serpentinite and the creeping section of the San Andreas fault"}]},{"@id":"https://cir.nii.ac.jp/crid/1362544418673015552","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The brittle-plastic transition and the depth of seismic faulting"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825894078520192","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Earthquake scaling, fault segmentation, and structural maturity"}]},{"@id":"https://cir.nii.ac.jp/crid/1362825894289158272","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Geochemical and microstructural evidence for interseismic changes in fault zone permeability and strength,