Fractal Analyses of Fractures, Grain Boundaries and Pore Structures of Granite and its Relation to Material Transport and Rheology.

Abstract

Fractal geometrical analyses of fractures, grain boundaries and pore size ditributions in a typical fresh granite from Inada, Japan have been studied in order to quantitatively characterize transport properties of rock textures. Box counting method reveals that these textures have fractal nature for scale ranges from 25 nm to 10 mm and their box fractal dimensions are estimated to be around 1.5. Microcrack ditributions in feldspars have higher fractal dimensions than those in quartz showing more tortuous nature. This observation is in agreement with two diffusion pathways having different tortuosities proposed on the same granite. Fractal analyses of fracture networks in a granite bore hole have indicated that the fractal dimension can also be an indicator of groundwater permeability by representing regularity and connectivity of the networks. The quantitative treatment of rock textures are thus important in predicting material transport properties such as diffusivity and permeability. They are also fundamental in evaluating the rock deformation rates. 1.•@ ‚Í ‚ ¶ ‚ß ‚É •@ Šâ•Î ‚Ì Š" ‚ê-Ú,-± ŠE‚â ŠÔOE""™‚Ì •s ˜A'±-Ê‚Ì •\ '¢ ‚Í,"Á ‚É•…‚Ì ' ¶ •Ý‰º‚Å‚Ì Šâ •Î ' † ‚Ì •¨ Ž¿ˆÚ"® •E‰» Šw"½‰ž‚AEŠâ •Î ‚Ì-¬ "®"Á•« ‚ð •l ‚¦ ‚é •ã ‚Å,-{ Ž¿"I ‚È-ð Š" ‚ð ‰Ê ‚½ ‚µ‚Ä‚¢ ‚é. ‚µ ‚© ‚µ ‚È‚ª ‚ç,‚± ‚ê ‚ç ‚ð 'è-Ê "I ‚É"c ˆ¬ ‚· ‚é "w-Í‚Í ‚± ‚ê ‚Ü ‚Å‚ ‚Ü‚è ‚È ‚³ ‚ê ‚Ä‚± ‚È‚© ‚Á‚½.•Å ‹ß,‰ä •X‚Í ‰Ô ›¼Šâ ‚Ì Š" ‚ê-Ú,-± ŠE,ŠÔ OE"•\ '¢ ‚ð ƒt ƒ‰ ƒNƒ^ƒ‹ Šô‰½ Šw‚ð-p ‚¢ ‚Ä'è-Ê "I ‚É•\ OE»‚µ,‚Ü ‚½Šâ •Î ŠÔOE"•…' † ‚Ì •¨ Ž¿‚Ì ŠgŽUOEW •" ‚Ì 'ª 'è 'l ‚© ‚ç Šâ•Î ' † ‚Ì •¨ Ž¿ˆÚ"®‚Ì ‹ü ‹È "x ‚ð •" 'è ‚µ,‚± ‚ê ‚ç-¼ ŽÒ ‚Ì ŠÖOEW ‚ð •] ‰¿‚µ ‚ae ‚¤ ‚AE‚µ ‚Ä‚¢ ‚é.‚³ ‚ç ‚É,•í ‰·‚Å‚Ì Šâ •Î ŠÔOE" •…' † ‚Ì •¨ Ž¿‚Ì ŠgŽUOEW •" ‚© ‚ç,•‚ ‰·‚Å‚Ì-± ŠEŠgŽUOEW •" ‚ð•" 'è ‚µ,‚Ü ‚½,-¬ 'Ì ‚Ì 'g •¬ ‚É ‚ae‚é Šâ •Î-± ŠE‚Ì ‚Ê ‚ê ‚ð •l-¶‚µ,-¬ 'Ì ' ¶ •Ý ‰º‚Å‚Ì Šâ •Î ‚̘c‚̘c '¬ "x ‚ð •" 'è ‚µ‚½. ‚± ‚± ‚Å‚Í,•¡ ‚Ü‚Å‚Ì ‰ä•X‚Ì OE¤‹ † ‚Ì OE‹‰Ê ‚É•V ‚½‚È'ª 'è OE‹‰Ê ‚ð ‰Á ‚¦ ‚Ä,Šâ •Î ' † ‚Ì •s ˜A'±-Ê‚Ì •\ '¢ ‚â˜A‚â˜A'± •« ‚Ì 'è-Ê "I "c ˆ¬ ‚AE‚» ‚ê ‚ÉŠî ‚Ã ‚-•¨ Ž¿ˆÚ"®•E-¬ "®‚Ì 'è-Ê "I ‚È •] ‰¿‚É ‚‚¢ ‚ÄŠT•à ‚· ‚é. 2.•@ ‰Ô ›¼Šâ ‚Ì 'g •D ‚Ì ƒt ƒ‰ƒNƒ^ ƒ‹ •« •@ •z •¨ •EŠâ •Î ' † ‚Ì •¨ Ž¿ˆÚ"®‚Í,"-'R ‚Ü‚¸Š‚Ü‚¸Š" ‚ê-Ú‚â ƒ} ƒCƒN ƒ• ƒNƒ‰ ƒb ƒN‚ð'Ê ‚µ ‚Ä‹N ‚± ‚é.•Å ‹ß,Šâ •Î ' † ‚Ì Š" ‚ê-ÚOEn‚â ŠÔOE"•\ '¢ ‚Ì •V ‚µ ‚¢ •\ OE»Žè-@‚AE‚µ‚Ä ƒt ƒ‰ ƒNƒ^ƒ‹ Šô‰½ Šw‚ª-p ‚¢ ‚ç ‚ê Žn‚ß ‚Ä ‚« ‚½.‚µ ‚© ‚µ‚È ‚ª ‚ç,-á ‚¦ ‚Î,‚ ‚é Šâ •Î ‚Ì Š" ‚ê-Ú‚Ì •ª •z ‚ª ƒt ƒ‰ ƒNƒ^ƒ‹ "I ‚Å‚» ‚Ì ƒt ƒ‰ ƒNƒ^ƒ‹ ŽŸ OE³‚ª1.6‚Å ‚ ‚é ‚± ‚AE‚ª ‚í ‚© ‚Á‚½ ‚AE‚µ ‚Ä,‚» ‚ê ‚ª ‰Ê ‚½ ‚µ‚Ä ‚Ç ‚¤ ‚¢ ‚¤ˆÓ‹`‚ª‚¤ˆÓ‹`‚¤ˆÓ‹`‚ª ‚ ‚é ‚Ì ‚© ‚AE‚¢ ‚¤ "_ ‚É ‚Í,‚Ü ‚¾-¾‰õ‚È•û OEü‚à ‚¯ ‚ª ‚Å ‚« ‚Ä ‚¢ ‚È ‚¢.Š" ‚ê-Ú‚Ì OE`•¬ •ê ‚Ì ‰ž-Í•ê "™‚Ì ƒp ƒ‰ ƒ• •[ ƒ^•[ ‚É'è •« "I ‚ÉŠÖ˜A‚¯ ‚ç ‚ê ‚Ä ‚« ‚½‚É‚· ‚¬ ‚È‚¢.•¨ Ž¿ˆÚ"®‚AE‚Ì ŠÖ˜A‚É ‚‚¢ ‚Ä ‚àOE¤‹ † ‚ª ‚È ‚³ ‚ê ‚Ä‚¢ ‚é ‚ª, ‚Ü‚¾-¾‰õ‚È'è-Ê "I ‚È•l ‚¦ •û ‚ª Šm-§‚µ ‚Ä‚¢ ‚È ‚¢.‚± ‚ê ‚Ü‚Å ‚Ì 'n ‹…‰È Šw‚É ‚¨‚¯‚¨‚¯ ‚é ƒt ƒ‰ ƒNƒ^ƒ‹ ‚ÉŠÖ‚· ‚é OE¤‹ † ‚Í,'n •k ‚⠉ΎR"™Žå‚É 'n ‹…•¨-•Šw"I ‚È-Ê‚Å‚Ì ‰ž-p ‚ª ' † •S ‚Å‚ ‚è,•¨ Ž¿ˆÚ"®‚â Šâ •Î 'g •D ‚AE‚Ì ŠÖ˜A ‚É‚¨‚¢‚É‚¨‚¢ ‚Ä‚Í ‚Ü‚¾‚Ü‚¾"-"W"r •ã ‚É‚ ‚è,‚» ‚Ì-L OEø•« ‚ð ‹^ ‚¤ OEü‚« ‚à '½‚¢.‚» ‚± ‚Å,‚± ‚± ‚Å ‚Í,'˜ ŽÒŽ© •g ‚Ü‚¾OE¤‹ † "r •ã ‚Å-¢ Šm-§ ‚Å‚Í ‚ ‚é ‚ª,‚ ‚¦ ‚Ä-¢ ŠJ 'ñ ‚Ì-̈ae ‚Ö‚Ì ' § •í ‚Ì Žp•¨ ‚𠎦 ‚· ‚½‚ß ‚É,Šâ •Î ‚Ì Š" ‚ê-Ú,-± ŠE,ŠÔ OE" •\ '¢ ‚Ì ƒt ƒ‰ ƒNƒ^ ƒ‹ •« ‚AE ŠgŽU‚â •Z " §-¬‚AE‚Ì ŠÖ˜A ‚ð-\Ž@ "I ‚É•q ‚× ‚½‚¢. 2.1•@ƒ{ ƒb ƒNƒX•E ƒJ ƒEƒ"ƒe ƒBƒ" ƒO-@‚É ‚ae ‚é OE‹•» ŠOOE`,-± ŠE ‚Ì ƒt ƒ‰ƒNƒ^ ƒ‹ ŽŸ OE³ •@ ‚Ü‚¸,"ú-{ ‚Ì 'ã •\ "I ‚È•V'N ‚È‰Ô ›¼Šâ ‚Å‚ ‚éˆï‚éˆï •é OE §ˆî "c ‰Ô ›¼Šâ ‚ɂ‚¢ ‚Ä,•¡ ‰ñ •V ‚½‚É,-l •X‚È •û-@‚Å‚» ‚Ì 'g •D‚Ì ƒt ƒ‰ ƒNƒ^ƒ‹ ŽŸOE³‚ð ‹• ‚ß ‚Ä‚Ý‚½.•Å ‚àˆê‚àˆê "Ê"I ‚È ƒt ƒ‰ ƒNƒ^ ƒ‹ ŽŸOE³‚Ì ‹• ‚ß •û ‚̈ê‚Ìˆê ‚Â ‚É,ƒ{ ƒbƒNƒX•E ƒJ ƒEƒ"ƒe ƒBƒ" ƒO-@‚ª ‚ ‚é.‚· ‚È‚í ‚¿,‚ ‚é •½-Ê ‚É•\ '¢ ‚ª ‚ ‚é •ê • ‡,‚± ‚ê ‚ð ‚ ‚é 'å ‚« ‚³s‚Ì •³ •û OE`‚Å‚¨OE`‚Å‚¨‚¨OE`‚Å‚¨‚¨‚Á‚Ä‚ä ‚«,•½-Ê'S 'Ì ‚Ì •³ •û OE` ‚Ì ‚¤ ‚¿ •\ '¢(-±ŠE ‚â Š" ‚ê-Ú"™‚Ì •s ˜A'± •ü)‚ð ŠÜ‚Þ ‚à ‚Ì ‚Ì •" N(s)‚ð •" ‚¦ ‚é.‚» ‚µ‚Ä,•³ •û OE`‚Ì 'å ‚« ‚³s‚ð-l•X‚É•Ï ‰» ‚³ 1995"N2OEŽ24"ú Žó-• *•@ "OE‹ž 'å Šw'å Šw‰@-•ŠwOEnOE¤ ‹ † ‰È('nŽ¿Šw‹³ Žº)