Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/note/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5...

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47 Ǚ 3 ǖ NJþ3ùnjƵȢ 3.1 ÿĵ ÿĵ4ɴijńÿĵɴɡijńÿĵ1Ă»F.-Fɵijńÿĵ4ɴŀÃσ.Ƌ= e F4 3C1ɴ1 3ɒş-ȉGFÿĵ3.Jɵ3ɒ14Ũɑ3ɦ¯),0ɵ -4ɴijńÿĵ-40ÿĵJɡijńÿĵ.ǮǎFɵɡijńÿĵ4ɴȷĤŨɑ1ĊFɵï ŰŠ1Ė0ŀÃÄDG&.ɴ$3ÿĵ3ĂɅ¸4ijńÿĵ-Ð?DG,FɴFŀ ÃCE@Ă0ŀÃÄDGF.ɴŀÃJ×Eɕ,@ƌƺƋF4ƑƋ (permanent strain) . ä5GFƋŦDž1ƌFɵ3ÿĵ3ńȩJûń (Plasticity) .ä7ɵ<&ɴïŰŠ14ɴƋ3Ũ ɑÿÊ1Ċ&ŀÃɴF4ŀÃ1Ċ&ȸĪ-ƋÿÊƶFɵ3ńȩJǟń (Viscocity) .äK-Fɵijńÿĵ-E0DɴŨɑĊń3Fÿĵ@Fɵ.1ɴ3ńȩ4 anelasticity (time-dependent elasticity) .ä5G,FɵFţßDĂ0ŀÃJÄ,uĎ1 )&.ɴŰ Š3ûńÿĵɉ4Ũɑ..@1ýÄFɵGJRote.äK-FɵuţɴFţß1Ă0 ÿJz,$GJuĎ1 *.ɴŀÃ4Ũɑ..@1xFɵGJŀÃDZå.äK-Fɵ ĝLj3úÝɴGD3ɡijńÿĵ4ɴĝLj1ÄDG,FŀÃɱÑÄŀÃɲ0F¤-) ,@ɴĊò,F.Ǹ&ţCɵijńƿÿĵ÷ɴûń÷0/3¸ɬ4ɴÿĵ°JƅöÊ F&?3¸ɬ-EɴljǓĔȦ1C),ÿIF9@3-Hɵ FţßDğȑƿ14uƃ0ŀÃJÄ,ĝLjțŠJÿĵ"&.3ɴŀÃ.Ƌ3ɒC 63C0țɯ-ÿĵ&ĝLjțŠ3ƃĈJ Fig. 3.1.1(a) . (b) 1Ǎ&ɵFig. 3.1.2 4ơĎG FŀÃ.Ƌ=3ɒ3²öƿ0œFȀJƅĭƿ1Ǎ&@3-Fɵ * Ɨ) -4ɴțŠ$ 1ÄDG,FÃJ őFǺÃJĄĆ?F.JNJþ.ä7.1FɵFig. 3.1.2 (a)

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Page 1: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

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Ǚ 3ǖ� NJþ3ùnjƵȢ

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Page 2: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

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(c) ��� "����������ɸ (3.2.19)

.0Eɴh\rUlpOapQt4Ɵė Fɵ � ��-ɴ A 4 1�D9ɰƉ3Ľ

Ėɉ-�F�DɴδAJɔE0�Ė�� F.�ɴ�w 3*3úÝ3h\rUlpȔŝɉ4ǚ��ɵǯĵijń�3úÝɴRn[R�Ï�ɢǒýÄ Fɚ1Ȕŝ�GFh\rUlpOapQtɱ�F�

4Ǡ°��DȔŝ�GFOapQtɲgJOapQtȔŝƳ (Energy release rate, available energy release

rate) .ä7ɵg4

(3.2.20)

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53

-z�DGFɵ�3¤4ijń�3ĀɅüƹ-3üƹų�14CD!ɴÃċƿưŇ13=1C),Ɠ

<Fɵ.�1ɴüƹų��ÿ�uĎɴ�F�4ȄɈuĎ3.�ɴ$G%Gɴ

(3.2.21)

.ū�Fɵg3�.Jÿ�ŎŲų�3x-3ƋOapQtȔŝƳ (strain energy release rate) .ä7�

.@�Fɵ���ɴ -1ȵ9&C�1ɴȄɈuĎ3ų�x-4ƋOapQt4Ȕŝ�G!ɴȶ1

ýÄ Fɵ�3�.�Dɴg JƋOapQtȔŝƳ.4�I!ɴÏ1OapQtȔŝƳ.ä7�.

1 Fɵ

� Rn[Rɢǒ3δA 3ýÄ1C),ɴ�3ÃċǠ3OapQt�DǮå.�, gδA 3OapQt

�ȾÁ10Fɵ�3OapQt�Rn[Rɢ3ĵŊ3��ARn[R3ÇƿȻȈ1ĿȎ0ȼÇOa

pQtɱƖÇ3OapQtɲ.�,�Ʒ�GFɵ [ç 1] ³Ʌ1ŀÃƣJá<0�0D5ɴyôȩćȩ1Ĕ�,@ (2.13) �ŊEǕ*�.JșŦ�0��ɵ@��3.�ɴ�D�3ų���)&D$3�.1*�,@ȵ90��ɵ

[ç 2ɻñǴțɯ1CF post-failure3œFȀ�1*�,ǸĒ"Cɵ [ç 3ɻóɟ�ɴ�E1ȄɈuĎx-ƶ�,�F. F.ɴ/3C�0çɪ�ƶ�F�ɴ<&ɴ�E1ÿ�ŎŲ3ų�-ƾƶ�,�F. F./3C�0çɪ�ƶ�F�JȢ#Cɵ�D1ɴóɟ4/3C�0üƹų�-ƾƶ�,

�F.Ǹ�F9��JȢ#Cɵ

3.3 ŀÃŐĂ�ş 3.3.1� NJþƃĭ.ŀÃŐĂ�ş � Ɖǜ1ȵ9F�ɴGriffice1CG5ɴNJþ4Ƨòƿ0ÂGǀ (crack) �ŐĂ�Ć?F�.1C),

ƾƶ Fɵ�3Ǹ�ţ4ɴ�-@ŔƷ�GFũȽƿ0Ǹ�ţ-�Fɵ�3Ǖú-NJþJȢ�C�.

Fig. 3.3.1

Fig. 3.3.2

Page 8: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

54

F.�ɴu¢3Ƨò crack3âí1ƶ�FŀøġJǸ�F�.�ɈȎ-�FɵFig. 3.3.14 crack

3ɞĈɫĽɍµǃ-�F�ɴ�3C�0 crack 4ɴşċƿ14ɴuƃ0ŀÃ�«�,�FȺǭ�³

1�FɢJǸ�ɴ�3ɢJ4�> 2Ʃ-3ÿ��yȺǭ-�EɴɢJ.��,ǂ�1Ö;�Ý�Ã

�0�@3.�,×EŌIGFɵ�3×EŌ�ţ14�1ɶȷE�Fɵu*4ÂGǀJÒ=Jő*

ǔĉ.�,Ō�@3-ɴǔĉ4ā�3úÝȆ�ſ´ĉ.�,ŌIGFɵ�ţ4Ò=30�yȺǭɢ

.�,Ō�@3-�Fɵ Fig. 3.3.214ɴzţß1Ò�ŷJȨȷ�& crackJɴŋĦ0ſ´ĉ-ȳ��&.�ɴſ´ĉâí1

ƶ�FŀÃ3¸ġ�Ǎ�G,�Fɵſ´3ɎȰ3Ɏ�J 2a�LJȰ3Ɏ�J 2b . F.�ŰŠ1 y

= ± ∞ -ŀà {σy}∞ �«�,�F.�ɴÂGǀ®Ǘ-3ŀà {σy}max 4�

(3.3.1a)

-�Eɴ®Ǘ3ŪƳ ρ (= b2/a) � ρ << a 3.��

� (3.3.1b)

3C�1ȉ�GF�(Sih and Liebowitz, 1968, FractureɴII, Academic Press)ɵα 4ƪƉ­3Ďş-�ŀÃ

ɛ~�ş.ä5GF�α4țŠēƕ. crackēƕ3ɒ��ǂ�-�Eɴcrackĵư� crackēƕ1CD

!ǚ��.�ɱcrack�ǂ�ɲ-�G5țŠēƕ�ÿI),@ÿID0�ɱ´ĉ3âE3ŀÃJŅ¬

�,=F.Ȃ�ɲɵ σt JÂGǀ®Ǘ�Dª�1ɜG&ɢ1ƶ�FŕǯŀÃ. F.ɴ

(3.3.2)

.ȉ�Gɴρ 0 -4ɴɔE0�ÂGǀ3®Ǘ1ȳ�.�H1�G�ƶ�Fɵ <&ɴſ´ĉ®Ǘ

ȳ¨3 x Ȱw3ŀøġ4ɴ0 ≤ * << aɴr << a 3.�ɴ

(3.3.3)

Fig. 3.3.3

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55

�GD3ŋĦ0ſ´öÂGǀ�DļDGFȔ4ɴÂGǀ3®Ǘ3��ȳ¨JJɕ�, ρ 0 . F

.ɴÒ=30� crack 1Ĕ FȔ1uǿ Fɵ

�w4ɴıÃöÂGǀ (tension crack) Jſ´ȳ�-ȉ�&úÝ3@3-�FɵCEuȁƿ14ɴ

Ò=30�ÂGǀ (crack)� 3ÿĵ�F�4NJþƃĭJɴMode�(opening), Mode �(inplane sliding),

. Mode (antiplane sliding) 1¸Ȕ�,Ǹ�ɴďɚ3NJþJ�GD3�!G�3kt_ɴ�F�4ɴ

�GD3ȌÝ.�,ȔŸ FɵFig. 3.3.34�GD3kt_JîǍ�&@3-�FɵMode�3 crack 4ɴıÃöNJþ (tensile fracture)ɴMode�.4ÀšNJþɱshear fractureɲ1Ĕŀ�& crack -�Fɵ

î1��FīƄ (x, y, z) 3×Eţ4NJþÃċ1��FȷĤ3ǢŲ-�FɵîǍ�&Ʌ¸4ɴcrack ¾

Dz3uɅ-�Eɴ�3Ʌ¸3ŪƳÍĸɱRn[R3Íĸɲ4ɴ¾Dz�ǁǯ-�F.ȳ�-�FǐĪ

1Ă��ɴîǍ�G,�FɅ¸3ēƕ4Ė��@3.Ǹ�Fɵ�3C�0úÝɴÜȰţß3ÿ� u, v,

w4 (3.3.4)

-ȉ �.�-�FɶƉ­3ú10FɵɈ2ÝI"3ÓƵ�Dɴ�GD3ú4

(3.3.5)

1¸Ȕ-�Fɵ��-ɴRn[R4 z= constant 3ɢ3uɅ –a ≤ x ≤ a 1�GDG&¹EȲ=-�Fɵ(A)4ĦɢƋ=3ɶƉ­ijńȢɴ (B) 42�E1ɒ FijńȔJƷ�,ȉ �.�-�Fɵ(C) 1

CF crack®Ǘ-3ŀÃ4 (A), (B) 1CEƶ�FĂ�0ŀÃ1Ə9,ƪȑ-�FǐĪ1Ė��ɱ&

.�5ɴǯĵNJþÃċ¯ɏɴ1976ɴĜűį�ɴøɭɮɲɵMode�.�3úÝ4 (A)ɴMode3ú

Ý4 (B) 3Ȕ�D$GD��FúJȖǛ F�.�-�FɵCrack ®Ǘ-3ŀÃ4 r 0 - r-1/2 3

ƯƽńJ@*ɵ�x4�GD3ɦJÜkt_1*�,Ǎ�&@3-�Fɵ *) Mode IɱɐÙĵÿĵɲ

ɴ (3.3.6)

Mode II ɱɢ³Àšĵÿĵɲ

ɴ� (3.3.7)

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56

Mode IIIɱɢĀÀšĵ�F�4dzÀšĵÿĵɲ

ɴ� � (3.3.8)

��-ɴ ɴ

ν 4hL[XrƏɴG4¿ńƳ-�Fɵ uȁ1ɴcrack ®Ǘâí1��F�ƕǯţß θ = 0-3ŀà {τi} (= t{σx, σy, σz, τxy, τyz,τzx)) 4ƱǕ0 3*3kt_�D3Ȕ3å.�,ɴ

(3.3.9)

3C�1ȉ�GFɵ��-ɴVIɴV�ɴV4ɴ

VI = t{1, 1, 2ν, 0, 0, 0}, V� = t{0, 0, 0, 1, 0, 0}, V = t{0, 0, 0, 0, 1, 0} (3.3.10)

.ū�Fɵ&'�ɴ(3.3.9) 1��F σz (≡ τ3) 4ĦɢƋ3úÝ-�EɴĦɢŀÃ-4 σz =0 -�Fɵ

Þƃ1ɴcrack ɢw3ÿ� {ui} @ɴθ = ±π .Ƕ��.1C), KIɴK�ɴK JƷ�,ū�FɵKIɴ

K�ɴK4ŀÃŐĂ�ş.ä5GFɵŀÃŐĂ�ş3Ɖ­4 [ŀÃ]×[Ɏ�]1/2 -�Eɴ2Ɖ­Rn[

R3úÝɴ�x3C�1ĎǷ�GFɵ

(3.3.11)

ŀÃŐĂ�ş K.®Ǘ�ŪƳÍĸ ρ -�FRn[R®Ǘ-3ŀÃJƏȱ F.

(3.3.12)

3ɒ�Jĕ��.�-�Fɵ��5ɴ(3.3.11) 1 (3.3.3)ɴ(3.3.12) 1 (3.3.1) �F�4 (3.3.2) J�¯

�,ɴ

(3.3.13)

�ļDGFɵŀÃɛ~�ş α 4ɴcrack ĵư�ǂ�3.�ɴ$3ēƕ1�Ċ�0�ɉ-�)&31Ĕ�ɴK 4 crack 3Ɏ��Ɏ�0F.Ă��0Eɴēƕ1�Ċ Fɉ.�,ĎǷ�G,�Fɵ<&

�3�ş4ɴcrack 3Ɏ�3ĦţŻ1Ə��, crack ®Ǘ-3ŀÃ�Ă��0F�.Jȉ�,�Fɵ 3.3.2� ŀÃŐĂ�ş.OapQtȔŝƳ Rn[R3ĬɎǯw1Rn[R�ŊɎ FúÝ4ɴOapQtȔŝƳ.ŀÃŐĂ�ş.3ɑ1ǝÏ

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57

0ɒ���FɵǝÏ3&?1ɴRn[Rɢǒ3ĽĖýÄ δA�1CFh\rUlpOapQt3ȔŝJɴÿ�ŎŲ3úÝ1*�,Ǹ�C�ɵh\rUlpOapQt3Ȕŝɉ� �4�3úÝɴƋO

apQt3Ȕŝɉ1:�0D0�ɵ �J�x3C�0ȾǐJǸ�,Ț� Fɵ

(1) Rn[R3®Ǘ1δA3¹GȲ=J¯GɴRn[Rɢ14$G�¾1�Ʒ�,�&ŀÃ.ǚ��

ŀÃJ (ɴRn[R�ɐ�0�C�1�,��ɵ

(2) ȉɢ1�Ʒ�,�FŀÃJĺ 1Ɵė�", 0.�ɴRn[RɢJɐ�",ǾƸȉɢ. Fɵ

��-ɴ(1) 3Ⱦǐ-ɴ¹EȲ=J�F&?1ĿȎ0OapQt4��-4Ȣ�0�ɵ(1) �ǩI)

&ŨƩ-4ƋOapQt3ÿÊ40�ɵƋOapQt3ÿÊ4 (2) 3Ⱦǐ-ƶ�Fɵ�x-4ɴ(2) 3Ⱦǐ-ƶ�FƋOapQtÿÊJkt_ I 3úÝJ�1.),39Fɵ

� Fig. 3.3.4(a) 4Rn[RŊɎ�¾3ưŇJǍ ɵ�3.� y = 0ɢ3Rn[R®Ǘ�D x3�Ƕ1

�Ʒ�,�Fŀà σy(x) 4ɴ�3.�3ŀÃŐĂ�şJ KI(A). F.ɴ

(3.3.14)

-�FɵuţɴFig. 3.3.4(b) 1Ǎ C�1ɴzţß3Ò�δB3Ʌ¸� xţß1δa'��Ę�&3(ɴ

0I(ɴδA = δB⋅δa 3ɢǒýÄ��)&3(3ŀÃŐĂ�şJ KI(A+δA) .ū�.ɴθ = ± π .�

��.1C),ɴŊɎĹ3 crack ɢw3�FƩ x3ÿ� v(x) 4ɴ

(3.3.15)

.ū�Fɵ��-ɴ�4Rn[R3Ȕ�DƓ<FĎş-�FɵC),ɴ�������δAŐĂ Fɑ1 x =0

�D x = δa 3Ëɑ3Rn[Rɢ-0�GF�� gδB⋅δa4ɴ

(3.3.16)

-�Fɵ�<ɴδa 0 3ƀɔJ.F.ɴ

(3.3.17)

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58

�D1�G4ɴ

� � &'�ɴE’ = E ;ĦɢŀÃ3úÝɸ� E/(1-ν2);ĦɢƋ3úÝ (3.3.18)

.ū�F�.�¸�),�Fɵ��-ɴν 4hL[XrƏ-�Fɵ

� uȁ1v*3ÿĵƃĭ�ƞò�,�FúÝɴ

(3.3.19)

-�FɵȊǒ¸ɒş3Üɦ4ƱǕ-�F�Dɴ(4.7), (4.8), (4.9) JƷ�,ɴ�

(3.3.20)

.ū��.�-�Fɵ�

3.4� NJþùƤ� [ÕǸūɸȍŶȋusěÙŽăɄɴĝLjÃċ¯ɏɴŵ�Ăċ·ƭ�ɸElasticity, Fracture and Flow,

J. C. Jaeger, MethuenɸťůŰŠċ�ǰɴĝ3Ãċɴ�è] Ť1ȵ9&C�1ɴǻńNJþ.ɓ�.14şċƿ14ŦDž0Ë»�0�ɵ�FNJþùƤ4ǻńNJ

þ�Ȫ�FúÝ14NJþùƤ.�,ɴɓ��Ȫ�FúÝ14ɓ�ų�.�,Ʒ�DGFɵ�3C�

1Ʒ�DG,�&��*�3NJþùƤ (criterion of failure) J�x1Ǩ� Fɵ

3.4.1 ³Ʌřśȓȟ (Coulomb 3ƵȢ) �3ƵȢ3ŊǕ4 18{ǡŮ3 Coulomb3ďɯ1<-��3;FɵCoulomb 4ĝLjAð3ñǴțɯ3ǪŹ�Dɴ��Fɢ1Ĕ FÀšŀÃJ τɴõǁŀÃJ σ . F.�

(3.4.1)

JŬº1Ƣȭ FC�0ɢ1NJþ�Ȫ�Fɵ�.Ǹ�&ɵ��-ɴıÃJ + 1.)&�.1CEɴ

– ǘÛ4ñǴŀÃJȉ ɵτ0 4¶DŽà (cohesion) .ä5GFĎşɴµ 4³Ʌřś�ş (coefficient of

internal friction) .ä5GFĎş-�Fɵ � Fig. 3.4.1 1�FC�1ɴšɢ A �źư3ŰŠ1ȄɈ P JÄ�&úÝJǸ�Fɵƕǯ�ȄɈţß

1 α ©�&šɢ BB’ -4ɴɢ83ƕǯŀà σb .ɢ-3ÀšŀÃ4 τb 4

(3.4.2)

.ū�Fɵ

��-ɴ�D&?,ñǴJƊɴ�&�),ɴPJƊ. F.ɴσb >0 4ɢ1ß��ƕǯŀÃɴτb > 0 4ɢ1Ɣ),xţ (B’ ţß) 1ß��ŕǯŀÃJȉ ɵɢ-3řś�şJ µ . F.ɴɢ3 9

E1ō FŀÃ4 µσbɴ�&�),ɴɢJ 9D"C�. FŭÆÀšŀÃ τs 4

(3.4.3)

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59

-�Eɴ 9E� τs = τ0 3.�1ƾƶ F. G5ɴ

(3.4.4)

.0EɴCoulomb criterionJļFɵ�w4ĻŴ0�G,�& Coulomb criterion 3ƮƵƿ0Ȕɇ-@

�Fɵ���ɴ³Ʌřś.��ƁŁ�ĝLj3NJþ-4ŦNj-40�.���.�DɴĝLj3NJþ1

Ĕ�,ɴ�3Ȕɇ4ŊEǕ&0�3-40��.��ņȏ@�F (�ĝLjÃċ¯ɏ�)ɵ � ǘÛJǸň�,ɴ(3.4.3) 4

(3.4.5)

.ū�Fɵτs �ŬĂ10FC�0ţß- 9E�Ȫ�F. F.ɴ$3ţß4ɴ

(3.4.6)

-z�DGF�Dɴ�GCEɴ

(3.4.7)

�ļDGFɵ 0I(ɴNJþɢ�ȄɈ3Ȱ.0 ȓ4ɴřś�ş1C),Ɠ<),�F�.10Fɵ

�3úÝ3 Mohr3ŀô4 Fig. 3.4.2 3C�1ū�Fɵ

� .�H-ɴĝLj�ǔə³1ñà p3ƚ�JáK-�F.�14ɴƕǯŀÃσb3�IE1ɴŭÆƕ

ǯŀÃσe = σb - p �Ʒ�DGFɵ 0I(ɴ

ɵ (3.4.8)

�GJ Paterson (1978, Experimental Rock Deformation – The Brittle Field, Springer-Verlag) 4 Terzaghi

rule (Terzaghi, 1945, Stress conditions for the failure of saturated concrete and rock, Proc. Am. Soc. Test.

Mat., 45, 777-792).äK-�Fɵďɯƿ14ɴ��5 Handin et al. [Handin, J., Hager, R. V., Friedman,

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60

M., Feather, J. N., 1963, Experimental deformation of sedimentary rocks under confining pressure; pore

pressure effects. Bull. Am. Assoc. Petrol. Geol., 47, 717-755] 1C),�3Ǹ��C�ŊEǕ*�.�Ǎ

�G,�Fɵ

3.4.2 ŬĂÀšŀÃȟ (Tresca 3ƵȢ) 1870ħɥ Tresca�Ɋę3ûńÿĵJljǓ�,ļ&ǪȢ.�IG,�Fɵ�3ȟ3Ưľ4ɴñǴIJ

Ī.Į)ıEIJĪ�ǚ��0F�.-�Fɵďɚ14ɴĝLjATrRot^-4ñǴIJĪ4Į)ı

EIJĪ3 10£ǐĪ�Fɵ�3�.�Dɴ�GD3ŰŠ14Ĵ,4<D0�ɵ

3.4.3 ŀôÉǫǯȟ (Mohr3ƵȢ) 1900ħɥɴMohr4ɴÀšŀà τ �ƕǯŀà σ 1C),Ɠ<FuϤ τ0 1ȿ F�ɴŬĂĮ)

ıEŀÃ�uϤ T010)&.�ɴNJþ���F.Ǹ�&ɵ 0I(ɴ

(3.4.9)

-�FɵNJþ���F.�3ŀÃưŇJ Mohr ´-ȉ .ɴ -1ȵ9&C�1ɴ(3.4.8) 4ŀô

3ÉǫǯJȉ ɵ�3ȟ-4ɴNJþIJĪ4~ɑ�ŀÃ3Ă��14�Ċ�0�ɵ

� τ = f(σ) 1*�,ɴƉ3�.�ȕ�Fɵ(1) ɠƐñx-4NJþ4ƾƶ�0��.�džDG,�F�

Dɴ�3Ūǯ� σ < 0 - σ ȰJ¹F�.40�ɵ(2) σ1 ��F¤1ȿ F. σ3 1ƪɒ�1NJþ���F.���.�Dɴ�3ĭ-ȉ�GFŀôÉǫǯ4ɴτ = 0 -ŭɔ0ÍĸJŭ Fŀô1

ŕ FɱFig. 3.4.3 ÕƬɲɵ�&�),ɴ�3ĭ4ɴσ1 ȰJõǁ1¹Eɴ��@�3Ʃ-uĎ3Ū

ƳÍĸJŭ FŪǯ3ĭ-ȉ�G0�G50D0�ɵ 0I(ɴ

(3.4.10)

-�Fɵ

Ɨ) ŪƳÍĸ r 4ɴ

(3.4.11)

.�H-ɴσ1 . σ3 -ĎǷ�GF Mohr 3ŀô4ɴ

(3.4.12)

��-ɴ

(3.4.13)

.��.ɴ(3.4.12) 4ɴ

(3.4.14)

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61

�<ɴMohr´3Íĸ� p3ɒş.�,ɴF(p) -z�DGF.�ɴw3ĭ4ɴ

(3.4.15)

-�Fɵp3ĽĖɉÿÊ dp 1Ĕ�,ɴ(3.4.15) 4ɴ

(3.4.16)

JƢ&�0�DÿIFɵ�GCEɴ

(3.4.17)

0I(ɴ�3C�1�,ļDGF σ . τ 3ɒ�4 (3.4.9) �F�4 (3.4.12) 3ɒ�@Ƣ&�,�F4!-�FɵFig. 3.4.4 1Ǎ�G,�FŝƮǯ4ɴ�3C�0ɒ�JƢ& ɒş3u*-�Fɵ

� �<ɴF(p) �ǁǯ3.�ɴ(3.4.15) �F�4 (3.4.17) �DļDGF σ . τ 3ɒ�@ǁǯ-�Fɵ

�3�.�Dɴ³Ʌřśȓȟ (Coulomb 3ƵȢ) 4ŀôÉǫǯȟ3Ư»0úÝ.���.�-�

3.4.4 ÀšƋOapQtȟ �ŀÃJ σ1, σ2, σ3, $GD3¥ĠŀÃJ s1, s2, s3 .ū�ɵ��-ɴ¥Ġŀà si 4

(3.4.18)

-�Fɵ�3.�ɴyÿɉ J1, J2, J3 4

(3.4.19)

uţɴƋOapQtWJ¥ĠŀÃ-ȉ .ɴ

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62

(3.4.20)

��-ɴµ 4¿ńƳɴK 4ɡñǴƳ-�Fɵ

� ɓ� (yielding) 4īƄ3×Eţ1ƪɒ�1��Fɵ<&ɴĦôŀÃ4ɓ�3Ⱦǐ1ĶɣJ�C;

�0�ɵ�3�.�Dɴvon Mises4ɓ�ų� (criterion of yielding) 4ĠŀÃ1ɒ Fyÿɉ J2'�

1�IF.Ǹ�ɴŰŠ3Ďş σ0 1Ĕ�,ɴ (3.4.21)

�ŊEǕ*.�ɴɓ��ƶ�F.�&ɵ�GJɴvon Mises3ɓ�ų�.ä7ɵ<&ɴHuber (1904) .

Hencky (1924) 4ÀšƋOapQt��FuϤ1ȿ�&.�ɓ��ƶ�F.��ȟJŗæ�&�ɴ

�3ȟ4ɴw3ĭ�D¸�FC�1ɴvon Mises3ų�.Þ�ǪŹJz�Fɵvon Mises4şċƿ0

Ȏȡ�D�3 criterionJĕ�&�ɴHuber-Hencky4$G1ƮƵƿ0ȔɇJz�&.@ȕ�Fɵuţɴτ04±ɢ�ÀšŀÃɴ.ä5GFɵ<&ɴNadai (1950?) 4±ɢ�ÀšŀÃ��FuϤ1ȿ�&.

�ɓ����F.Ǹ�&ɵτ0 �±ɢ�ÀšŀÃ.ä5GFƵƸ4ɴτ0 � Fig. 3.4.5 1�FC�0ɢ

1«�ÝÀšŀÃJȉ�,�F�D-�Fɳ)ɵ

� von Mises3 criterion4Ɋę0/-4Ȃ�ŊǕ�,�F�.�džDG,�F�ɴĝLj3ǻńNJþ3

ȟŦ14ɂ¹-40�.łIG,�Fɵ

ɳ)ν ţß1ƕǯJő*ɢ1«�ŀÃfR^pJ Tνɴ$3ƕǯŊ¸J N. F.ɴÀšŊ¸(ÝÀšŀÃ) τ 4ɴ

īƄȰJ�Ȱţß1.Eɴ�ŀÃJσi. F.ɴτ2 4ɴ

.ū�Fɵ

Fig. 3.4.5

Page 17: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

63

3.5 � Griffith 3ƵȢ 3.5.1 ǻńŰŠ3ƵȢIJĪ ŰŠ�č°1ôu-�),ɴ°�ƈɖJáK-�0�.�,ɴÓĈɑĮÃ$3�3ǸĒ�DƵȢƿ

1ƒ?DGFNJþIJĪJɴ$3ŰŠ3ƵȢIJĪ (theoretical strength or molecular strength) .��ɵ�

3C�1�,ļDGFIJĪ4ɴŰŠ3IJĪ3wɔ¤10F.Ǹ�DG,�Fɵ

� Ţ�� crack3ƶŊ4Ţ&0 2*3ɢJƶŊ Fɵ2*3Ï�ɢǒ3NJšɢJ�F31ĿȎ0OapQtW4 γ JÏ�ɢǒ�&E3ȉɢOapQt. F.ɴ

W = 2 γ (3.5.1)

-�FɵNJšɢ4ɴNJšɢ3|¦1}K-�FÓĈ3ɑ1ǂ�1}K-�FǪÝÃ1�(È),ɴ

|¦1Į�ɜ &?3��1C),�DGFɵW 4$3&?3��.Ǹ�,C�ɵ2 *3ÓĈɑ3Ȯɜ.ŀÃ.3ɒ�4.Fig. 3.5.11�FC�0Ūǯ--ȉ�Gɴ��4Ķ3Ʌ¸-ȉ�GFɵ��-ɴ

ƆȰ x 4Ƌ�0�.�3ÓĈɑɑɘ a0 �D3!G-�Eɴσ th4Į�ɜ .�1ĿȎ0ŬĂ3ŀ

Ã-ɴƵȢIJĪJȉ ɵ�3ŪǯJɴ

(3.5.2)

-ȳ� F.ɴ�� W4

(3.5.3)

3C�1ȉ�GFɵ 0I(ɴ

(3.5.4)

�ļDGFɵÓĈɑɑɘ3Ƌ ε 4 ε = x/a0-ȉ�GFɵuţɴx << a03.�ɴmrSƳ E4ɴȳ�

ƿ1

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64

(3.5.5)

.ū�F�Dɴ(5.4) . (5.5) �D λ JƛÔ�,ɴ

(3.5.6)

�ļDGFɵ�3C�1�,ɴŰŠ3ƵȢIJĪ�ļDGFɵ

� γ 4ƥȇưŇ-4ȉɢıÃ-�Fɵ�3ďơ4ìɝ-�FɵƁƻƒ?DGF σth 3¤4ɴ2000

kgf/mm2ɼ5000 kgf/mm2 ǐĪ�F�4 E/10ǐĪ-�F.Ņ¬�G,�F�ɴȷĤ3ɊęŰŠ3ơĎ

¤4ɴ�GCE@ 1ż0�� 2żĖ��ɵ 3.5.2 Griffith 3ƵȢ ǻńNJþ4ɴuĪ crack�ȻȈ�Ć?F.ɴƀ?,ȸ�ȸĪ-�Ś�ɴNJš�ƶ�FNJþ-�Fɵ

�3ƴȦJOapQt1ɒ FyČĎƴȦ.�,.D�&3�ɴGriffith 3ǻńNJþ3ƵȢ-�FɵGriffith 3ƵȢ-4ɴcrack ɢ3Ţ&0ƶŊ1C),Ȕŝ�GFh\rUlpOapQt�NJšɢ3

ƶŊ1ĿȎ0OapQt1ǚ��0)&.�1ɴNJþ3�Ę���Fɵ

� �5.1 1ȵ9&ďɯ¤.ƵȢ¤.3ɀ�JȟŦ F&?1ɴGriffith 4ɴŰŠ³Ʌ14ƶŴĽĖ0

ƈɖ��EɴŰŠ1 σ 0FŀÃ�ÄI),�F.�ɴ�GD3 cracks ~3�!G���Ę�Ć?

F�.1C),ŰŠ3NJþ���F.Ǹ�&ɵ�<ɴNJþ3ƾƶų�JOapQtȔŝƳ gJƷ�

,�DI ɵcrack �Ï�ɢǒ'��Ę F31ĿȎ0��J 2 γ .�ɴ�GJ .��.ɴƾƶų�4ɴ

(3.5.7)

-�Fɵ�3.�3ǽƹ3ŀÃJ σc . F.ɴNJþƾƶ3ĿȎų�4OapQtbnrV3w�

(3.5.8)

-�Fɵ*Ɨ)

*Ɨ)� �3Ʌ¸4ɴƉ3C�1Ǹ�,@C�ɵuĎŀà σ 3x1�F crack 30�ŰŠ1ɴRn[R�ƶ�F�.

1CFh\rUlpOapQt3ÿÊ δΠ 4

δΠ = δWs + δWg – δΠ∗

-�Fɵ��-ɴδWs4ƋOapQt3ýĸɴδWg4ȉɢOapQt3ýĸɴ– δΠ∗4ĀÃh\rUlp3Ɵė

¸-�Fɵ��-ɴÏ�Ò�3ŷJȨȷ�& 2cJRn[R3Ɏ�. Fſ´ö crack JǸ�F.ɴ

δWs =πσ2c2/E, δWg = 4cγ,

<&ɴĀÃh\rUlp3ĠJŀÃɱĀÃɲuĎ.�,Ǹ�F.ɴδΠ∗ =2δWs,Ɨ*) �&�),ɴ

δΠ = 4cγ - πσ2c2/E

δΠ �Ɵė�Ć?F c 3Ɏ�Jɴ∂Π/∂c=0.�,ƒ?F�.�-�FɵɺĝLjÃċ¯ɏɻ

Page 19: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

65

Ɨ*) δWs 4Ɂţüƹ3ŀÃ.ÿ�JƤɠƿ1ÿÊ�",ļDGFƋOapQt3ĠɴδΠ∗ 4Ɂţüƹ3ŀÃJuĎ.

�,ĀɅ3Ǡ�ŰŠ10 ��1ǚ��ɵɁţüƹ-3ÿ�4�!G@ǚ���Dɴǯĵijń3�Ď�ŊEǕ*ɔ

EɴδΠ∗ =2δWs �ŊEǕ*ɵ � �ţɴRn[R��Ę F.�ɴRn[R®Ǘ3ŀÃ4ƵȢIJĪJȫ�,�F-�H�ɵRn[

R®Ǘ3ÍĸJ a0 ǐĪ. F.ɴɁţ3ŀÃJ σc’.�&.�ɴ®Ǘ-3ŬĂŀÃσmax4

(3.5.9)

.0F�Dɴ�G�ƵȢIJĪ1ǚ��.Ǹ�F.

(3.5.10)

JļFɵ�GJσc .Əȱ F.ɴσc’< σc-�EɴOapQtų��DļDGFIJĪσc4ɴRn[R

®Ǘ3ŀÃ�ƵȢIJĪJȬ�F�.1C),�Ę F.��ų�J@Ƣ&�,�F�.�I�Fɵ

3.5.3� Griffith 3ƵȢ.NJþùƤ a. Griffith��%� Mohr����� !$

Fig. 3.5.2 1�FC�1ɴ2*3�ñǴŀà P)Q�«�,�Fŷ3~1 crack��FɵcrackDz-

3Į)ıEŀÃ4 crack 3ɎȰ.�ŀÃȰ.3©� θ 1CD!ɴcrack Ǘȳ¨-ŬĂ10F�ɴ$

3Ă��4 crack Ǘ3ŪƳÍĸ.ɴ�ŀÃɴP . Qɴ©� θ 1C),Ɠ<FɵĦɢŀÃưŇJ�Ď

�,ɴInglis (1913: Trans. Roy. Inst. Naval Architects, 55, Pt. I, 219-230: See Jaeger, 1962 or 1964: Elasticity,

Fracture and Flow, Methuen & Co. LTD) 4

(3.5.11)

. Fſ´īƄ ξɴη (Fig. 3.5.3 ÕƬ) JƷ�,ŀøġJļ&ɵx' . y' 4 Fig. 3.5.2 1�FC�

1.DG&īƄ-�FɵCcoshξ . Csinhξ 4$G%G ξ=constant -z�DGFſ´3ɎȰ.LJȰ-

�F.*� �<ɴſ´J ξ0 �1CE@̸Ė��0FC�1ŋĦ0@31 F.ɴRn[Rɢ1Ɣ)

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66

&ţß3ƕǯŀÃ ση(ξ0, η) 4

(3.5.12)

-�FɵŰŠ~1āş3 cracks �-&D?1ţ߸ġ�,�F@3.�ɴ�3~-Ŭº1 ση(ξ0, η)

�ŬĂ10FC�0 crack 3ß� ψcr .�Ƕ η J@.?F�.1C),ɴGriffith (1924) 4

(3.5.13)

P = St, if (3P + Q) < 0 (3.5.14)

(P – Q)2 – 8St(P + Q) = 0, if (3P + Q) >0 (3.5.15)

Jĕ�&ɵ&'�ɴQ > Pɵ��-ɴSt 4 crackɢ1õǁ1uȰ3ıÃ�«�.�3ŰŠ3NJþIJĪ

-�F .Ȕɇ�G,�F (Fig. 3.5.4 ÕƬ)ɵ � ��-ɴGriffith 3ƵȢ. Mohr 3ŀôÉǫǯȟ3ɒ�JȠ9C�ɵQ . P �z�DG,�F

.�ɴŰŠ~1«� τɴσ J Mohr 3ŀô-ȉ .ɴ

ɵ (3.5.16)

�&�),ɴ(5.15) JƢ& ŀô4

(3.5.17)

�3ŀô3Éǫǯ4ɴ(5.17) -ȉ�GFɒ��ɴ(P + Q) 3ĽĖ0ÿÊ1Ĕ�,@ɴ &G,�

F�.-�F�Dɴ

Page 21: Ù3 Ö Êþ3ù Ì µkymmt.la.coocan.jp/NOTE/4_第3章.pdf47 Ù3 Ö Êþ3ù Ì µ " 3.1 ÿ 5 ÿ 54 t 3 Dÿ 5 t a 3 Dÿ 51 » F . - F u 3 Dÿ 54 t @Ãσ. =e3 R F 4 3C 1 t1 3 R _- GFÿ

67

(3.5.18)

.��ɴ

(3.5.19)

CEƒ?F�.�-�Fɵ�3ĭ�Dɴ

(3.5.20)

JļFɵ�GJɴ(5.17) 1�¯ F�.1C),ɴ

(3.5.21)

�3ĭ4 τ =0, σ = -St JɤƩ. FŝƮǯ-�FɵďɚɴĝLj3ñǴIJĪ��F Mohr´3Éǫǯ4ŝƮǯ-ȳ�-�FC�1@ȏ�Fɵ�3�.4ĻŴ Griffith ƵȢ3ƊĴńJǍ șŏ.Ǹ�DG,�&ɵ *Ɨɲſ´3ţǐĭ4

b. Griffith��%� Coulomb ��%

� Coulomb 3ƵȢ14ɴ³Ʌřś�ş3Ȕɇ1ɒ�,��D�çɪȑ�GFúÝ@�FɵCEũȽ

ƿ0ȔɇJ F&?14ɴŰŠ~14ŤĊ3 crack �ƶŴĊò F.�� Griffith 3ƵȢ1ǕǼ�

&Ȕɇ�0�G,@C�ɵ��-4ɴGriffith 3ƵȢ3Ǖú�D Coulomb 3ƵȢ3Ďńƿ0ȔɇJ

ț=Fɵ <!ɴCoulomb 3ƵȢ4ùůƿ1"KšNJþ3NJþų�Jz�F@3.Ǹ�DGF�Dɴ"Kš

ÂGǀ3ŐĂJǸ�F�.1 FɵŬ@ÏǤ0ȟŦ4 § 2.5.1 1ȵ9&@3.ùůƿ1Þ�-�FɵCrack ®Ǘ1ƶ�FŀÃ3Ă��4ɴcrack ®Ǘ3ÿ�3ǔɑĽ¸�DļDGFɵÿ�4 crack 3ē

ƕ�ǚ��G5Ɂţ-Ä�DG&ŀÃ. crack ³3ŀÃ3Ġ1Ə� Fɵ�&�),ɴcrack ®Ǘ

3ŀÃɛ~�ŤĊ crack 3 9E1C),ƶ�,�F. G5ɴcrack ®Ǘ1ƶ�FŀÃɛ~4ɴ

Ä�DGF"Kšŀà . 9E1C),ƶ�FōÃ.3Ġ

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68

(3.5.22)

1Ə� F-�H�ɵ�<ɴÂGǀ3ŐĂ� -Ȫ�F. F.ɴ

(3.5.23)

JļFɵ��-ɴ 4ÂGǀ1«�ƕǯŀÃ-�Fɵ§ 2.5.1 3úÝ.3ɀ�4ɴ�G�ɴțŠ3NJþ-40� crack 3œFȀ�1Ĕ�,�IG,�F.�H-�H�ɵ�3ȟŦ1çɪ��F.

G5ɴƧò crack 3 9EJ¾ŗ. F�.3ąĴńAɴTerzaghi rule Jɗ14ȟŦ-�0��.ɴĹ139F 3āƃńJȟŦ-�0��.0/-�H�ɵ�

�w1ȵ9&çɪJ×Eɕ�14CEȝǧ0ƅö�ĿȎ-�Fɵ��-4ɴÂGǀ.�,ŷJȨ

ȷ�&ɶƉ­3@3JŅĎ�ɴFig. 3.5.5 1�FC�0Ȍş3Ė�0 crack ��FȰw1}K-ƂŊ

�GFu*3Ă�0"KšĢJ"Kš crack .Ǹ�,ɴ$GJĂ crack .C;�ɵÜĖ crack 4$3Ɏ�1Ə9,̸1Ȇ� �ɑJ@*ɵÜĖ crack 3ɑ4NJþ�G,�0�NrYR^0ŰŠ-

-�,�FɵĂ crack 3ɢ1ƶ�FǂĔƿ0ÿ�4ɴijńƿ0@3.ɡijńƿ0@.�D0F�ɴ

ɡijńƿ0@34Ė crack ɑ1�FNrYR^0ŰŠ�NJþ F�.1C),ƶ�Fɵ�3NJþJ

ȺǪ.ä;�ɵ<&ɴNJþ�ƾƶ F<-1ƶ�FĂ crack ɢ3ǂĔÿ�4$3 crack 3ĥCE@

Ė��.�,���ɵ�G4ùůƿ1ǯĵijńȢ-Ȝ�-�F�.J ș�C�. F&?-�Fɵ

�w3�ĎJ.@1NJþJǸĒ F�ɴ��-4ɴNJþJǠ3OapQt3ƟėJ�)&Ă crack 3ŐĂ-�F.ĎǷ Fɵ

� Ďńƿ0ȥȢ.�,ɴw1ȵ9&ȺǪ'�-4"Kš crack 3ŐĂ4Ȫ�D0�ɵ<&ɴĂ crack

®Ǘ3ŀÃ�ŰŠ3ƵȢIJĪ1ȿ�,@ɴĂ crack ®Ǘ3�Ę�Ȫ�F.4ɔD0�ɵŰŠ3NJþ

�Ȫ�F14ɴȺǪ�Ȫ�F3.ÞŨ1Ă crack ®Ǘ3ŀÃ�ŰŠ3NJþIJĪ1ȿ�0�G50D

0�ɵȺǪ1C),Ă crack ɢ3ǂĔÿ��ýÄ F�.1CE$3®Ǘ- crack 3ŐĂ�ɐĆ

F.��@3-�Fɵ�3úÝɴ JĂ crack JÏu3~ǔ0 crackɱGriffith crackɲ.�&.�1$3ŐĂ1ĿȎ0ŀÃɴ JĖ�0ÂGǀ�ȺǪ F&?1ĿȎ0ŀÃ. F.ɴNJþ�Ȫ�F

.�1țŠ1ÄI),�F"KšŀÃτ 4ɴ

(3.5.24)

-0�G50D0�ɵNJþ�Ȫ�F.�14ɂĴ0"KšŀÃ JƷ�,ɴ (3.5.25)

.ȉ�,C�H�ɵ��-ɴ 4 Jȉ &?'�3ɉ-�Eɴ 4Ǘ30�ÂG

ǀ3NJþɴ 0I(ɴ �ɢ3řś 9E1ĿȎ0ŀÃ-�F�.ȉ�,�Fɵuţɴ 4

"Kš crack ³�ǔƘ3úÝ-ǂĴ�,�FɵȺǪ�&Ė crack 1ĎĤƿ0 9EJBF"5ɴ$

3ȟŦ4 -1ȵ9&@3.Þƃ-�Fɵ

� ��-ɴȺǪ1ɚ�,��FNrYR^ŰŠ3NJþ@ Coulomb 3ƵȢ1�&�),�F.�C

�ɵNrYR^Ʌ¸�"Kš crack 3ɢ°�1Ð?FÂÝJ s .�ɴ"Kš crack 3ɢ1��FƕǯŀÃ3ĦôJ σ . F.ɴNrYR^Ʌ¸1«�ƕǯŀà 4 ɴ�&�),ɴ

$3"KšIJĪ 4

(3.5.26)

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69

-�Fɵ&'�ɴs 4̸1Ė��@3. Fɵ�GDJNJþ�"F1ĿȎ0ɢ°�-3Ħô"K

šŀà 4 s J�D1Ė�� F.ɴ

(3.5.27)

-�Eɴ�IBFřś½�ĕ�GFɵ�GJ³Ʌřś�ş.řś�ş3ǚ�ń.ä;�ɵ(3.5.27) J

(3.5.25) 1�¯ F.ɴ

(3.5.28)

.0EɴƧò crack 1ɒ F Coulomb 3ƵȢ�ļDGFɵ

� .�H-ɴĖ crack 3~1 ñà p 3Ɯ�J�GF.ɴ -�Eɴ

(3.5.29)

3.�1"Kš crack 3ŐĂ�4�<F�.10F�DɴTerzaghi rule �ȟŦ-�Fɵ�3C�0

3Ɵė4ƕǯŀÃ�Ė crack ɑ3NrYR^ŰŠ1ɛ~�0�.��jP`Wi1C),�Fɵ

�&�),ɴCEuȁƿ14ɴĖ crack 3~�Ă�0ɡñǴƳ.Ė�0¿ńƳJ@*ŰŠ-Ƣ&�

G,�,@C�ɵ�3úÝ1@ɴ"KšŀÃ'��Ė crack ɑ8ɛ~ F�.1CE 10F�.�Đŧ1�Ņ-�Fɵ 3ƀɔ-4ɴĂ�0"Kš crack 4ǤǞ1 Criffith crack .�,ŌIG,@C�@310H�ɵ 0I(ɴa) 1ȵ9&úÝ1ģDŽ�0�'H��ɵ

�3çɪ4Ǚɷǖ3šĚ3"KšIJĪ1�K FȥȢ1@đŕ1ɒ��,�Fɵ 3.6� ŬİorRȟ 3.6.1� NJþ3ǬȖƿńȩ

ȷĤɴ�FƮƵɉJǵEȴ�ơĎ F.ɴơĎȞĠJƶ�FɵơĎȞĠ4ɴơĎ~3§ƫ�Dƶ�

F@3.Ǹ�DGɴ§ƫ3éşJƟė�"FÅÃ1C),Ė�� F�.�-�FɵƮƵɉ3uǑ

-�FIJĪJơĎ F.ɴơϤ15D*��ƶ�F�.�džDG,�FɵFig. 3.6.1(a) 4ȃĞĝ-ơĎ�G&uȰñǴNJþIJĪ3cV^Sniɴ (b) 4$3Ǧǒ¸ġ-�FɵIJĪ�ƀ?,ĩ�ĥJ

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-�Fɵ(b) 4ƂŊȎǥ3�(ɴŬIJ3Ȏǥ�þG&.�1°��NJþ F.Ǹ�Fk]p-�Fɵ � Ǚ i Ƽǀ3Ȏǥ�Ǡ1Ä�DG&ŀÃσ<-þG0�-�FNjƳ (NjƳ¸ġɒş)J Pi(σ) . Fɵ

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Fɵ�3 Pi(σ)4¡ɩĪ.@ä5GFɵ(a) 3úÝɴŀÃJ 0�D σ <-ýÄ�"&.�1ɴ�!G

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(3.6.1)

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(3.6.2)

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(3.6.4)

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(3.6.5)

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(3.6.6)

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ɴ (3.6.7)

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(3.6.8)

-ȉ�GFɵ

3.6.3� ŬİorRȟ.Weibull ¸ġ� NjƳ¸ġ.�,�ȉƿ0@314ƊȐ¸ġ��F�ɴƊȐ¸ġ4NjƳÿş x �Ëɑ [- ∞, ∞] -Ď

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(3.6.9)

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J�Ď�&ɵ&'�ɴm > 0, a > 0 -�Fɵ�3ɒşJƷ�F.ɴŀÃJ 0�D x <-ýÄ�"F.�1 1¢-@ crack�ƶ�FNjƳɱNjƳ¸ġɒşɲW(x) 4

(3.6.10)

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(3.6.11)

.0FɵNjƳđĪ� g(x) -ȉ�GF¸ġJWeibull¸ġ (Weibull distribution) .ä7ɵW(x) 4$3

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1Ǎ�&ɵmJĂ�� F.¸ġ3ĥ4Ʋ�0FɵmJWeibull3ôuń�ş (coefficient of uniformity)

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�Fɵ�3�.�Dɴ��5 Scholz (1990: The mechanics of earthquakes and faulting, Cambridge Univ.

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Yamamoto (1999?) 4�3Ǹ�J¼Ʒ F�.1C),ɴĝLj3ñǴNJþIJĪ�ȟŦ-�F�.JǍ

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