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47
Ǚ 3ǖ� NJþ3ùnjƵȢ
3.1 ÿĵ ÿĵ4ɴijńÿĵɴɡijńÿĵ1Ă» F�.�-�Fɵijńÿĵ4ɴŀÃσ.Ƌ= e3ɒ��
�F�4� �
3C�1ɴ1 �3ɒş-ȉ�GFÿĵ3�.J��ɵ�3ɒ�14Ũɑ3ɦ�¯),�0�ɵ��
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ɑÿÊ1�Ċ�&ŀÃɴ�F�4ŀÃ1�Ċ�&ȸĪ-ƋÿÊ�ƶ�Fɵ�3ńȩJǟń (Viscocity)
.äK-�Fɵijńÿĵ-�E0�DɴŨɑ�Ċń3�Fÿĵ@�Fɵ.�1ɴ�3ńȩ4 anelasticity
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,@ɴĊò�,�F.Ǹ�&ţ�C�ɵijńƿÿĵ÷ɴûń÷0/3¸ɬ4ɴÿĵ°�JƅöÊ
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� �Fţß�Dğȑƿ14uƃ0ŀÃJÄ�,ĝLjțŠJÿĵ�"&.�3ɴŀÃ.Ƌ3ɒ��C
6�3C�0țɯ-ÿĵ�&ĝLjțŠ3ƃĈJ Fig. 3.1.1(a) . (b) 1Ǎ�&ɵFig. 3.1.24ơĎ�G
FŀÃ.Ƌ=3ɒ�3²öƿ0œFȀ�Jƅĭƿ1Ǎ�&@3-�Fɵ*Ɨ)� ��-4ɴțŠ�$�
1Ä�DG,�FÃJ ő FǺÃJĄ�Ć?F�.JNJþ.ä7�.1 FɵFig. 3.1.2 (a) 4ɴ
48
NJþ¾1Ă�0ûńÿĵJ F�ɴNJþ1CFŀÃɓx�Ńƨ-40�úÝ-�FɵFigure 3. 1.2 (b)
4ɴNJþ3¾3ûńÿĵ�Ė��ɴNJþ1��ŀÃɓx�Ă��úÝ-�Fɵ¾ǹ3ÿĵJĬńNJ
þ (Ductile Fracture)ɴĹǹ3NJþJǻńNJþ (Brittle Fracture) .C7ɵNJþ1CFƖÇ3ƶŊ4ɴɰ
ȸ1�Ę FNJþ�F�4ɰȸ1�Ś F 9E1C),��0IGFɵƖÇ3ƶŊJ��NJþJ
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ŀÃ-Ƌɒ�14ɴûńÿĵ (plastic deformation) �Ń1Ă��0FƴȦ��Fɵ�GJɴɓ�ɱyieldɲ.ä7ɵɓ��Ć<FŀÃ14ɓ�ɱƩɲŀÃɱyield point stressɲ�F�4ɓ�IJĪ (yielding strength)
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Ʌ-4Ĭńƿ0ûńÿĵ�ÎȬ�,ȻȈ�,�F.ȕ�Ǹ��ƴòĤȤƿ-�FɵĬńƿÿĵ�Î
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3C�0ÿĵ3ƃĭ1C),ŜɆ�G,�Fɴ 0I(ɴĝLj3NJþIJĪ1C),Ɠ<),�F�
.10Fɵóƍ³3IJĪ¸ġ4ƠĪ.ƋȸĪJz�F.ɴĝLj3NJþIJĪƯńɱÿĵƯńɲ�Dƒ
?F�.�-�Fɵ�3C�1�,Ɠ<Fóƍ³3IJĪ¸ġJ Brace-Goetze Strength Profile.ä7
úÝ��Fɱ��5ɴP. Molnar, 1992: In Fault Mechanics and Transport Properties of Rocks, Academic
Pressɲɵ��-4ɴĝLj3NJþIJĪ.�,4řś�ş�Ʒ�DGFɵ�3C�0k]p-óƍ³3
ŀøġJǸ�F.�14ɴřś�ş�ɈȎ0ķÂJŹ& �.10F.���.�Đŧ1ŖĒ-
�C�ɵ � �w3óƍ³3ÿĵ.ŀÃ3ɒ�4ɴóƍ�Ĥ1ûńƿ0ÿĵɱƚÇɲJá>NJþJ�),ÿĵ
�,�F�.J¾ŗ1�,�Fɵ�G4ɴóƍ3h\rUlpOapQtɱƋOapQtɲ4Ĥ1
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� *Ɨ)� Fig. 3 1.11Ǎ�G,�FǻńNJþ3úÝ14ɴNJþĹ (post-failure) 3ŀÃ-Ƌ=3ɒ��ɴNJþJƾƶ�"FțɯƇ3¿ń1C),ÿIF�.�džDG,�Fɵ 0I(ɴ¿ń3Ă��ƇžJƷ�F�.1C),ɴĖ�0
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&ƋOapQt�Ȕŝ�Gɴ$G�țŠ1Ĕ�,��J Fɵ$3��ɉ4 0I(¿ń3Ė��țɯƇ:/Ă�
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49
țŠÿĵ3 post failure1��FœFȀ�JȠ9,ɴNJŘȾǐ (break down process) JŦD�1�C�. FljǓ@ȈIG,�F (&.�5ɴOhnaka 3Ŭȳ3ljǓɹóɟċ�ǚ3ȣƦ)ɵ&'ɴpost-failure1��FŀÃƋɒ���Jȉ �1*�,4CEƝ�ǸĒ�ĿȎ-�F.Ǹ�DGF (Ǚ 6ǖ~3ĽĖNJþIJĪ¸ġƅöJÕƬ)ɵ
3.2� NJþ.OapQt ɺÕǸūɸĜűį�ɴǯĵNJþÃċ¯ɏɴøɭɮɻ
3.2.1� ƋOapQt.ĀÃ�� Fig. 3. 2.1 (a) 1Ǎ C�1ɴijń�1�Ʒ FÃJ P.�ɴP1C),ƶ�FȄɈƩ3ÿ�J u.
Fɵijń�~1�FRn[R3ɢǒJ A. F.�ɴȄɈ P 4 u . A 3ɒş-
(3.2.1)
.ū�F-�H�ɵ�<ɴcrack 3ɢǒ�δA '�ýÄ�&. F.ɴijń�4ÿĵ�A �0F.
Ǹ�,C��DɴFig. 3.2.2 (a) �D¸�FC�1ɴÞu3ÿ�1Ĕ�,Ĥ1ɴ
(3.2.2)
-�Fɵ
� Āà P 1C),ÿ�� u 10F<-3ɑ1ĀÃ��3ijń�10 ��ɱĀÃ��ɲ Uex 4
(3.2.3)
-�EɴFig. 3.2.2 (a) 1��,Ķ�*�DG&ɧ÷3ɢǒ-Ǎ�GFɵ
ijń�10�G&�3��4ɴijń�~1Ƌ=OapQtW.�,ȅ�DGFɵ 0I(ijń�
�@*ƋOapQtW4ɴ
Fig. 3.2.1 Fig. 3.2.2
50
(3.2.4)
-�Fɵ�<ɴ P . u �Þuţß1�F.�ɴ$G%G3Ă��J P. u-ȉ"5ɴ(3.2.4) CEɴ
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3.2.1(a) 1�FC�0ba1C),Ä�DG,�F@3.�ɴ�3ba1Ä�DGFà P* .ba
3ÿ�ɱ�6ɲ u* .3ɒ�J Fig. 3.2.2(b) 1�FC�0@3-�F. Fɵ
Figure 3.2.1(b) 3C�1ijń� VJba1*0�ɴu + u* ��F¤10F<-Į)ı)&��-
ïĎ�C�ɵijń�.ba4ɋEÝ�3ưŇ1�F.Ǹ�DGF�DɴP* = P-�Fɵ�3.�3
Ã.ÿ�3ɒ�� Fig. 3.2.2(c) 1îǍ�G,�Fɵijń�.ba4 a Ʃ-ɋEÝ),�Fɵ�3úÝɴǠ°��@*OapQt4 Oae-í<G&ɢǒ-z�DGFɵ
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(3.2.6)
1C),ļDGF.�ɴ�3ÃJh\rUlpÃɴΠ*(u) JĀÃ3�ƷǠ3h\rUlpOapQ
t.ä7ɵ(3.2.6)CEɴΠ*(u) 4
(3.2.7)
-�DI�GFɵ��-ɴu0 4�ņ-�Fɵ®1ȵ9&ba3úÝɴu0J Fig. 3.2.2c) 1�Ǎ�G
,�FƩ e 1.F.ɴ+ Π*(u) 4ba1ȅ�DG&ƋOapQt1ǂĴ FɵĀÃ� u1CD!u
Ď3.�14ɴȷĤɴu0 = 0 1Ƀ6ɴ
(3.2.8)
.��ɵP �ɈÃ1CFȄɈ-�F.�ɴwĭ4ÿ� u 1Ĕ�, Pu'�ɈÃh\rUlp��x
F�.Jȉ�,�Fɵ
� ĀÃ3�ƷǠJá>Ǡ°�3ÃċƿOapQtJh\rUlpOapQt.ä6ɴΠ .ū��.
1 Fɵ�&�),ɴΠ 4
(3.2.9)
-�FɵɋEÝ�3ưŇ-4ɴ
(3.2.10)
-�Fɵ [ç] ĭ (2. 4) �ǯĵijń�1Ĕ�,ŊEǕ*�.JɴCEuȁƿ0ĵ-șŦ"Cɵ
51
3.2.3� Rn[R3�Ę1CFh\rUlpOapQt3Ȕŝ ijń�1ɢǒ A+δA 3Rn[R��Fijń��ɴ�2.2 -ȵ9&@3.Þu3h\rUlpÃ3
@.1�F.�ɴP = P(u, A+δA) [ < P(u, A)] JƢ&�**ɴijń�14 u + δu 3ÿ��ƶ�,ɋ
EÝ�3ưŇ10FɵFig. 3.2.2 (c) 1��,4Ʃ c3�Ƕ-ɋEÝ�ɵ�3ɋEÝ�3ưŇ1��
Fh\rUlpOapQt4 Oce-í<G&ɢǒ1ǂĴ FɵuţɴƩ a-ɋEÝ�3ưŇ1�Fijń�~3Rn[R3ɢǒ A�ɋEÝ�J (** A + δA 10)&. G5ɴɋEÝ�3�Ƕ4
P = P*(u) 1Ɣ),Ʃ c 1ǏÇ Fɵ$3.�Rn[R3ɢǒ3ýĂ1C), Oac-í<G&ɢǒ
1ǂĴ Fh\rUlpOapQt3Ɵė�ƶ�Fɵh\rUlpOapQt3ÿʸJδΠ�δΑ .
F.ɴ
(ɢǒ Oac) < 0 (&'�ɴδA > 0) (3.2.11)
.ū�Fɵ.�H-ɴδA3ÿÊ�ĀÃuĎ3ų�-Ȫ�FúÝ14ɴac4ƐĦɴÿ�uĎ33ų�
-Ȫ�F.�14ɴõǁ-�FɱFig. 3.2.2 ÕƬɲɵ
� Fig. 3.2.2 (c) 1��,ɴ δΠ* (ɢǒ bacd1ǂĴ) 4ĀÃ�ijń�V10�&�� δUex 1ǚ��ɵ
ijń��0�G&�� δUex 4ɴuɅ4ƋOapQt.�,ȅ�DGF�Dɴ$3Ġ4ɴ
ɴ (3.2.12)
.0Eɴh\rUlpOapQt�Ɵė F�.10Fɵ
3.2.4 OapQtɐŝƳ �x-4ɴč°ijń�3ĽĖÿĵ3=JŌ�@3. Fɵ�3.�ɴƋOapQtđĪɒş w4
(3.2.13)
52
-�Fɵcijpq 4V\M[daV-�Fɵijń�1á<GFÂGǀ3ɢǒ�Ă��:/ɴȷĤ4ɴV
\M[daV�Ė��0Fɵ��-ɴijń���F�ǒ V3ijń�1ȅ�DGFƋOapQtW4
(3.2.14)
-�&�DGFɵFig. 3.2.3 (a), (b), (c) 4$G%Gǯĵijń�1��FRn[Rɢ3ĽĖýÄ δA1
CFh\rUlpOapQt3ÿÊ1*�,ɴÿ�uĎɴȄɈuĎɴ�C6ɴĀÃ�uȁ3h\r
Ulp-z�DGFúÝ3Üų�1*�,ɴƅĭƿ1Ǎ�&@3-�Fɵ
� Üų�x-3OapQtÿÊ4�x3C�10Fɵ
(a) ���� (�� �) ���ɸ
-�F�Dɴ
(u = uĎ)ɵ (3.2.15)
0I(ɴδA3ÿÊ1C),ĀÃ���J�0�C�0ų�x1�FǠ-4ɴh\rUlpOap
Qt3ÿÊ4ƋOapQt3ÿÊ1ǚ��ɵ<&ɴδA3ýÄ1C),ƋOapQt4Ȕŝ�GFɱƟ
ė Fɲɵ (b) �#&'�� �(���ɸ
ƋOapQt4�
(3.2.16)
-�EɴƋOapQt4ýÄ FɵĀÃ��4
δUex = �abd"c" = 2δW (3.2.17)
�&�),ɴ
(3.2.18)
.0Eɴh\rUlpOapQt4Ɵė Fɵ��-ɴh\rUlpOapQt4Ɵė F�ɴƋ
OapQt�ýÄ F�.1̸Ɨņ FĿȎ��Fɵóƍ³3NJþ�óƍ³1ȅ�DG&Oap
Qt3ȔŝJņã F. G5ɴOapQt3Ȕŝ�ȈIGFɧ÷�F�4h\rUlpOapQ
t�ĎǷ�GFǠ�/3C�0@3-�F��Ă�0çɪ-�Fɵ
(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)
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$3�.1*�,@ȵ90��ɵ
[ç 2ɻñǴțɯ1CF post-failure3œFȀ�1*�,ǸĒ"Cɵ [ç 3ɻóɟ�ɴ�E1ȄɈuĎx-ƶ�,�F. F.ɴ/3C�0çɪ�ƶ�F�ɴ<&ɴ�E1ÿ�ŎŲ3ų�-ƾƶ�,�F. F./3C�0çɪ�ƶ�F�JȢ#Cɵ�D1ɴóɟ4/3C�0üƹų�-ƾƶ�,
�F.Ǹ�F9��JȢ#Cɵ
3.3 ŀÃŐĂ�ş 3.3.1� NJþƃĭ.ŀÃŐĂ�ş � Ɖǜ1ȵ9F�ɴGriffice1CG5ɴNJþ4Ƨòƿ0ÂGǀ (crack) �ŐĂ�Ć?F�.1C),
ƾƶ Fɵ�3Ǹ�ţ4ɴ�-@ŔƷ�GFũȽƿ0Ǹ�ţ-�Fɵ�3Ǖú-NJþJȢ�C�.
Fig. 3.3.1
Fig. 3.3.2
54
F.�ɴu¢3Ƨò crack3âí1ƶ�FŀøġJǸ�F�.�ɈȎ-�FɵFig. 3.3.14 crack
3ɞĈɫĽɍµǃ-�F�ɴ�3C�0 crack 4ɴşċƿ14ɴuƃ0ŀÃ�«�,�FȺǭ�³
1�FɢJǸ�ɴ�3ɢJ4�> 2Ʃ-3ÿ��yȺǭ-�EɴɢJ.��,ǂ�1Ö;�Ý�Ã
�0�@3.�,×EŌIGFɵ�3×EŌ�ţ14�1ɶȷE�Fɵu*4ÂGǀJÒ=Jő*
ǔĉ.�,Ō�@3-ɴǔĉ4ā�3úÝȆ�ſ´ĉ.�,ŌIGFɵ�ţ4Ò=30�yȺǭɢ
.�,Ō�@3-�Fɵ Fig. 3.3.214ɴzţß1Ò�ŷJȨȷ�& crackJɴŋĦ0ſ´ĉ-ȳ��&.�ɴſ´ĉâí1
ƶ�FŀÃ3¸ġ�Ǎ�G,�Fɵſ´3ɎȰ3Ɏ�J 2a�LJȰ3Ɏ�J 2b . F.�ŰŠ1 y
= ± ∞ -ŀà {σy}∞ �«�,�F.�ɴÂGǀ®Ǘ-3ŀà {σy}max 4�
(3.3.1a)
-�Eɴ®Ǘ3ŪƳ ρ (= b2/a) � ρ << a 3.��
� (3.3.1b)
3C�1ȉ�GF�(Sih and Liebowitz, 1968, FractureɴII, Academic Press)ɵα 4ƪƉ3Ďş-�ŀÃ
ɛ~�ş.ä5GF�α4țŠēƕ. crackēƕ3ɒ��ǂ�-�Eɴcrackĵư� crackēƕ1CD
!ǚ��.�ɱcrack�ǂ�ɲ-�G5țŠēƕ�ÿI),@ÿID0�ɱ´ĉ3âE3ŀÃJŅ¬
�,=F.Ȃ�ɲɵ σt JÂGǀ®Ǘ�Dª�1ɜG&ɢ1ƶ�FŕǯŀÃ. F.ɴ
(3.3.2)
.ȉ�Gɴρ 0 -4ɴɔE0�ÂGǀ3®Ǘ1ȳ�.�H1�G�ƶ�Fɵ <&ɴſ´ĉ®Ǘ
ȳ¨3 x Ȱw3ŀøġ4ɴ0 ≤ * << aɴr << a 3.�ɴ
(3.3.3)
Fig. 3.3.3
55
�GD3ŋĦ0ſ´öÂGǀ�DļDGFȔ4ɴÂGǀ3®Ǘ3��ȳ¨JJɕ�, ρ 0 . F
.ɴÒ=30� crack 1Ĕ FȔ1uǿ Fɵ
�w4ɴıÃöÂGǀ (tension crack) Jſ´ȳ�-ȉ�&úÝ3@3-�FɵCEuȁƿ14ɴ
Ò=30�ÂGǀ (crack)� 3ÿĵ�F�4NJþƃĭJɴMode�(opening), Mode �(inplane sliding),
. Mode (antiplane sliding) 1¸Ȕ�,Ǹ�ɴďɚ3NJþJ�GD3�!G�3kt_ɴ�F�4ɴ
�GD3ȌÝ.�,ȔŸ FɵFig. 3.3.34�GD3kt_JîǍ�&@3-�FɵMode�3 crack 4ɴıÃöNJþ (tensile fracture)ɴMode�.4ÀšNJþɱshear fractureɲ1Ĕŀ�& crack -�Fɵ
î1��FīƄ (x, y, z) 3×Eţ4NJþÃċ1��FȷĤ3ǢŲ-�FɵîǍ�&Ʌ¸4ɴcrack ¾
Dz3uɅ-�Eɴ�3Ʌ¸3ŪƳÍĸɱRn[R3Íĸɲ4ɴ¾Dz�ǁǯ-�F.ȳ�-�FǐĪ
1Ă��ɴîǍ�G,�FɅ¸3ēƕ4Ė��@3.Ǹ�Fɵ�3C�0úÝɴÜȰţß3ÿ� u, v,
w4 (3.3.4)
-ȉ �.�-�FɶƉ3ú10FɵɈ2ÝI"3ÓƵ�Dɴ�GD3ú4
(3.3.5)
1¸Ȕ-�Fɵ��-ɴRn[R4 z= constant 3ɢ3uɅ –a ≤ x ≤ a 1�GDG&¹EȲ=-�Fɵ(A)4ĦɢƋ=3ɶƉijńȢɴ (B) 42�E1ɒ FijńȔJƷ�,ȉ �.�-�Fɵ(C) 1
CF crack®Ǘ-3ŀÃ4 (A), (B) 1CEƶ�FĂ�0ŀÃ1Ə9,ƪȑ-�FǐĪ1Ė��ɱ&
.�5ɴǯĵNJþÃċ¯ɏɴ1976ɴĜűį�ɴøɭɮɲɵMode�.�3úÝ4 (A)ɴMode3ú
Ý4 (B) 3Ȕ�D$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)
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$3ēƕ1�Ċ�0�ɉ-�)&31Ĕ�ɴK 4 crack 3Ɏ��Ɏ�0F.Ă��0Eɴēƕ1�Ċ Fɉ.�,ĎǷ�G,�Fɵ<&
�3�ş4ɴcrack 3Ɏ�3ĦţŻ1Ə��, crack ®Ǘ-3ŀÃ�Ă��0F�.Jȉ�,�Fɵ 3.3.2� ŀÃŐĂ�ş.OapQtȔŝƳ Rn[R3ĬɎǯw1Rn[R�ŊɎ FúÝ4ɴOapQtȔŝƳ.ŀÃŐĂ�ş.3ɑ1ǝÏ
57
0ɒ���FɵǝÏ3&?1ɴRn[Rɢǒ3ĽĖýÄ δA�1CFh\rUlpOapQt3ȔŝJɴÿ�ŎŲ3úÝ1*�,Ǹ�C�ɵh\rUlpOapQt3Ȕŝɉ� �4�3úÝɴƋO
apQt3Ȕŝɉ1:�0D0�ɵ �J�x3C�0ȾǐJǸ�,Ț� Fɵ
(1) Rn[R3®Ǘ1δA3¹GȲ=J¯GɴRn[Rɢ14$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)
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)
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,
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)
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.���.�-�
Fɵ
3.4.4 ÀšƋOapQtȟ �ŀÃJ σ1, σ2, σ3, $GD3¥ĠŀÃJ s1, s2, s3 .ū�ɵ��-ɴ¥Ġŀà si 4
(3.4.18)
-�Fɵ�3.�ɴyÿɉ J1, J2, J3 4
(3.4.19)
uţɴƋOapQtWJ¥ĠŀÃ-ȉ .ɴ
62
(3.4.20)
��-ɴµ 4¿ńƳɴK 4ɡñǴƳ-�Fɵ
� ɓ� (yielding) 4īƄ3×Eţ1ƪɒ�1��Fɵ<&ɴĦôŀÃ4ɓ�3Ⱦǐ1ĶɣJ�C;
�0�ɵ�3�.�Dɴvon Mises4ɓ�ų� (criterion of yielding) 4ĠŀÃ1ɒ Fyÿɉ J2'�
1�IF.Ǹ�ɴŰŠ3Ďş σ0 1Ĕ�,ɴ (3.4.21)
�ŊEǕ*.�ɴɓ��ƶ�F.�&ɵ�GJɴvon Mises3ɓ�ų�.ä7ɵ<&ɴHuber (1904) .
Hencky (1924) 4ÀšƋOapQt��FuϤ1ȿ�&.�ɓ��ƶ�F.��ȟJŗæ�&�ɴ
�3ȟ4ɴw3ĭ�D¸�FC�1ɴvon Mises3ų�.Þ�ǪŹJz�Fɵvon Mises4şċƿ0
Ȏȡ�D�3 criterionJĕ�&�ɴHuber-Hencky4$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
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
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(3.5.3)
3C�1ȉ�GFɵ 0I(ɴ
(3.5.4)
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ƿ1
64
(3.5.5)
.ū�F�Dɴ(5.4) . (5.5) �D λ JƛÔ�,ɴ
(3.5.6)
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� 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�
Dɴ
(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
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
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Fig. 3.5.2 1�FC�1ɴ2*3�ñǴŀà P)Q�«�,�Fŷ3~1 crack��FɵcrackDz-
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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�
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66
&ţß3ƕǯŀÃ ση(ξ0, η) 4
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�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)
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F�.-�F�Dɴ
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 ��%
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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
68
(3.5.22)
1Ə� F-�H�ɵ�<ɴÂGǀ3ŐĂ� -Ȫ�F. F.ɴ
(3.5.23)
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ȷ�&ɶƉ3@3JŅĎ�ɴFig. 3.5.5 1�FC�0Ȍş3Ė�0 crack ��FȰw1}K-ƂŊ
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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@
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®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$3®Ǘ- crack 3ŐĂ�ɐĆ
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.�1țŠ1ÄI),�F"KšŀÃτ 4ɴ
(3.5.24)
-0�G50D0�ɵNJþ�Ȫ�F.�14ɂĴ0"KšŀÃ JƷ�,ɴ (3.5.25)
.ȉ�,C�H�ɵ��-ɴ 4 Jȉ &?'�3ɉ-�Eɴ 4Ǘ30�ÂG
ǀ3NJþɴ 0I(ɴ �ɢ3řś 9E1ĿȎ0ŀÃ-�F�.ȉ�,�Fɵuţɴ 4
"Kš crack ³�ǔƘ3úÝ-ǂĴ�,�FɵȺǪ�&Ė crack 1ĎĤƿ0 9EJBF"5ɴ$
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
$3"KšIJĪ 4
(3.5.26)
69
-�Fɵ&'�ɴs 4̸1Ė��@3. Fɵ�GDJNJþ�"F1ĿȎ0ɢ°�-3Ħô"K
šŀà 4 s J�D1Ė�� F.ɴ
(3.5.27)
-�Eɴ�IBFřś½�ĕ�GFɵ�GJ³Ʌřś�ş.řś�ş3ǚ�ń.ä;�ɵ(3.5.27) J
(3.5.25) 1�¯ F.ɴ
(3.5.28)
.0EɴƧò crack 1ɒ F Coulomb 3ƵȢ�ļDGFɵ
� .�H-ɴĖ crack 3~1 ñà p 3Ɯ�J�GF.ɴ -�Eɴ
(3.5.29)
3.�1"Kš crack 3ŐĂ�4�<F�.10F�DɴTerzaghi rule �ȟŦ-�Fɵ�3C�0
3Ɵė4ƕǯŀÃ�Ė crack ɑ3NrYR^ŰŠ1ɛ~�0�.��jP`Wi1C),�Fɵ
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70
� �3ȟ�D=F.ɴŰŠ3IJĪ4ɴŰŠ�á>Rn[R��Ę�Ć?FÑÄŀÃ3Ă��J�D
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0I(ɴǙ i Ƽǀ3ȎǥJ×E·�&Ǝɛë�DɴN ¢3ȎǥJ.E'�ɴ$GD1��FŀÃ
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71
Fɵ�3 Pi(σ)4¡ɩĪ.@ä5GFɵ(a) 3úÝɴŀÃJ 0�D σ <-ýÄ�"&.�1ɴ�!G
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(3.6.2)
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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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(3.6.9)
72
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
¸ġɒş-�FɵWeibull¸ġ4®1ȵ9&IJĪ¸ġ3ų�JƢ&�,�Fɵ̧ ġɒş3�JFig. 3.6.3
1Ǎ�&ɵmJĂ�� F.¸ġ3ĥ4Ʋ�0FɵmJWeibull3ôuń�ş (coefficient of uniformity)
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(3.6.12)
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IJĪ¸ġ Q(σ) 4
(3.6.13)
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(3.6.14)
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(3.6.15)
73
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á>C�0ǚ�ǒ3Ȏǥ1¸Â�,Ǹ�F.ɴn4ŰŠ3�ǒ V1Ə� Fɵ 0I(ɴ (3.6.16)
-�Eɴ�G4ŰŠIJĪ3ēƕÆŹJƴ �.10Fɵ
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