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Zhuetal.gratefullyacknowledged.PartofthisworkwascarriedoutattheUniversityofAlberta,Canada.Theauthorsaregrate-fultoProf.N.R.Morgensternforgivinginvaluableguidanceonthisstudy.DuringD.Y.Zhu’sstudyleaveinCanada,supportedbytheUniversityofHongKong,Dr.J.H.Chenprovidedusefulhelp,aswellasdiscussionsonthework.TherevisionofthisworkwaspartiallysupportedbytheNa-tionalNaturalScienceFoundationofChina(grantNo.40472138)andtheLaboratoryofHazardPreventionandMitigationatChinaThreeGorgesUniversity.

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AppendixA.Solutionforthefactorofsafety

Solvingeqs.[18a]and[18b]forη1andη2,oneobtainsT0+

1

T1+1

[A1a]ηFF2T21=

s

G0+sFG1+

s

FG2sS0+

1

S1+1[A1b]ηFFS22=

G0+FG1+

s

F2G2s

where

[A2a]T0=A3B2 A2B3;

T1=A3B′2+A′3B2 A2B′3 A′2B3;

T2=A′3B′2 A′2B′3

[A2b]S0=A1B3 A3B1;

S1=A1B′3+A′1B3 A3B′1 A′3B1;

S2=A′1B′3 A′3B′1

[A2c]G0=A1B2 A2B1;

G1=A1B′2+A′1B2 A2B′1 A′2B1;

G2=A′1B′2 A′2B′1

Substitutingeqs.[A1a]and[A1b]intoeq.[18c]andrear-rangingyieldsacubicfunctionofFs,asfollows:[A3]F3s+t2F2

s+t1Fs+t0=0

where[A4a]tD0= 1T2+D2S2+D3G2E1T0+E2S0+E3G0

[A4b]tE1=1T2+E2S2+E3G2 D1T1 D2S1 D3G1

E1T0+E2S0+E3G0[A4c]tE2=

1T1+E2S1+E3G1 D1T0 D2S0 D3G0

E1T0+E2S0+E3G0

Equation[A3]isrewrittenas: 3

[A5] Fts 2 3 +p Fts 2

3

+q=0where[A6a]p= t223

+t

1[A6b]q=

127t32 1

3t1t2+t0Solvingeq.[A5]givestheexpressionforthefactorofsafety

Fsasineq.[20].