Mechanism of action of cracks water on rock landslide in rainfall

J. Cent. South Univ. Technol. (2010) 17: 1383-1388包SpringerDOI: 10.1007511771-010 0646-6Mechanism of action of cracks water on rock landslide in rainfallWU Yong(吴永)+2, HE Si-ming(何思明)2, LI Xin-po(李新坡)",21. Key Laboratory of Mountain Hazards and Surface Process, Chinese Academy of Sciences,Chengdu 610041, China;2. Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chengdu 610041, China◎Central South University Press and Springer- Verlag Berlin Heidelberg 2010Abstract: In worldwide, the most common triggering factor of rock landslides is extended and intense rainfall. However, differentfrom the soil slope failure caused by softening action of infiltration rainwater, the mechanism of rock landslide in rainfall is not clear.From the view of fracture mechanics, the propagation of cracks on rock slope and the development of sliding surface were researched.Then based on hydraulics formulas and using Sweden arc method, the influence of crack water on stability of rock slope wasquantitatively studied. Finally, an example was given to check the theoretical approach. The result shows that the development ofsliding surface of rock slope is mainly caused by crack propagation under hydrostatic pressure when the stress intensity factor K atcrack tip is bigger than the toughness index of rock fractures Kic, and the failure of slope is the result of hydraulic action of crackwater and the softening of materials on sliding surface when the depth of crack water is bigger than a minimum value hmin.Key words: crack water; fracture mechanics; propagation; hydraulics; Sweden arc method; rock landslideconductivity, such as the way how the water flows into1 Introductionslope and what role of water plays are not clear，whichaffects the stability of rock slope greatly.Rock landslide is a dynamic evolution process inIn fact, the rock slope failure due to rainfall is awhich rock slope slides down rapidly along the slidingcomplex geological problem [13]. It involves thesurface. As a kind of prevailing disaster in mountains,interaction of a number of hydraulic and geologicalthey generally cause serious damage and great fatalitiesfactors. As is shown in Fig.l, rock masses usuallybecause it usually occurs unexpectedly and move rapidly.contain a number of cracks that may become potentialAlthough many factors such as earthquake andsliding surfaces when they propagate to connct eachengineering excavation can induce the rock slope failure,other or weak interlayer. While the sliding surface forms,the most common and important one is also the rainfallthe rainwater flows in and results in the failure of slopewater according to many investigations and engineeringeventually. During this process， the decrease ofpractices [1-2].mechanical properties of weak interlayer and hydraulicMany studies [3- 6] were undertaken by otheraction generated on the new sliding surface have a majorresearchers to investigate the effect of rainfall on slopeinfluence on the slope stability.stability. TERZAGHI [7] firstlypresented thaCracks on sloperainfall-induced landslides are caused by increased porepressures and seepage forces during periods of intenseraifall. BRAND [8- 9] recognized that it is the increasedpore pressure that decreases the effective stress in thesoil, thus reducing the soil shear strength, and eventuallyresulting in slope failure. Similarly, recent works [10-12]Rock slopeillustrated the role of factors such as rainfall intensity,Rockbedrainfall pattern and soil strength on slope stability.However, the main focus ofplaced on the effects of rainfall infiltration on soil slopestability. Very limited work can be found on theCrack and fllingfailure mechanism of rock slope in rainfall with lowFig1 Cracks and中国煤化工Foundation item: Project(2008CB425802) supported by the National Basic Research Program ofCHCNMHGbytheNationalNatural Science Foundation of China; Project(9R2200200) supported by the West以. suy of SciencesReceived date: 2010- -03- 26; Accepted date: 2010-08- 05Corresponding author: WU Yong, PhD; Tel: +86- 15928074439; E-mail: wyhongyu@ 163.com.1384J. Cent. South Univ. Technol. (2010) 17: 1383- 1388Here from the view of fracture mechanics, thσ=ywh(3)mechanism of cracks propagation and sliding surfacedevelopment were studied clearly firstly. Then based onwhere Y'w is the bulk density of water.Thus, stress intensity factor K at crack tip can behydraulics formulas, the forced state of sliding surfacewritten as:including the action of crack water was analyzed.Finally, according to the Sweden arc method, the wholestability of rock slope with the influence of crack waterKp= axwh2π2(4)was quantitatively studied with an example, whichwhere a= -0.682 8 [15].illustrates the failure mechanism of rock slope in rainfallObviously, K grows continually with the incrementeventually.of crack water and results in the propagation of crackwhile it satisfies:2 Mechanism of propagation of cracks onrock slope under intensive rainfallK> Krc5)where Kic is the toughness index of rock fractures.As a kind of geologic body, rock slopes have beenFor the Cracks flldl with water, the value of K justexisting in nature for millions of years, and manydepends on their depth. Hence, to summary up the abovemicrostructures such as joints and cracks have formed inequations, a critical depth he can be given to determine .weathering. Among these different fractures, some arewhether the water filleld cracks can propagate:closed and cannot drain rainfall water out timely. Thus,the high hydrostatic pressure generates, which induces( Krche = 0.75(6)the failure of cracks eventually.Taking crack mouth as the origin, and building xWhen the crack is full of water and its depth isaxis along the cracks， the propagation model o1water-filled rock crack under hydrostatic pressure can bebigger than h, the crack starts to extend. Thus, thesimplified as a semi-infinite plane question (Fig.2).criterion on crack propagation can be expressed as:Acording to the principles of fracture mechanics [14]，h≥he(7)when an arbitrary distributed“the local stress" o(x) actsSpecially note that the critical depth is a very usefulon the crack surface, the stress intensity factor on its tipparameter in hazard control engineering. Because onlyisthose cracks whose depth is bigger than he can propagateK=aσvπh(1)and cause the failure of slope in intense rainfall, it is easyto ascertain dangerous rock slope by contrasting thewhere K is the stress intensity factor on crack tip; a iscrack depth with ho.shape factor; h is crack depth; and σ is the maximumstress acting on crack surface and can be expressed as:3 Hydraulic action of crack waterσ= σ(x)(2)When the depth satisfies Eq.(7), the crack will start>(刮)"n=0\hto propagate and keep extending until it connects withHere the maximum stress σ acting on crack face is:the weak interlayer in intense rainfall. Thus, a newsliding surface, as a seepage channel, is formed. Then,with the flowing of rainwater, the sliding surface issoftened and the slope static balance is broken byhydraulic action, which results in the failure of rockHydrostaticpressureslope eventually.It is often assumed that the failure of slope isconfined to circular planes. As shown in Fig.3, a typicalrock mass whose sliding surface is an arc with radius ofrhR can be divided into N slices equally according toSweden arc method, where θ and l are respectively thecentral angle and base length of each slice, i is the .ordinal of slice and G is the mass of slice i.Rock中国煤化工3.1 Hydrostatid|Y片CNMHGeFig.4 shows the action ot crack water seepage onFig.2 Calculation model of hydraulic fracturebottom of slice i. Assume the seepage free head at points.J. Cent. South Univ. Technol. (2010) 17: 1383-138813853.2 Hydrodynamic pressure on sliding surface0Besides, a kind of dynamic water pressure also8generates when seepage flows through the continuous2 "-fillings on sliding surface, which decreases the slopestability directly by dragging slope body downward[17-18] constantly.R! |According to the continuum theory [19]， thedynamic pressure in seepage region is:fs=xwJ(13)where fs and J are the dynamic water pressure vector andhydraulic gradient vector, respectively.By integrating to Eq(13), the concentrated force ofFig.3 Analysis model based on Sweden arc methodseepage dynamic pressure acting on fllings of slice i is .jiven:Fillings on slip surfaceE=j"JonYwJ,drdy = mwlxwJ,(14)dwhere w and n are the width and porosity of fllings onsliding surface, respectively; and J; is the hydraulicgradient can be expressed as:J.二h+lsinB,-h(15)RockbedFig.4 Action of seepage of crack water on sliding surfacewhere h_+lsinβr -h; is the head loss of seepage on slidingsurface of slice i.c and d is hi-1 and h, respectively, the hydrostaticAccording to the principle of force balance, the dragpressures vertical to sliding surface at points c and d areforce of seepage acting on bottom of slice i can be[16]:determined by:[Pc=wh_F_ nwyw[h_+Isinβ-h](8)(16)(Pa=Xwh2lTake point C as the origin and create x axis along cd,Specially note that the seepage drag force lw doesthus the distribution of hydrostatic pressure on cd can benot always exist unless the seepage can keep flowingexpressed as:when the water depth is bigger enough. According to thecontinuum theory, the minimum water depth that allowsp=pe-;(pc-pa+xwlsinβ)，0≤x≤l(9)seepage to occur can be expressed aswhere B; is the inclination of the bottom of slice i and canhmin =ηNRθ- ROy sin B;(17)be obtained by the following equation:β,=n8+(-2日(10)where n is the unit length head loss of seepage.where δ is the inclination of OM in Fig.3; and point M is3.3 Force analysis on sliding surface of slice ithe tip of crack on trailing edge of slope.As shown in Fig.5, the stability of slice i isIntegrating x in Eq.(9), the equivalent concentrateddetermined by inter-slice forces P: and P+1, mass G,force of hydrostatic pressure at bottom of slice i isresultant normal force N; and shear resistance T. Whileobtained as:with the flowing of crack water in, it begins to decrease(Pc-Ps+Y.IsinB)-lfor hydraulic action mentioned above.Ped =(11)Due to the action of hydrostatic pressure σw inThus, the average compressive stress vertical toEq.(12), the av'中国煤化士ng surface ofsliding surface caused by seepage can be written as:slice i decreasesad _ rw(h_-h:+lsin B)G cos B,THCNMH G(12)σ=°!“7wVi-1-151“P)(18)2l.1386J. Cent. South Univ. Technol. (2010) 17: 1383- 1388Note that when Vw=0, k is slope stability factor|bwithout influence of crack water.G5 Example and analysis/PHere take a typical high cut slope in Hanyuansection of Sichuan- -Tibet highway as an example. Theslope is composed of cretaceous sandstones and aPLcdominant crack with depth of 16 m has developed ontrailing edge during long term weathering (Fig.6).d|T;According to field investigation, the crack whichinfluences the slope stability mostly has extended toweak interlayer. The bulk density of slope material isFig.5 Forces acting on typical slice24.75 kN/m3 and the potential sliding surface is an arcwith radius R of 20 m (see Table 1).Hence, the average shear strength Iy can be given byFig.7 shows the relationship between stress intensitythe Mohr-Coulomb failure criterion as follows:τf=c+|「G,cosB_ 21.(--h, +lsinβ)]tanφ (19R|!/ 3.31 m, c=2 MPa, φ=24°)Fig.8 Influence of depth of crack water on slope stability6 Conclusionswithout action of seepage (h0<3.31 m, c=2.8 MPa, 0=34)(1) The main reason for the failure of rock slopesOn the contrary, with the flowing of crack waterwith deep cracks in rainfall is the hydraulic action andinto weak interlayer when ho > 3.31， the seepagesoftening action of crack water flowing in slidinghydrodynamic pressure generates, and the mechanicalsurface.properties of sliding surface decrease gradually, which(2) With the increase of water depth ho, the stressall are bad for slope stability.intensity factor K grows quickly until its peak value ofFig.9 shows the variation of stability factor with theKIc.mechanical properties when ho=hmin. The result ilustrates(3) The critical depth is an important parameterk decreases continually from 1.32 to 0.90 with thewhich determines whether the crack filled with water canchange of (c, ?) from initial value (2.8 MPa, 34°) topropagate. Only the cracks whose depth is bigger than hesaturation value (2.0 MPa, 24 ). Obviously, even withoutcan extend and cause the slope failure in intense rainfall.consideration of hydrodynamic pressure, the crack water(4) In order to ensure the seepage to flow in thealso plays an important role in slope stability whenfllings on sliding surface, the minimum depth of crackseepage occurs in sliding surface.water must be bigger than hmin.As shown in Fig.10, the slope stability will keep(5) Comp中国煤化工mechanicaldecreasing with the increment of water in crack whenproperties (c aninfluence ofho> hmin. 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