1、tensilestresses. Flexural toppling failure occurs by tensile stress caused by the momentdue totheweightof theinclinedsuperimposedcantilever-likerockcolumns.Hence,geo-structural defects that may naturally exist in rock columns are modeled by aseriesofcracksin maximum tensilestressplane.The magnitude
2、and locationmaximumtensilein rockcolumnswithpotentialflexuraltopplingdetermined.Then, theminimum factorsafetyforcolumns arecomputed by meansof principlessolidand fracturemechanics,independently.Next,a new equationis proposed to determine the length of critical crack in such rock columns. It hasbeen
3、shown thatiflengthof naturalcrack issmallerthan the lengthof criticalcrack, then the result based on solid mechanics approach is more appropriate;otherwise,resultobtainedbased on theprinciplesof fracturemechanicsismoreacceptable.Subsequently,stabilizationof the prescribedslopes,some newanalytical re
4、lationships are suggested for determination the length and diameterof the required fullygrouted rock bolts. Finally, for quickdesign ofrock slopesagainst flexural toppling failure, a graphical approach along with some designcurvesare presentedbywhich an admissible inclination of such rock slopes and
5、orallrequiredfullygroutedrock boltsInaddition,a casestudy has been used for practical verification of the proposed approaches.Keywords Geo-structural defects, In-situ rock structural weaknesses, Criticalcrack length. . .1.IntroductionRock masses are natural materials formed in the course of millions
6、 of years.Since during their formation and afterwards, they have been subjected to highvariable pressures both vertically and horizontally, usually, they are notcontinuous, and contain numerous cracks and fractures. The exerted pressures,sometimes, produce joint sets. Since these pressures sometimes
7、 may not besufficiently high to create separate joint sets in rock masses, they can producemicro joints and micro-cracks. However, the results cannot be considered asindependent joint sets. Although the effects of these micro-cracks are not thatpronounced compared withlargesize joint sets, yetthey m
8、ay cause a drastic changeof in-situ geomechanical properties of rock masses. Also, in many instances, dueto dissolution of in-situ rock masses, minute bubble-like cavities, etc., areproduced, which cause a severe reduction of in-situ tensile strength. Therefore,one should not replace this in-situ st
9、rength by that obtained in the laboratory.On the other hand, measuring thein-situstrengthinteractioncomplex parameters isimpractical.an appropriateapproachestimationof the tensile strength should be sought. In this paper, by means of principles of solid and fracture mechanics, a new approach for det
10、ermination of the effect of geo-structural defects on flexural toppling failure is proposed.2. Effect of geo-structural defects on flexural toppling failure2.1. Critical section of the flexural toppling failureAs mentioned earlier, Majdi and Amini 10 and Amini et al. 11 have proved that the accurate
11、factor of safety is equal to that calculated for a series of inclined rock columns, which, byanalogy, is equivalent to the superimposed inclined cantilever beamsas shown in Fig. 3. Accordingto the equations of limit equilibrium, the moment M and the shearing force V existing in variouscross-sectiona
12、l areas in the beams can be calculated as follows:(5)( 6)Since the superimposed inclined rock columns are subjected to uniformly distributed loadscaused by their own weight, hence, the maximum shearing force and moment exist at the very fixedend, that is, at x= :(7)(8)If the magnitude of from Eq. (1) is substitutedof shearing force and the maximummoment of equivalentinto Eqs. (7) and (8), then the magnitudes beam for rock slopes are computed as follows:(9)(10)where C is a dimensionless geometrical parameter that is related to the inclinations
copyright@ 2008-2022 冰豆网网站版权所有
经营许可证编号:鄂ICP备2022015515号-1