地质岩土英文文献翻译.docx

1、地质岩土英文文献翻译International Journal of Rock Mechanics and Mining SciencesAnalysis of geo-structural defects in flexural toppling failureAbbas Majdi and Mehdi AminiAbstractThe in-situ rock structural weaknesses, referred to herein as geo-structural defects, such as naturally induced micro-cracks, are ext

2、remely responsive to tensile stresses. Flexural toppling failure occurs by tensile stress caused by the moment due to the weight of the inclined superimposed cantilever-like rock columns. Hence, geo-structural defects that may naturally exist in rock columns are modeled by a series of cracks in maxi

3、mum tensile stress plane. The magnitude and location of the maximum tensile stress in rock columns with potential flexural toppling failure are determined. Then, the minimum factor of safety for rock columns are computed by means of principles of solid and fracture mechanics, independently. Next, a

4、new equation is proposed to determine the length of critical crack in such rock columns. It has been shown that if the length of natural crack is smaller than the length of critical crack, then the result based on solid mechanics approach is more appropriate; otherwise, the result obtained based on

5、the principles of fracture mechanics is more acceptable. Subsequently, for stabilization of the prescribed rock slopes, some new analytical relationships are suggested for determination the length and diameter of the required fully grouted rock bolts. Finally, for quick design of rock slopes against

6、 flexural toppling failure, a graphical approach along with some design curves are presented by which an admissible inclination of such rock slopes and or length of all required fully grouted rock bolts are determined. In addition, a case study has been used for practical verification of the propose

7、d approaches.Keywords Geo-structural defects, In-situ rock structural weaknesses, Critical crack length1.IntroductionRock masses are natural materials formed in the course of millions of years. Since during their formation and afterwards, they have been subjected to high variable pressures both vert

8、ically and horizontally, usually, they are not continuous, and contain numerous cracks and fractures. The exerted pressures, sometimes, produce joint sets. Since these pressures sometimes may not be sufficiently high to create separate joint sets in rock masses, they can produce micro joints and mic

9、ro-cracks. However, the results cannot be considered as independent joint sets. Although the effects of these micro-cracks are not that pronounced compared with large size joint sets, yet they may cause a drastic change of in-situ geomechanical properties of rock masses. Also, in many instances, due

10、 to dissolution of in-situ rock masses, minute bubble-like cavities, etc., are produced, which cause a severe reduction of in-situ tensile strength. Therefore, one should not replace this in-situ strength by that obtained in the laboratory. On the other hand, measuring the in-situ rock tensile stren

11、gth due to the interaction of complex parameters is impractical. Hence, an appropriate approach for estimation of the tensile strength should be sought. In this paper, by means of principles of solid and fracture mechanics, a new approach for determination of the effect of geo-structural defects on

12、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 factor of safety is equal to that calculated for a s

13、eries of inclined rock columns, which, by analogy, is equivalent to the superimposed inclined cantilever beams as shown in Fig. 3. According to the equations of limit equilibrium, the moment M and the shearing force V existing in various cross-sectional areas in the beams can be calculated as follow

14、s: (5) ( 6)Since the superimposed inclined rock columns are subjected to uniformly distributed loads caused by their own weight, hence, the maximum shearing force and moment exist at the very fixed end, that is, at x=: (7) (8)If the magnitude of from Eq. (1) is substituted into Eqs. (7) and (8), the

15、n the magnitudes of shearing force and the maximum moment of equivalent beam for rock slopes are computed as follows: (9) (10)where C is a dimensionless geometrical parameter that is related to the inclinations of the rock slope, the total failure plane and the dip of the rock discontinuities that e

16、xist in rock masses, and can be determined by means of curves shown in Fig. Mmax and Vmax will produce the normal (tensile and compressive) and the shear stresses in critical cross-sectional area, respectively. However, the combined effect of them will cause rock columns to fail. It is well understo

17、od that the rocks are very susceptible to tensile stresses, and the effect of maximum shearing force is also negligible compared with the effect of tensile stress. Thus, for the purpose of the ultimate stability, structural defects reduce the cross-sectional area of load bearing capacity of the rock

18、 columns and, consequently, increase the stress concentration in neighboring solid areas. Thus, the in-situ tensile strength of the rock columns, the shearing effect might be neglected and only the tensile stress caused due to maximum bending stress could be used.2.2. Analysis of geo-structural defe

19、ctsDetermination of the quantitative effect of geo-structural defects in rock masses can be investigated on the basis of the following two approaches.2.2.1. Solid mechanics approachIn this method, which is, indeed, an old approach, the loads from the weak areas are removed and likewise will be trans

20、ferred to the neighboring solid areas. Therefore, the solid areas of the rock columns, due to overloading and high stress concentration, will eventually encounter with the premature failure. In this paper, for analysis of the geo-structural defects in flexural toppling failure, a set of cracks in cr

21、itical cross-sectional area has been modeled as shown in Fig. 5. By employing Eq. (9) and assuming that the loads from weak areas are transferred to the solid areas with higher load bearing capacity (Fig. 6), the maximum stresses could be computed by the following equation (see Appendix A for more d

22、etails): （11）Hence, with regard to Eq. (11), for determination of the factor of safety against flexural toppling failure in open excavations and underground openings including geo-structural defects the following equation is suggested: （12）From Eq. (12) it can be inferred that the factor of safety a

23、gainst flexural toppling failure obtained on the basis of principles of solid mechanics is irrelevant to the length of geo-structural defects or the crack length, directly. However, it is related to the dimensionless parameter “joint persistence”, k, as it was defined earlier in this paper. Fig. 2 r

24、epresents the effect of parameter k on the critical height of the rock slope. This figure also shows the limiting equilibrium of the rock mass (Fs=1) with a potential of flexural toppling failure.Fig. 2. Determination of the critical height of rock slopes with a potential of flexural toppling failur

25、e on the basis of principles of solid mechanics.View Within Article2.2.2. Fracture mechanics approachGriffith in 1924 13, by performing comprehensive laboratory tests on the glasses, concluded that fracture of brittle materials is due to high stress concentrations produced on the crack tips which ca

26、uses the cracks to extend (Fig. 3). Williams in 1952 and 1957 and Irwin in 1957 had proposed some relations by which the stress around the single ended crack tips subjected to tensile loading at infinite is determined 14, 15 and 16. They introduced a new factor in their equations called the “stress

27、intensity factor” which indicates the stress condition at the crack tips. Therefore if this factor could be determined quantitatively in laboratorial, then, the factor of safety corresponding to the failure criterion based on principles of fracture mechanics might be computed.Fig. 3. Stress concentr

28、ation at the tip of a single ended crack under tensile loadingSimilarly, the geo-structural defects exist in rock columns with a potential of flexural toppling failure could be modeled. As it was mentioned earlier in this paper, cracks could be modeled in a conservative approach such that the locati

29、on of maximum tensile stress at presumed failure plane to be considered as the cracks locations (Fig. 3). If the existing geo-structural defects in a rock mass, are modeled with a series cracks in the total failure plane, then by means of principles of fracture mechanics, an equation for determinati

30、on of the factor of safety against flexural toppling failure could be proposed as follows: （13）where KIC is the critical stress intensity factor. Eq. (13) clarifies that the factor of safety against flexural toppling failure derived based on the method of fracture mechanics is directly related to bo

31、th the “joint persistence” and the “length of cracks”. As such the length of cracks existing in the rock columns plays important roles in stress analysis. Fig. 10 shows the influence of the crack length on the critical height of rock slopes. This figure represents the limiting equilibrium of the roc

32、k mass with the potential of flexural toppling failure. As it can be seen, an increase of the crack length causes a decrease in the critical height of the rock slopes. In contrast to the principles of solid mechanics, Eq. (13) or Fig. 4 indicates either the onset of failure of the rock columns or the inception of fracture development.Fig. 4. Determination of the critical height of rock slopes with a potential of flexural toppling failure on the basis of principle of fracture mechanics.View Within Article3. Comparison of the results of the t