地質(zhì)巖土英文文獻(xiàn)翻譯-冶金礦山地質(zhì)-工程科技-專業(yè)資料

1、 HYPERLINK /science/journal/13651609 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 in

2、duced micro-cracks, are extremely 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

3、 a series of cracks in maximum 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 mechani

4、cs, independently. Next, a 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, th

5、e result obtained based on 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 de

6、sign of rock slopes against 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

7、verification of the proposed approaches.Keywords Geo-structural defects, In-situ rock structural weaknesses, Critical crack lengthIntroductionRock masses are natural materials formed in the course of millions of years. Since during their formation and afterwards, they have been subjected to high var

8、iable pressures both vertically 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 pro

9、duce micro joints and micro-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. Als

10、o, in many instances, due 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 i

11、n-situ rock tensile strength 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 g

12、eo-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 HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=

13、02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&se

14、archtype=a l bib10#bib10 10 and Amini et al. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769

15、&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l bib11#bib11 11 have proved that the accurate factor of safety is equal to that calculated for a series of inclined rock columns, which, by analogy, is equivalent

16、to the superimposed inclined cantilever beams as shown in HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volu

17、me)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0015#f0015 Fig. 3. According to the equations of limit equilibrium, the moment M and the shearing force V existing in various cross-sectional areas

18、in the beams can be calculated as follows: QUOTE * MERGEFORMAT (5) QUOTE * MERGEFORMAT ( 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=: Q

19、UOTE * MERGEFORMAT (7) QUOTE * MERGEFORMAT (8)If the magnitude of from Eq. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA

20、%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l eq0005#eq0005 (1) is substituted into Eqs. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2

21、F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=

22、a l eq0035#eq0035 (7) and HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor

23、=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l eq0040#eq0040 (8), then the magnitudes of shearing force and the maximum moment of equivalent beam for rock slopes are computed as follows: QUOTE * MERGEFORMAT (9) QUOTE * MERGEFORM

24、AT (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 exist in rock masses, and can be determined by means of curves shown in HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S

25、6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193

26、a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0020#f0020 Fig. HYPERLINK /science?_ob=MathURL&_method=retrieve&_udi=B6V4W-51S6MPM-1&_mathId=mml11&_user=1002865&_cdi=5769&_pii=S1365160910002091&_rdoc=2&_issn=13651609&_acct=C000050159&_version=1&_userid=1002865&md5=6ad0d3c6892bf2c4096ef2960e1f4493 o Cl

27、ick to view the MathML source Mmax and HYPERLINK /science?_ob=MathURL&_method=retrieve&_udi=B6V4W-51S6MPM-1&_mathId=mml12&_user=1002865&_cdi=5769&_pii=S1365160910002091&_rdoc=2&_issn=13651609&_acct=C000050159&_version=1&_userid=1002865&md5=fb55299f343683568ccdab727aff8629 o Click to view the MathML

28、source 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 understood that the rocks are very susceptible to tensile stresses, and the effect of

29、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 columns and, consequently, increase the stress concentration in neighboring s

30、olid 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 defectsDetermination of the quantitative effect of geo-structural defects in rock

31、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 transferred to the neighboring solid areas. Therefore, the solid areas of the rock

32、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 critical cross-sectional area has been modeled as shown in HYPERLINK /science?_o

33、b=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersio

34、n=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0025#f0025 Fig. 5. By employing Eq. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%

35、232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l eq0045#eq0045 (9) and assuming that the loads from weak areas are transferred to the solid areas w

36、ith higher load bearing capacity ( HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_

37、docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0030#f0030 Fig. 6), the maximum stresses could be computed by the following equation (see HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=0

38、2%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&sea

39、rchtype=a l s0070#s0070 Appendix A for more details): QUOTE * MERGEFORMAT （11）Hence, with regard to Eq. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%23201

40、1%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l eq0055#eq0055 (11), for determination of the factor of safety against flexural toppling failure in open

41、 excavations and underground openings including geo-structural defects the following equation is suggested: QUOTE * MERGEFORMAT （12）From Eq. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_it

42、em&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l eq0060#eq0060 (12) it can be inferred that the factor of safety ag

43、ainst 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. HYPERLINK

44、 /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=

45、1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0035#f0035 Fig. 2 represents 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.

46、Fig. 2. Determination of the critical height of rock slopes with a potential of flexural toppling failure on the basis of principles of solid mechanics. HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=

47、rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0035#f0035 View Within Article2.2.2. Fracture mechani

48、cs approachGriffith in 1924 HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanch

49、or=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l bib13#bib13 13, by performing comprehensive laboratory tests on the glasses, concluded that fracture of brittle materials is due to high stress concentrations produced on the crac

50、k tips which causes the cracks to extend ( HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_

51、sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l f0040#f0040 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 ten

52、sile loading at infinite is determined HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort

53、=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l bib14#bib14 14, HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_

54、list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l bib15#bib15 15 and HYPERLINK /science?_ob=ArticleURL&_udi=B

55、6V4W-51S6MPM-1&_user=1002865&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865

56、&md5=193a876539f4f40f9b7ce694ccd3ee51&searchtype=a l bib16#bib16 16. They introduced a new factor in their equations called the “stress intensity factor” which indicates the stress condition at the crack tips. Therefore if this factor could be determined quantitatively in laboratorial, then, the fac

57、tor of safety corresponding to the failure criterion based on principles of fracture mechanics might be computed.Fig. 3. Stress concentration 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 fail

58、ure could be modeled. As it was mentioned earlier in this paper, cracks could be modeled in a conservative approach such that the location of maximum tensile stress at presumed failure plane to be considered as the cracks locations ( HYPERLINK /science?_ob=ArticleURL&_udi=B6V4W-51S6MPM-1&_user=10028

59、65&_coverDate=02%2F28%2F2011&_rdoc=2&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235769%232011%23999519997%232893767%23FLA%23display%23Volume)&_cdi=5769&_sort=d&_docanchor=&_ct=17&_acct=C000050159&_version=1&_urlVersion=0&_userid=1002865&md5=193a876539f4f40f9b7ce

60、694ccd3ee51&searchtype=a l f0045#f0045 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 determination of the factor of safety against flexural toppling failu