【正文】 o bees 1. In this case Eq. (14a) reduces to the following equation, by which the critical length of the crack can be puted directly: (14b)It must be born in mind that Eq. (14b) leads to underestimate the critical length of the crack pared with Eq. (14a). Therefore, for an appropriate determination of the quantitative effect of geostructural defects in rock mass against flexural toppling failure, the following 3 conditions must be considered: (1) a=0。s crosssection can be puted as follows: 7. ConclusionsIn this paper, geostructural defects existing in the insitu rock columns with the potential of flexural toppling failure have been modeled with a series of central cracks. Thereafter on the basis of principles of both the solid and fracture mechanics some new equations have been proposed which can be used for stability analysis and the stabilization of such rock slopes. The final outes of this research are given as follows: 1. Geostructural defects play imperative roles in the stability of rock slopes, in particular, flexural toppling failure. 2. The results obtained on the basis of principles of solid mechanics approach indicate that the length of cracks alone has no influence on the determination of factor of safety, whereas the value of joint persistence causes a considerable change in its value. On the other hand, the factor of safety obtained based on principles of fracture mechanics approach is strongly influenced by both the length of existing cracks in rock columns and joint persistence as well.3. The critical length of cracks represents the equality line of the results obtained from both approaches: solid mechanics and fracture mechanics.4. If the length of the crack is less than the critical length, failure is considered to follow the principles of solid mechanics. However, if the length of crack increases beyond the critical length, the rock column fails due to high stress concentration at the crack tips, according to the principles of fracture mechanics.5. The present proposed equations are also converted into some design graphs that can be used for ease of application and to reduce manual lengthy calculations for determining the critical height of rock slopes with the potential of flexural toppling failure.6. In this paper, on the basis of principles of both solid mechanics and fracture mechanics some equations are proposed to determine the safe length and the diameter of the fully grouted rock bolts for stabilization of rock slopes with the potential of flexural toppling failure.7. For simplicity of putations, some design graphs for determination of the length of the fully grouted rock bolts for stabilization of rock slopes with the potential of flexural toppling failure are also presented.8. Slope stability analysis of the Galandrood mine shows the new approach is well suited for the analysis of flexural toppling failure.國際巖石力學(xué)與工程學(xué)報(bào)地質(zhì)結(jié)構(gòu)缺陷對彎曲傾倒破壞的影響作者：Abbas Majdi and Mehdi Amini摘要原位巖石弱點(diǎn)，在此統(tǒng)稱為地質(zhì)結(jié)構(gòu)缺陷，如自然誘發(fā)的微裂紋，對拉應(yīng)力有很大影響。因此，一種去估算拉伸強(qiáng)度的適當(dāng)方法被尋求。這些數(shù)據(jù)也顯示了有潛在彎曲傾倒破壞巖體（1）的極限平衡。為了方便應(yīng)用，這些方程被應(yīng)用于以下物理和力學(xué)性能條件下的研究： ，γ=20為了更深入的比較，裂紋長度為不同的值時(shí)，方程（13）的結(jié)果也顯示在圖11中。kN/m3， δ=45176。在方程（12）和（13）中，如果安全系數(shù)被任何一個(gè)允許值取代，計(jì)算參數(shù)t將顯示混合巖柱的厚度，他可以等于安全的錨桿長度。如果裂紋長度小于臨界長度，是在固體力學(xué)基礎(chǔ)之上的巖柱破壞；但是，如果裂紋長度的增加超出臨界長度，是在斷裂力學(xué)基礎(chǔ)上因裂縫尖端高應(yīng)力集中造成的巖柱破壞。研究的最終結(jié)果列出如下：地質(zhì)結(jié)構(gòu)缺陷在巖質(zhì)邊坡的穩(wěn)定上，特別是在彎曲傾倒破壞上扮演著重要的角色。本文提出了一種確定完全灌漿錨桿規(guī)范的方法以增強(qiáng)巖體穩(wěn)固。因此，根據(jù)上述設(shè)計(jì)曲線設(shè)計(jì)邊坡時(shí)，為了達(dá)到最終設(shè)計(jì)安全的目的，必須降低基于安全所需的因素。在第三種情況下，地質(zhì)結(jié)構(gòu)缺陷的長度遠(yuǎn)遠(yuǎn)大于裂紋臨界長度，巖柱因裂縫變大產(chǎn)生破壞，在斷裂力學(xué)原理基礎(chǔ)上的方程（13）將被用于分析。由此可以看出，一個(gè)裂紋長度的增加導(dǎo)致巖石邊坡臨界高度的下降。在本部分，為了分析彎曲傾倒破壞上的地質(zhì)結(jié)構(gòu)缺陷,一系列橫截面上的裂縫已被設(shè)為藍(lán)本。有時(shí)這些壓力不足夠高以創(chuàng)建單獨(dú)的節(jié)理結(jié)構(gòu)面，但它們能產(chǎn)生微縫和微裂紋，這種結(jié)果不能被視為產(chǎn)生獨(dú)立聯(lián)合集。 Selection of critical slopes for rock columns with the potential of flexural toppling failure based on principles of solid mechanics when k=..Fig. 7. otherwise, the 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 design 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 verification of the proposed approaches.Keywords Geostructural defects, Insitu 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 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 produce micro joints and microcracks. However, the results cannot be considered as independent joint sets. Although the effects of these microcracks are not that pronounced pared with large size joint sets, yet they may cause a drastic change of insitu geomechanical properties of rock masses. Also, in many instances, due to dissolution of insitu rock masses, minute bubblelike cavities, etc., are produced, which cause a severe reduction of insitu tensile strength. Therefore, one should not replace this insitu strength by that obtained in the laboratory. On the other hand, measuring the insitu rock tensile strength due to the interaction of plex parameters is impractical. Hence, an appropriate approach for estimation of the tensile strength should b