【正文】 Galandrood礦邊坡的穩(wěn)定性分析表明：文中提出的新方法非常適合彎曲傾倒破壞的分析。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。根據(jù)極限平衡方程，在每一梁的任何截面上，剪應(yīng)力與存在于相應(yīng)縱切面的應(yīng)力相等。在某些情況下，一個具有長度T的單錨桿可能因穿過有潛在彎曲傾倒破壞巖柱的總破會面而無法保證巖柱的穩(wěn)定性。在方程（12）和（13）中，如果安全系數(shù)被任何一個允許值取代，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。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，如果這些滑動不知何故被阻止，那么預(yù)期的穩(wěn)定性將大大降低。m，通過圖12設(shè)計(jì)坡度將是63 176。kN/m3， δ=45176。因此，根據(jù)上述設(shè)計(jì)曲線設(shè)計(jì)邊坡時，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。如果巖柱現(xiàn)有裂縫長度小于裂紋臨界長度，基于固體力學(xué)原理可以使用設(shè)計(jì)曲線得到如圖12和13所示，這是巖質(zhì)邊坡的設(shè)計(jì)目的。第四章 有潛在彎曲傾倒破壞穩(wěn)定巖質(zhì)邊坡的估計(jì)巖石邊坡和溝道，除了土壤和巖石填入的高度取決于自然地形，因此必須考慮理想的安全的邊坡設(shè)計(jì)。為了更深入的比較，裂紋長度為不同的值時，方程（13）的結(jié)果也顯示在圖11中。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。在這一部分方程（14a）簡化為下面的公式，其中裂紋的臨界長度可直接計(jì)算： (14b)我們必須牢記方程（14b）與方程（14a）相比將導(dǎo)致裂紋臨界長度偏小。通過方程（12）和（13），推導(dǎo)出了裂紋長度，在此部分被稱為裂紋臨界長度，可以計(jì)算如下： （14a）是裂縫平均臨界長度的一半。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由此可以看出，一個裂紋長度的增加導(dǎo)致巖石邊坡臨界高度的下降。方程（13）表明基于斷裂力學(xué)原理計(jì)算的抵抗彎曲傾倒破壞的安全系數(shù)與“聯(lián)合持久”和“裂縫長度”直接相關(guān)。因此，如果這個參數(shù)在實(shí)驗(yàn)室里能定量的確定，那么相應(yīng)的安全系數(shù)（基于斷裂力學(xué)原理的破壞判據(jù)）可能被計(jì)算出來。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。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。因此，巖柱原位拉伸強(qiáng)度和剪切的共同作用可能被忽略，只有由于最大彎曲應(yīng)力引起的拉應(yīng)力可以被使用。Mmax 和Vmax將分別產(chǎn)生法向（拉伸，壓縮）的應(yīng)力和臨界面上的剪應(yīng)力。因此，一種去估算拉伸強(qiáng)度的適當(dāng)方法被尋求。有時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。最后，為抵抗巖石彎曲傾倒破壞而進(jìn)行的快速設(shè)計(jì)，根據(jù)一些設(shè)計(jì)曲線，一個形象化的方式被提出，通過這種方法巖質(zhì)邊坡的傾角和所有完全灌漿錨桿的長度是可以確定的。其次，巖柱的最小安全系數(shù)是可以通過固體和斷裂力學(xué)原理單獨(dú)地計(jì)算出來。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。 Selection of critical slopes for rock columns with the potential of flexural toppling failure based on principles of solid mechanics when k=..Fig. 7.m, aca=MPa, γ=20kN/m3, k=.In any case studies, a safe and stable slope height can be determined by using Eqs. (12) and (13), independently. The two equations yield two different slope heights out of which the minimum height must be taken as the most acceptable one. By equating Eqs. (12) and (13), the following relation has been derived by which a crack length, in this paper called critical length of crack, can be puted: （14a）where ac is the half of the average critical length of the cracks. Since ac appears on both sides of Eq. (14a), the critical length of the crack could be puted by trial and error method. If the length of the crack is too small with respect to rock column thickness, then the ratio t/(t?2ac) is slightly greater than one. Therefore one may ignore the length of crack in denominator, and then this ratio 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。 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 topp