1 引言

傾倒破壞(Toppling Failure) 這個詞最初是由是Goodman and Bray在上世紀70年代提出, 意指一組平行節(jié)理的巖體朝著邊坡方向發(fā)生的傾倒破壞。按照Goodman and Bray(1976)的分類, 傾倒破壞可以分為三種形式: (a) 塊體傾倒(Block Toppling); (b) 屈曲傾倒(Flexural toppling); (c) 塊體屈曲傾倒(Block flexure toppling). 如下圖所示. 

過去的公眾號文章中多次討論過傾倒破壞, 參看如下的鏈接.   

屈曲傾倒破壞(flexural toppling failure)

邊坡工程---巖體邊坡的破壞模式

巖土邊坡的破壞類型(C3)(Failure types of slope)

Chuquicamata(丘基卡馬塔)露天礦巖石力學研究

除了上面所述的三種傾倒模式外, Wyllie and Mah(2004)也討論過另一種傾倒模式,稱之為次傾倒模型(Secondary toppling modes). 這種破壞模式主要由巖石風化以及人類活動引起. 最典型的情形是坡腳開挖引起邊坡上部巖體發(fā)生傾倒破壞, 如下圖(d)所示. 這種現(xiàn)象在修建山區(qū)高速公路時經常遇到, 特別是出現(xiàn)在水平層理的砂巖和頁巖中.

2 傾倒破壞的分析方法

按照Goodman and Bray(1976)的分析, 傾倒破壞必須滿足下面的條件:

其中, 

---邊坡面的傾角(Dip of slope face);

---不連續(xù)巖體的內摩擦角(Internal friction angle of plane/joint);

---不連續(xù)巖體的傾角(Dip of plane/joint)

如果不連續(xù)面傾到邊坡面并且其走向小于30度, 那么就有可能傾倒破壞, 這可以使用赤平極射投影方法來求解, 如上圖(e)所示. 一個更專業(yè)的求解方法是使用DIPS軟件. 在此基礎上, Rocscience發(fā)展了一個基于靜力平衡的傾倒破壞分析軟件RocTopple. 傾倒破壞最先進的分析方法是由Cundall提出的離散元法, 目前這樣的分析方法有: UDEC，3DEC, PFC, Slope Model等。

3 塊體傾倒數據集

在過去, 已經發(fā)展出一個屈曲傾倒數據集"flexural toppling failure", 在此基礎上發(fā)展出目前的塊體傾倒"Block Toppling"數據集. 這個數據集的內容主要包括在下面兩個數據集中:

(1)\Step-Path-Failure(Discontinuity Persistence)

(2) \lattice spring model

進一步的優(yōu)化還在進行之中.

4 參考文獻

[1] Duncan C. Wyllie (2018) Rock Slope Engineering Civil Applications. Fifth Edition. 621p. (pdf)

[2] Guzman, R. S., et al. (2015). "Creep Modeling as a means to Interpret the Behavior of the West Wall of the Chuquicamata Open Pit." Integrating Innovations of Rock Mechanics: 11-18.

[3] Allen, R. H. and X. Duan (1995). "Effects of Linearizing on Rocking-Block Toppling." Journal of Structural Engineering-Asce 121(7): 1146-1149.

[4] Alejano, L. R., et al. (2018). "Block toppling stability in the case of rock blocks with rounded edges." Engineering Geology 234: 192-203.

[5] Tatone, B. S. A. and G. Grasselli (2010). "ROCKTOPPLE: A spreadsheet-based program for probabilistic block-toppling analysis." Computers & Geosciences 36(1): 98-114.

[6] Barla, G., M. B. Brunetto, G. Gerbaudo and A. Zaninetti. 1995. Physical and Mathematical Modelling of A Jointed Rock Mass for the Study of Block Toppling. In Fractured and Jointed Rock Masses. Proceedings, (Lake Tahoe, June 3-5, 1992), pp. 647-653. Rotterdam: A. A. Balkema.

[7] Brideau MA, Stead D (2010) Controls on block toppling using a three-dimensional distinct element approach. Rock Mech Rock Eng 43:241-260.

[8] Nichol, S. L., et al. (2002) Large-scale brittle and ductile toppling of rock slopes. Canadian Geotechnical Journal. 39: 773-788.

[9] Goodman, R. E. and J. W. Bray (1976). TOPPLING OF ROCK SLOPES.

[10] Lanaro, F., L. Jing, O. Stephansson, and G. Barla. 1997. "DEM modelling of laboratory ests of block toppling."  International Journal of Rock Mechanics and Mining Sciences 34 (3-4):173-e1. 

[11] Muraoka, R. and R. Hashimoto (2019). Improvement of the discontinuous deformation analysis for the rocking motion. 5th ISRM Young Scholars' Symposium on Rock Mechanics and International Symposium on Rock Engineering for Innovative Future, YSRM 2019.

[12] Vanneschi, C., et al. (2019). "Investigation and modeling of direct toppling using a three-dimensional distinct element approach with incorporation of point cloud geometry." Landslides 16(8): 1453-1465.

[13] Lanaro, F., et al. (1997). D.E.M. modelling of laboratory tests of block toppling. International Journal of Rock Mechanics and Mining Sciences. 34: 173.e171-173.e115.

[14] Scavia, C., et al. (1990). "Probabilistic Stability Analysis of Block Toppling Failure in Rock Slopes." International Journal of Rock Mechanics and Mining Sciences 27(6): 465-478.

[15] Wyllie, D. C. 1980. Toppling Rock Slope Failures, Examples of Analysis and Stabilization. Rock Mechanics, Vol.13, pp.89–98.

[16] Amatruda G, Castelli M, Rouiller JD. Block toppling mechanism due to progressive failure of rock bridges. Felsbau 2004; 22(2):8–15.