3D slope stability analysis by the limit equilibrium method of a mine waste dump. A. Reyes & D. Parra

Transcription

1 3D slope stability analysis by the limit equilibrium method of a mine waste dump A. Reyes & D. Parra

2 Conference Sponsors AMEC Earth & Environmental Ausenco BASF Chemical CETCO ConeTec DOWL HKM Engineering Analytics, Inc. Gannett Fleming Golder Associates, Inc. Knight Piésold and Co. MWH MineBridge Software, Inc. Paterson & Cooke Robertson GeoConsultants, Inc. SRK Consulting, Inc. Tetra Tech, Inc. URS Community Sponsor CDM Smith

3 Introduction Modern mining in South America Material storage facilities are design and built in the rugged, mountainous and aggressive Andes terrain. Main geotechnical challenges are dealing with slope stability and earth work.

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9 The limit equilibrium method Most slope stability problems are solved using the limit equilibrium (LE) method, mainly because of its simplicity and understanding. Fredlund & Krahn (1977) compared the most used 2D procedures of slices, unifying the FS equations for each one of them.

10 2D limit equilibrium procedures Procedure Equilibrium condition satisfied Assumptions Bishop simplified (Bishop 1955) Janbu simplified (Janbu et al. 1956, Janbu 1973) Vertical force and overall moment Vertical and horizontal forces Side forces are horizontal Comparison purposes Side forces are horizontal Spencer (Spencer 1967) All conditions Interslice forces are parallel and normal force acts at the center of the base of the slide Morgenstern & Price (Morgenstern & Price 1965) General Limit Equilibrium (Fredlund et al. 1981) All conditions All conditions Interslice shear force is related to the interslice normal force by X/E = λf(x) Rigorous procedures Interslice shear force is related to the interslice normal force by X/E = λf(x) Modified after Duncan & Wright (2005)

11 3D limit equilibrium procedures Duncan (1996), Albatanieh (2006), Soares (2011), Akhtar (2011) and Kalatehjari & Ali (2013) made extensive reviews of existing 3D LE procedures published since Geotechnical practitioners have not fully accepted 3D procedures compared with the several 2D procedures used nowadays.

12 Procedure Anagnosti (1969) 3D limit equilibrium procedures Theoretical basis Morgenstern & Price Hungr et al. (1989) Bishop and Janbu simplified Lam & Fredlund (1993) Yamagami & Jiang (1996, 1997) Huang & Tsai (2000) Hungr (2001) General limit equilibrium Slip surface geometry Not specified >1 Symmetric, rotational >1 Symmetric, generalized >1 Janbu simplified Symmetric, rotational >1 Limit equilibrium Generalized, semi spherical Morgenstern & Price FS 3D/2D >1 Symmetric >1

13 Procedure Chang (2002) 3D limit equilibrium procedures Theoretical basis Sliding block analysis Huang et al. (2002) Janbu generalized (1954, 1973) Slip surface geometry Asymmetric >1 Generalized >1 Chen et al. (2003) Spencer Generalized, rotational >1 Jiang & Yamagami (2004) Cheng & Yip (2007) Spencer and variational calculus Bishop and Janbu simplified, Morgenstern & Price Symmetric, rotational >1 Generalized, spherical >1 Zheng (2009) Limit equilibrium Generalized >1 Sun et al. (2012) Morgenstern & Price Generalized >1 FS 3D/2D

14 3D limit equilibrium procedures Despite the disagreement between researchers and confusion between practitioners, commercially available software uses columns and published 3D extensions of 2D LE procedures for 3D analysis. Akhtar (2011) compared 2D and 3D problems using LE method and finite element and finite difference procedures, showing: Spencer and Morgenstern & Price yield reasonable estimates of FS for 2D analysis. Spencer and Morgenstern & Price provide similar results with finite element and finite difference results for 3D analysis.

15 Slope stability state-of-practice Models are built using information from field investigation and an extensive laboratory program.

16 Slope stability state-of-practice Models are built using information from field investigation and an extensive laboratory program. Analysis is performed in 2D, using one or more cross-sections that are meant to be both representative and critical of the structure, simplifying its 3D geometry, 3D failure surface shape, length and soil variability. The engineer selects one ore more possible directions of sliding.

17 Slope stability state-of-practice Site conditions are challenging, many times resulting on over-conservative designs and high associated costs. Stabilizations solutions used vary among stability platforms, gentle slopes, buttressing, massive earth work and limiting the height of the facility.

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21 Cross-sections selected to be critical but not necessarily representative

22 Cross-sections selected to be critical but not necessarily representative

23 3D slope stability analysis of a mine waste dump One of the fastest-growing gold mining companies in Peru requested the design of its mine waste dump as a part of his long-term expansion plan. It needed to reach a capacity of 113 million tones (66 million cubic meters), within an area of 118 Ha. The angle of repose of the waste formed a slope of 1.5H:1V and had an overall slope of 2.5H:1V.

24 Geotechnical characterization It involved geotechnical-geological mapping, 123 test pits, 31 dynamic penetration tests, 91 standard penetration tests, 30 large penetration tests and 21 geotechnical boreholes, as well as laboratory tests. Many soil layers were found in the foundation, each one with different depth, location and shear strength parameters.

25 Geotechnical characterization Material Total unit weight (kn/m 3 ) Cohesion (kpa) Friction angle ( ) Mine waste rock Loose material Soft clay Coluvial soil Clayey alluvial soil Silty alluvial soil Sandy alluvial soil Gravelly alluvial soil Sandstone residual soil Granodiorite residual soil Bedrock

26 2D slope stability analysis The mine waste dump was divided in two zones. The critical sections of each zone was analyzed, yielding very poor results. Further analysis of nearby sections showed a high variability of FS because of foundation space variability. No stability platforms, pre-loading, buttressing or change in the overall slope were considered due to limited space and the minimum storage capacity specified.

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32 3D slope stability analysis A comprehensive 3D model was built, with plenty of topographic information, detailed mine waste layout, geotechnical information and knowledge of 3D slope stability mechanics. The SVSLOPE-3D software package (Fredlund & Thode 2011) from SoilVision Systems (2011) was used to created two models, one for each zone. The Spencer procedure was used. Over 30 sections were interpolated for each section, separated each by 50 m. 11 layers were successfully modeled by the software.

33 2D analysis section

34 2D analysis section

35 2D and 3D results The 3D effect was expected to be higher, but the irregular layout and heterogeneous foundation had different effects on the 3D FS. Analysis type Section/ Zone analyzed Static FS Pseudostatic FS Static 3D/2D ratio Pseudostatic 3D/2D ratio 2D D Zone D D Zone Aspect ratio

36 Conclusions Current state of practice on slope stability analysis involves the use of the LE method on 2D sections, preferring the Spencer and Morgenstern & Price procedures. 2D models are based on medium to large amount of geotechnical information. In special cases, such as the previously described, 3D analysis is viable only if: Overall geometry, distribution and soil strength parameters are known in detail. It is relatively simple to assume the directions of sliding and the failure surface shape. 2D analyses are over-conservative and its simplifications are too unrealistic.

37 Conclusions A particular case was evaluated, showing a practical example of the conditions describe above for a 3D analysis. Results were used in design. Common design of slopes should still be performed using 2D analysis. Regulatory agencies and codes should specify a minimum 2D FS as a design criteria. Higher values of the 3D/2D FS ratio are expected for translational failures, which is the case of heap leach pads, then further investigation is needed.

38 Thanks for your attention! Gracias por su atención!