Analysis of Shear Strength Non-linear Envelopes of Soil-Geomembrane Interface and its Influence in the Heap Leach Pad Stability
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1 Analysis of Shear Strength Non-linear Envelopes of Soil-Geomembrane Interface and its Influence in the Heap Leach Pad Stability D. Parra, Anddes Asociados S.A.C., Universidad Nacional de Ingeniería, Lima, Perú R. Valdivia, Anddes Asociados S.A.C., Lima, Perú C. Soto, Ausenco Perú S.A.C., Lima, Perú ABSTRACT The shear strength of the low permeability soil-geomembrane interface, commonly used in heap leach pad stability analysis, is obtained based on large scale direct shear laboratory testing, by using a rigid substrata in the lower box of the direct shear device. This paper presents a review of a large database of large scale direct shear testing, performed in low permeability soil, from different mining projects in Peru, and LLDPE and HDPE geomembranes, of different thickness and texture, in most of which a clear non-linear trend of the shear strength envelope have been observed. This study compares the influence of using linear and non-linear envelopes in the heap leach pad stability, considering two actual cases of shear strength envelopes and cases of different height of the heap. In addition, a discussion of the influence of high and low normal stresses in the interface shear strength is included, where the difference of this strength is important when linear or non-linear envelope is used. The linear envelope could overestimate the interface strength, and therefore, the factor of safety in the stability analysis, especially when very tall heap leach pads are analyzed (taller than 150 m), increasingly common in mining, where the vertical stress could be very high, much more higher than the capacity of the large scale direct shear equipments. RESUMEN La resistencia al corte de la interface suelo de baja permeabilidad-geomembrana, comúnmente utilizada en análisis de estabilidad de pilas de lixiviación, es obtenida a partir de ensayos de laboratorio de corte directo a gran escala, utilizando un substrato rígido en la caja inferior del equipo de corte directo. Este estudio presenta una revisión de los resultados de una gran cantidad de ensayos de corte directo a gran escala, realizados en interfaces de suelo de baja permeabilidad, provenientes de diferentes proyectos mineros en el Perú, y geomembranas de LLDPE y HDPE de diferente espesor y textura, en la mayoría de los cuales se ha observado una clara tendencia no lineal de la envolvente de resistencia cortante. Este estudio compara la influencia de usar envolventes lineales y no lineales en la estabilidad de una pila de lixiviación, considerando dos casos reales de envolventes de resistencia cortante y casos de pilas de lixiviación de diferentes alturas. Se incluye además una discusión de la influencia de altos y bajos esfuerzos normales en la resistencia al corte de la interface, donde la diferencia de esta resistencia es importante cuando se usan envolventes lineales o no lineales; en estos casos la envolvente lineal puede sobre estimar la resistencia de la interface, y por lo tanto, los factores de seguridad en el análisis de estabilidad, sobre todo cuando se analizan pilas de lixiviación de gran altura (mayores a 150 m), cada vez más comunes en minería, donde el esfuerzo vertical puede llegar a ser muy alto, por encima de la capacidad de los equipos de corte directo a gran escala. 1. INTRODUCTION In a previous study (Parra et al., 2010) the authors discussed the results of large scale direct shear testing for determining the shear strength of low permeability soil-geomembrane interface using two approaches which differed in the material used in the lower portion of the shear box: rigid substrata or overliner soil. In both cases the geomembrane was fixed with the textured side in contact with the low permeability soil, as recommended be typical heap leach pad design, while the smooth side is placed either in contact with the rigid substrata or with the overliner. The authors concluded that the testing with the rigid substrata provided more conservative results in terms of angle of friction and adhesion in the soil-geomembrane interface. Likewise, preliminary stability analysis, considering linear and non-linear strength envelopes, performed as part of that work, already indicated differences in the factor of safety for the stability analysis of a 100 m height heap. This work presents the review of the results of a large amount of large scale direct shear laboratory testing for determining the shear strength of a soil-geomembrane interface, and a comparative analysis of hypothetical cases of heap leach pads of different height is presented, using linear and non-linear envelopes.
2 2. LARGE SCALE DIRECT SHEAR TESTING REVIEW The shear strength of the soil-geomembrane interface is determined based on large scale direct shear lab testing (LSDS), according to ASTM D5321. In this test a low permeability soil sample is placed over a smooth or textured geomembrane sheet which is fixed to the device, and tested in direct shear condition. Typically the geotechnical lab reports the angle of friction and the adhesion of the soil-geomembrane interface based on the minimum square fit, which represents the interface shear strength. Because of the boom of the mining industry in Peru and to the significant increment of the metal prices experienced in the last years, a lot of mining projects have been carried out or are under development, including those related to the ore processing through heap leaching. Because of this a lot of laboratory testing data has been accumulated over the years, which has supported the heap leach pad design, such as LSDS testing for determining the shear strength of the soilgeomembrane interfaces, used for the geotechnical stability study of these facilities. Ausenco Vector s laboratory in Lima has a large database of interface results of LSDS testing carried out since In this database smooth and textured, HDPE and LLDPE and 1,5 and 2,0 mm thickness geomembranes are included. A total of 126 of soil-geomembrane LSDS tests of this database have been reviewed, with linear and non-linear behavior. A summary of the number of test results of each subcategory is presented in the following table: Table 1. LSDS testing results. Geomembrane Textured Side Smooth Side Linear Non-linear Sub-Total Linear Non-linear Sub-Total Total LLDPE HDPE Total Based on a comprehensive review of this large database of LSDS testing, we observed the following: These kinds of tests are usually performed with a minimum of 4 specimens, with the objective of obtaining a better definition of the strength envelope. The laboratory reports the results for peak and 7 cm displacement (post-peak) strength conditions. From the 126 test performed, 110 (87%) were carried out using LLDPE geomembrane and 16 (13%) with HDPE geomembrane. LLDPE geomembrane is frequently selected in heap leach pad design because of its better elongation characteristics, greater shear strength due to the better arrangement with the soil, and greater puncture resistance. This trend in the LLDPE geomembrane use has been observed more often in recent years. Interfaces between low permeability soil (clayey soil) and the smooth and textured side of LLDPE or HDPE geomembrane were tested. From the 96 interface testing results performed with textured geomembrane (LLDPE and HDPE), only 13 of them (14%) observed a linear trend of the strength envelope, while in 83 tests (86%) a non-linear envelope trend was observed. The linear trend is mainly observed in interface testing with the smooth side of LLDPE geomembranes, 15 tests (71%) of 21 in total. In most of the cases the strength envelope linear fit provides an adhesion value, which is not observed when the shear strength at low normal stresses is extrapolated. This fact is still more evident at 7 cm displacement and less evident in peak strength conditions. The angle of friction and adhesion obtained based on the linear fit, are highly variable, which is mostly likely due to varying soils; however, this discussion and analysis is out of the objective of the current paper. 3. COMPARATIVE ANALYSIS 3.1 Conditions and Analyzed Cases With the objective of evaluating the influence of the non-linearity of the soil-geomembrane interface strength envelope in the heap leach pad stability, a comparative analysis was performed analyzing hypothetical cases of heap leach pads and taking the interface shear strength properties corresponding to 2 actual cases from the reviewed database, which showed a very well defined non-linear strength envelope. A summary of the analyzed conditions is presented below:
3 Heap leach pads of 5 different heights were analyzed: 10, 50, 100, 150, 200 and 250 m. In the Figure 1 the 6 analyzed cases are presented. The 10 m case allow us to evaluate the first lift of the heap, where the slope is analyzed with the angle of repose and usually presents the most critical stability conditions of this kind of facilities. The 250 m case was analyzed in order to understand extreme conditions of a very tall heap. The intermediate cases correspond to actual conditions of heap leach pads in operation or in a project stage A 10 m lift stacking was used, placed in horizontal layers and with 2,5H:1V overall slope, which is typical in heap leach pads. Two cases of the soil-geomembrane interface strength envelope were considered, taken from the LSDS testing database. The 2 cases correspond to results of textured side LLDPE geomembrane versus low permeability clayey soil, with 2 thicknesses. In the Figure 2 the normal stress versus shear stress graphics for the 2 analyzed cases are presented. The thicknesses of the geomembrane were: Case 1: 1,5mm; and Case 2: 2,0mm. In the Figure 2 the linear envelope represents the best fit for the test results, while the non-linear envelope considers the actual behavior of the tested specimens, where the initiation of the non-linear envelope at (0,0), was assumed extrapolating the curve based on the lowest normal stress of the test. The following properties for the heap ore were considered: moist density of 18 kn/m 3 ; angle of repose of 1,33H:1V; linear strength envelope based on the Mohr-Coulomb criteria, with an angle of friction of 37 and zero cohesion. Although, it is known that granular soil strength is non-linear at high loads, in this paper the ore shear strength was kept constant in order to study only the effect of the interface non-linearity in the heap stability. A competent foundation was assumed, common case in several leach pads located in the Andes, because of this study does not consider the influence of the foundation in the heap stability. A leach pad uniform base was considered with 2% and 4% grades, which correspond to extreme cases of the initial leach pad platform. A 2% grade corresponds to a minimum condition for promoting the solution drainage, while 4% grade corresponds to a condition from which a stability dike could be required for heap ore containment. (a) (b) (c) (d) (e) Figure 1. Heap leach pad analyzed with different heights. a) 10m, b) 50 m, c) 100 m, d) 150 m, e) 200 m, f) 250 m. (f)
4 (a) Case 1, 1,5 mm LLDPE Figure 2. Normal stress versus shear stress. (b) Case 2, 2,0 mm LLDPE 3.1 Methodology The stability analyses for the described cases were performed by using the Slide program (Rocscience) through the Spencer method by limit equilibrium. For each case the linear and non-linear envelopes in each height of the analyzed heap were used. 3.2 Results In the Table 2 the factors of safety obtained for each analyzed case is presented, and for the different heights and base grade. In the Figure 3 a typical stability analysis result is presented, while the Figures 4 and 5 show the graphics of the factors of safety. Also, in order to observe the normal stress range in the interface equivalent to the heap height and the corresponding interface shear strength, considering linear and non-linear behavior, the average normal stresses in the critical failure surface along the soil-geomembrane interface for each height analyzed were calculated,. The average normal stresses in the soil-geomembrane interface are shown on the Figure 6, only for the Case 2. Height of the Heap (m) Table 2. Factor of safety obtained for the Cases 1 and 2. CASE 1 CASE 2 Grade = 2% Grade = 4% Grade = 2% Grade = 4% Linear Non-linear Linear Non-linear Linear Non-linear Linear Non-linear 10 1,64 1,00 1,64 1,00 1, , ,85 1,89 1,85 1,89 1,76 1,79 1,76 1, ,76 1,76 1,74 1,74 1,70 1,70 1,66 1, ,73 1,70 1,69 1,67 1,67 1,63 1,63 1, ,71 1,67 1,68 1,63 1,65 1,58 1,62 1, ,69 1,64 1,66 1,61 1,64 1,55 1,61 1,51
5 Figure 3. Typical output of the stability analysis. Figure 4. Height of the heap versus factors of safety. Case 1. Figure 4. Height of the heap versus factors of safety. Case 2.
6 Figure 6. Average normal stresses along the critical failure surface and envelope extrapolation. Based on the results above the following comments are presented: The trend of the factors of safety is similar for the 2 analyzed cases and for 2 and 4% grades. The 10 m one lift analysis provides a relatively low factor of safety in all the analyzed cases, but this is still more evident in the case of non-linear envelope, mainly because of the significant difference of the shear strength at low normal stresses, as observed in Figures 2 and 6. For 50 and 100 m heaps the factors of safety are similar or same, both for linear or non-linear envelope, which is explained because of the average normal stresses along the interface, which represents these heights, provide similar shear strength for linear and non-linear envelope, as observed in Figure 6. For 150 m heaps and taller, lower factors of safety with the non-linear envelope are obtained, which is explained by the difference of the shear strength between both envelopes, which is bigger and bigger as the normal stress increases, as observed in Figure 6. For heaps taller than 100 m, a decrease of the factors of safety is observed when 4% grade is analyzed in comparison with 2% grade. 4. SHEAR STRENGTH AT HIGH AND LOW NORMAL STRESSES 4.1 Envelope Extrapolation The shear strength at high normal stresses, greater than those applied in typical LSDS test, is usually obtained extrapolating the testing results between the applied normal stress range. In the Figure 6 an extrapolation of the linear and non-linear envelope at stress greater than 800 kpa (maximum normal stress of the database) is presented. There are some aspects which deserve the following comments: As can be observed the average normal stress for very tall heaps, equal or greater than approximately 150 m, exceeds the maximum normal stress applied in the LSDS test of the database. Therefore, in order to analyze the stability of very tall heap leach pads, which induce high normal stresses along the soil-geomembrane interface, usually the strength envelope is extrapolated until reaching the required stress, as observed in Figure 6. When linear envelopes are used, the envelope extrapolation will provide an overestimation of the factors of safety of very tall heap leach pads, while the use of a non-linear envelope, although will provide lesser factors of safety, the results will be more reliable; however, the stability analysis results will depend in his case of the last value obtained in the LSDS test. In Figure 6 a LSDS fictitious result is presented, which would be obtained for a normal stress of 1400 kpa approximately, almost double than the capacity of the equipment used in the laboratory and commonly available, but which explains in an approximate manner how the strength envelope would be in this stress range. As can be observed, the difference between the linear and non-linear behavior is important and the factors of safety to be obtained will also show this difference.
7 This difference will still be greater if we consider that the ore of the heap will have a non-linear behavior also for high normal stress, which is typical for granular materials, but as it was stated before, the objective of this paper was the evaluation of only the interface non-linearity in the heap stability. The interface shear strength for high normal stress can be extrapolated in a more approximate manner for the nonlinear envelope case, if an arbitrary fit of the shear strength of the last testing result is performed, reducing slightly the obtained value, in order to avoid the overestimation of the factor of safety when a very tall heap leach pad is analyzed. 4.2 Interface Shear Strength at Low Normal Stress The first lift analysis of a heap leach pad, which is when low normal stresses are induced, is important because of typically low factor of safety is obtained. The criteria to be used for the definition of the non-linear strength envelope at low normal stress, considers a zero shear strength for a zero normal stress, taking (0,0) as the initiation of the strength envelope. In the Figure 7 a result of soil-geomembrane interface testing is presented considering a minimum normal stress of 50 kpa. As can be observed, the result for this low normal stress would confirm the criteria to use the coordinate origin as the initiation of the strength envelope. Figure 7. Shear strength at low normal stress. 5. CONCLUSIONS A large database of 126 LSDS testing performed in low permeability clayey soil with geomembrane has been reviewed. The testing program included smooth and textured LLDPE and HDPE geomembrane, of 1,5 ad 2,0 mm thickness. Most of these tests were performed by using textured LLDPE geomembrane, used frequently in the heap leach pad design; the results indicate a predominantly non-linear behavior of the strength envelope. The comparative study performed for evaluating the influence of the non-linearity of the soil-geomembrane interface strength in the typical heap leach pad stability, considered the following: two actual cases of non-linear envelope from the database, hypothetical cases of heap leach pad of different heights; and base grade of 2% and 4%, also typical. The analysis results for the first lift (10 m heap) and heaps greater than 150 m, provide lesser factor of safety when non-linear envelope is used comparing with linear envelopes, because of the difference of the shear strength of linear and non-linear envelopes which is observed for average normal stresses at the failure surface along the interface for this 2 cases. The average normal stress for heap leach pads higher than approximately 150 m, exceeds the maximum normal stress of LSDS testing equipment. Therefore, for the analysis of very tall heap leach pads it is necessary to extrapolate the shear envelope until reaching the required stress. In general, this extrapolation will provide an overestimation of the factor of safety of very tall heap leach pads; however, if non-linear extrapolations are used, it will provide more reliable results, with factors of safety less than those obtained by using a linear envelope. Also, the interface shear strength for high normal stress can be
8 extrapolated in a more approximate manner for the non-linear envelope case, if an arbitrary fit of the last testing result is performed, which avoids the overestimation of the factor of safety when very tall heap leach pads are analyzed. REFERENCES ASTM D Standard test method for determining the coefficient of soil and geosynthetic or geosynthetic and geosynthetic friction by the direct shear method. American Society for Testing and Materials, West Conshohocken, Pennsylvania, USA. Breitenbach, A.J., and Swan Jr., R.H. (1999). Influence of high load deformations on geomembrane liner interface strengths. Geosynthetics 99 Conference, Industrial Fabrics Association International, Boston, Massachusetts, Vol. 1, pp Ghazavi, M. and Ghaffari, J. (2008). Experimental determination of sand-geosynthetic interface parameters using large direct shear tests. The First Pan American Geosynthetics Conference & Exhibition, pp Koerner, R.M. and Koerner G.R. (2007). Interpretation(s) of laboratory generated interface shear strength data. GRI White Paper #10, Geosynthetic Institute 475 Kedron Avenue Folsom, PA USA. Parra, D., Soto, C. and Valdivia, R. (2010). Soil liner-geomembrane interface shear strength using rigid substrata or overliner. 9 th International Conference in Geosynthetic, pp Rocscience (2005). SLIDE: 2D Limit Equilibrium Slope Stability for Soil and Rock Slopes. User s Guide.
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