Analytical and numerical modeling of the effects of buttressing on slide-head toppling failure

Buttressing is a widely employed control measure for mitigating slope failure in various settings such as openpit mines, road sections, dams, and hilly or rocky terrains. This paper presents a study on the effects of buttressing, specifically concerning slide-head toppling failure. Drawing insights from a case study of slide-head toppling in Zambia, our investigation employs both analytical (limit equilibrium) and numerical (3DEC software) modeling techniques. The analytical and numerical models exhibit notable similarities in their schematics and overall results, revealing a subtle effect of buttressing in controlling slide-head toppling failure. This study contributes valuable insights into the nuanced role of buttressing in slope stability, with implications for optimizing buttress design parameters. While the overall findings suggest a modest influence of buttressing on slide-head toppling failure, further discussions delve into the specific implications and potential refinements for practical applications. Background Achieving slope stability (openpit mines and road sections) is of paramount importance in ensuring the sustainability of both the functionality as well as safety of mines, natural slopes and constructed highways. Several methods are employed to control and mitigate slope failure and one of them is the use of buttressing. This method has been a well-established practice for over six decades, involving the placement of rock fill on slope berms to control and mitigate failure.This paper addresses a significant research gap by exploring the effects of buttressing specifically on slide-head toppling failure, a complex secondary mechanism involving toppling and sliding of rock blocks on a slope [1-3]. Despite the extensive literature on buttressing, there is limited research, especially in the context of numerical and analytical modeling for rock slopes, particularly those prone to slide-head toppling. Methodology Limit equilibrium analysis. From the initial equations of slide-head toppling as originally proposed by Goodman and Bray [3], the equations can be modified to incorporate the effect/influence of buttress material on the overall equilibrium of the rock slope.A principle of critical-state strength for an infinite translational slope [4,5] is used to guide the limit equilibrium analysis for the slope and buttress material interaction. This interaction is illustrated in Fig. 1. Based on the infinite slope principle proposed by Taylor [4], it is possible to apply the same principle to the buttress material. Although not infinite, the buttress material has constant conditions and constant material properties at any depth. Any vertical column within the buttress material is thus the same by material and property definition as any other vertical column in all aspects along the buttress section. It is further assumed that the angle αf is approximately equal to the block stepping angle at the base of the blocks. The resisting force, Rb, against toppling of the blocks per meter of thick slice acting along Pn arm, according to Craig [5], would be: From Eqs. (8) and (9), it is observed that the buttress material has an overall resisting effect on the potential for slide-head toppling of the rock slope. Fig. 1 Interaction of the buttress material and slide-head toppling: (a) modified schematic layout of slide-head toppling failure,(b) overall illustration of buttressing on a slope as used to control slide-head toppling failure and (c) force interactionof buttress material vertical column and rock blocks undergoing slide-head toppling. Fig. 2 Displacement results of numerical modeling: (a) without buttress material and (b) with initial Hand Lh buttress material parameters (from analytical modeling). Numerical modeling. The numerical modeling was conducted using three-dimensional distinct element code, abbreviated as 3DEC 7.00 [6]. Similar parameters and geological characteristics of both the rock slope and the buttress material used for analytical modeling were also incorporated in the numerical modeling approach. Two model codes were written: one without the buttress material in place, and the other with buttress material. Modeling was done based on Mohr-Coulomb joint material modeling within the software. The comparison between the two was made based on the results of block displacement vectors (Fig. 2). Furthermore, the buttress material was placed on the model at a height and horizontal length similar to the analytical values. From Figs. 2a and 2b, under equilibrium, it can be noted that the maximum displacement values reduce from 16.3 mm to 12.9 mm once the buttress was introduced on the model. Results and discussion The results of both numerical and analytical modeling observed in the subsequent section have one thing in common: the buttress material has an effect in retaining the stability of a slope. The objective of this analysis was to develop a comparison of the effect of buttressing on the overall slope in terms of slide-head toppling failure. Thus, the comparison is basically drawn between the driving forces on the slope (toppling and sliding blocks) and the resisting forces generated by the buttress material under the limit equilibrium analysis method. Numerical modeling was developed as a further comparison and/or check on the outcome of the initial limit equilibrium analysis on the rock slope for the failure mechanism with buttressing as a failure control measure. Conclusion Depending on the scale of failure and buttress parameters, buttressing can be a relatively effective way to control slide-head toppling failure. From the analytical and numerical results, this method has proven very effective for small-scale failures on the slope with relatively small heights. This method can be further improved by varying buttress parameters on the rock slope, including the overall height, width/horizontal length and angle of the buttress. Overall, effectiveness of the buttress in controlling slide-head toppling on a rock slope rests entirely on the volume of the buttress material. The bigger the volume, the higher the resisting force. Selected references Samson A, Bowa VM, Chileshe PRK, Chinyanta S (2023) Review of the stability analyses for slide-head toppling failure mechanisms: a different perspective. Arab J Geo-sci 16:195 Samson A, Bowa VM, Chileshe PRK, Chinyanta S (2024) Design charts for jointed rock slopes susceptible to slide-head toppling failure. Geotech Geol 42:433–449 Goodman RE, Bray JW (1976) Toppling of rock slopes. In Proceedings of the specialty conference on rock engineering for foundations and slopes. American Society of Civil Engineers, New York Taylor DW (1948) Fundamentals of Soil Mechanics. 1st ed. John Wiley and Sons Inc., New York Craig RF (2004) Craig’s Soil Mechanics. 7th ed. Spon Press, Taylor & Francis Group, London and New York Itasca Consulting Group Inc (2022) Three-dimensional distinct element code

Analytical and numerical modeling of the effects of buttressing on slide-head toppling failure

Authored by: Abdul Samson, Victor Mwango Bowa, Peter RK Chileshe, Sydney Chinyanta and Ebelia Manda

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