Civil Engineering April 2022 | Vol 30 No 3

10 April 2022 Civil Engineering Geotechn i cal eng i neer i ng I n 2020, the draft ICOLD Tailings Dam Safety Bulletin stipulated that potentially liquefiable zones within a facility should be assumed to have liquefied, and the stability of the facility evaluated under these compromised strength conditions. This state is commonly analysed by assigning residual or post peak strengths where satu- rated contractive conditions occur. Should the assumption of residual strength conditions result in instability (commonly a factor of safety < 1.1), the Bulletin affords the engineer the opportu- nity to perform a liquefaction triggering assessment. This involves examining the effect that credible triggering events have on the material toward liquefaction, as opposed to assuming liquefaction. The challenge in assessing liquefaction triggers lies in the wide range of possible triggers and in the complex analyses required to assess these accurately. This article focuses on the latter. It does not aim to present a definitive guide to performing triggering analyses, but rather presents, in deliberately simplified terms, a critical state approach as a tool to aid in assessing triggering mechanisms. THE ROLE OF CONSTITUTIVE MODELS In the simpler Mohr-Coulomb constitu- tive model, a soil’s strength is controlled by effective stress in drained conditions and by undrained shear strength under undrained loading. Furthermore, elastic or elastic-perfectly plastic stress-strain relationships are commonly employed in these simpler models. While these may suffice for simple applications, they lack precision in instances where performance is controlled by complex soil behaviour. Critical state soil mechanics (CSSM) extends beyond simpler models to con- sider that a material’s behaviour is also a function of its density (or void ratio). More realistic stress-strain relationships and complex yield and hardening laws are incorporated. CSSM thus provides a framework which inherently accounts for changes in behaviour and strength with changes in density and stress. The NorSand constitutive model ac- curately captures the dilatant behaviour of dense soils and contractive behaviour of loose soils, making it suitable for modelling of silts and sands. The NorSand model is also able to capture aspects of liquefaction and was therefore selected for use in triggering assessments of various tailings facilities. A RECAP ON CSSM PRINCIPLES Unless the reader frequently works in the realms of CSSM, it is likely that The “critical state” of our tailings dams Katy O’Brien Geotechnical Engineer ARQ Geotech katy@arq.co.za Thomas O’Brien Pr Eng Director ARQ Geotech thomas@arq.co.za Beric Robinson Tailings Consultant BRT beric@tpms-sa.com Over the last few decades, design requirements for tailings storage facilities (TSFs) have become more elaborate and demanding. A critical state approach shows much merit as a tool to aid in assessing liquefaction trigger mechanisms. Figure 1 The theoretical CSL in e:p’ space and p’:q space e Γ 1 kPa ln(p’) q p’ 1 λ CSL 1 M CSL e c = Γ – λ ln p ’ q = Mp ’