Civil Engineering April 2022 | Vol 30 No 3

12 April 2022 Civil Engineering when the state parameter is positive, how- ever Shuttle and Cunning (2008) found that the boundary between contractive and dilative materials should be conser- vatively placed at ψ=-0.05, as shown in Figure 3. The state parameter can be deter- mined at varying depths within a TSF by interpretation of CPTu test results utilising various empirical methods. There is naturally quite a spread of state parameter data given the highly aniso- tropic and non-homogeneous response of tailings deposits to the CPTu test and it is necessary for the engineer to determine a representative or characteristic value. This characteristic state parameter may typically be determined using a 90% con- fidence level via statistical processing. A 90% confidence limit may seem stringent when compared to the 70% (cautious estimate) confidence typically used to introduce some conservatisms in soil parameter derivation. However, this stringency is motivated by the fact that stochastic simulation and physical testing have shown that the looser/ weaker material zones may control the overall tailings mass behaviour, and by the possible severe consequence of get- ting things wrong. Most saturated fine tailings materials (in South Africa at least) possess a posi- tive state parameter and are susceptible to liquefaction when sufficiently trig- gered. Liquefaction is brought on by a significant reduction in mean effective stress, resulting in loss of strength and “liquid” behaviour. Mean effective stress is defined as total stress less pore water pressure. A reduction in mean effective stress could thus be brought on by (1) a reduction in total stress or (2) an increase in pore pressure. Theoretical stress paths for contrac- tive materials are provided in Figure 4. The peak of the stress paths indicates the onset of liquefaction (instability locus), after which strain softening, and sudden loss of strength occurs. The stress paths then intercept the critical state line where critical state conditions (i.e. failure) arise. The following important points must be noted: Q Q Liquefaction and critical state are considered to be two separate conditions, although the onset of the former is usually rapidly followed by the latter Q Q Liquefaction is associated with sudden strain softening and strength loss (downward trend of the stress paths) which occurs after the stress paths pass the instability locus (the flow liquefaction line) Q Q Critical state conditions can also be reached without liquefaction occur- ring (in dense/dilative materials for example), but this happens under strain hardening conditions and is not associated with brittle behaviour Q Q Although isolated portions of the overflow material zone may undergo liquefaction or reach critical state, the confinement provided by the under- flow, starter or impounding wall may be sufficient to prevent mobilisation or failure of the facility. TRIGGERING ASSESSMENT Employing the NorSand constitutive model in staged stability analysis allows monitoring of stress state in relation to critical state over the continuum of Void ratio (e) Mean effective stress (ln(p’)) Contractive State Dilative state Critical state line Ψ = 0 Ψ = –0.05 Figure 3 Plot of CSL in e:p’ space, indicating contractive and dilative soil states Figure 4 Theoretical stress trajectories for contractive material Deviator stress (q) Mean effective stress (p’) Critical state line Flow liquefaction line