This is a response to de Freitas (2025). Discussion: Influence of air entrainment and gas kinetics on liquefaction triggering during tsunami loading. Géotechnique, https://doi.org/10.1680/jgeot.24.01163.
The authors would like to thank Dr de Freitas for his interest in their work and a description of an interesting laboratory experiment he performed with a former postgraduate student. Based on his description of the experiment, the authors suspect that an air pocket was created between the capillary fringe and the infiltration front propagating downward, which created an airlock. Wang et al. (1998) describe a similar experimental set-up. The airlock formed because the soil tube was confined between an artificial water table at the bottom of the soil column and the part open to the atmosphere was closed to the atmosphere by infiltrating groundwater at the top. If the rainfall infiltration occurred slowly enough and the head pressure at the top of the experimental apparatus was held relatively constant, then the pressure of the created airlock could eventually balance and potentially exceed the overburden pressure imposed by the weight of water and soil, leading to the experimental observations described by Dr de Freitas.
Tsunami loading is relatively slow, and tsunamis have long wavelengths, as discussed by Abdollahi & Mason (2019). Many researchers thus assume one-dimensional loading for computing tsunami-induced pore water pressure response, and a one-dimensional experimental set-up is likely to be reasonable for replication. For two- or three-dimensional slope stability application, the authors expect that air escape routes would be likely to prevent an airlock – as described by de Freitas’s one-dimensional experiments – from forming in the field. Accordingly, at a field scale, the authors suspect that the slope stability failures Dr de Freitas and his former student were concerned with are caused by a change in suction stress during rainfall infiltration. Lu & Godt (2008) studied the problem of unsaturated soil slope subjected to steady rainfall, and they developed an expression for the factor of safety against slope failure, F, using an infinite slope assumption:
where is the soil’s effective friction angle; is the slope angle; c′ is the soil’s effective cohesion; is the soil’s unit weight; Hs is the depth of soil above the failure plane; and is the suction stress. Notably, the suction stress is always less than or equal to zero, which leads to some confusion when discussing equation (19). As Lu & Godt (2008) show, during rainfall infiltration, when the degree of saturation in the unsaturated soil increases, the value of the suction stress moves towards zero (i.e. technically increases, although colloquially, many engineers would say that the suction stress decreases). As a result, the suction term in equation (19) also decreases and the overall factor of safety against slope stability decreases, until it reaches one or less, indicating slope failure. In addition, as infiltration and saturation of surficial soil occur, destabilisation of lateral downslope-directed gradients can develop.
Notwithstanding the foregoing discussion, the authors think that experiments like the one described by Dr de Freitas, with a few changes, would be useful to strengthen their model. For instance, the authors created their model to describe the physical process of tsunami inundation and drawdown atop a quasi-saturated sand bed containing entrapped gas bubbles; therefore, they did not consider an unsaturated sand bed like Dr de Freitas. In a quasi-saturated sand bed, the gas phase is not continuous, and gas bubbles are occluded within the pore space. The preceding distinction between quasi-saturated and unsaturated sand beds is important, because quasi-saturated sand beds have a relatively high degree of saturation with negligible suction – a condition the authors considered appropriate in sand beds below the tide level. In short, their model was developed to understand the influence that subtle differences in gas content could have on the pore water response and the interaction between fully saturated and quasi-saturated sediments during tsunami loading.
Although the experimental apparatus described by Dr de Freitas could only replicate the tsunami inundation process as designed, the authors submit that it could be augmented to simulate a tsunami drawdown process as well. Moreover, consideration of a fully unsaturated sand bed overlying saturated material is particularly relevant – and likely to be even more so than the quasi-saturated condition studied in the authors’ article – to infrastructure in the dynamic coastal foreshore and nearshore environments. Assuming that the one-dimensional loading simplification is valid (as in the authors’ article), an airlock could form during tsunami runup. Pressurisation of the airlock as the wetting front progresses (the ideal gas law) would be expected to peak when overburden pressure equals the airlock pressure, that is the point when sediment above the airlock is buoyed on a bed of pressurised air. The destabilising condition would most likely occur during tsunami drawdown because the overburden pressure attributed to the water column rapidly decreases, but the wetting front in the soil would not be likely to suddenly retreat (move upward) and depressurise the airlock. Although the preceding physical description is different from the reversal of flow and liquefaction of a quasi-saturated sand bed in the authors’ article, they are both fundamentally linked to rapid changes in a surface boundary condition attributed to retreat of the tsunami wave during drawdown, that is changes pore water pressure for a quasi-saturated sand bed and overburden pressure for the unsaturated case. Given their physical description, the authors speculate that the sediment transport and scouring caused by tsunami loading could be significant in the case of an unsaturated sand bed, which gives further credence to revisiting Dr de Freitas’s experimental apparatus. To the authors’ knowledge, no researchers have performed numerical or physical experiments to replicate the foregoing physics.
In closing, the authors would like to thank Dr de Freitas again for his interest in their work and the time he took to develop a discussion. His discussion provides further motivation to improve the model and compare it with relevant experimental results, design experimental apparatuses and perform field measurements. Hopefully others in our community are similarly inspired.
