MDPI publishes vertical‑drain large‑strain study

MDPI’s journal *Water* published an open-access study in March 2026 that revisits how engineers model consolidation around vertical drains in soft ground. The paper, “Nonlinear Large-Strain Consolidation of Vertical Drains with Coupled Radial–Vertical Flow Considering Hansbo’s Flow and Smearing Effects,” proposes a numerical model that combines large-strain deformation, coupled radial and vertical seepage, Hansbo’s non-Darcy flow treatment, smear effects and soil nonlinearity. (mdpi.com) The study matters because many vertical-drain calculations still simplify drainage as mainly radial and treat strains as small. The authors instead frame consolidation as a moving, nonlinear process in which settlement, pore-pressure dissipation and permeability changes interact as the soil deforms. The model was solved with a finite-difference scheme, and the paper says the scheme was checked by reducing the problem to a radial-consolidation case and comparing it with an analytical solution. (mdpi.com) ### Why did the authors add vertical flow to a vertical-drain model? The *Water* paper says earlier idealized consolidation theories for vertical drains focused mainly on radial flow, even though coupled radial-vertical seepage can develop in practice. The authors built the model to capture that interaction under large strain, rather than treating vertical drainage as negligible from the start. That distinction matters most in the early stage of consolidation, according to the paper. The authors report that vertical flow contributes primarily at the beginning of the process, before its effect fades relative to radial drainage. (mdpi.com) ### What do Hansbo’s flow and smear effects change in practice? Hansbo’s flow enters the model as a non-Darcy effect that can slow water movement through the treated ground. The paper says increasing the Hansbo flow parameter *m* and the threshold hydraulic-gradient parameter *I1* “markedly slows down” consolidation. (mdpi.com) Smear effects describe the disturbed zone created around a drain during installation, where permeability is reduced. The authors say consolidation develops fastest when permeability within the smear zone follows a parabolic distribution, underscoring that the assumed smear profile can change predicted drainage performance. (mdpi.com) ### When can engineers still use a radial-flow-only simplification? The paper identifies one threshold that designers can use as a screening check. The authors say that when the ratio of soil-layer thickness to the radius of the influence zone, H/re, exceeds 10, the effect of vertical flow becomes negligible and consolidation can be approximated reasonably with a radial-flow-only model. (mdpi.com) That finding does not remove the need to check installation disturbance or nonlinear soil behavior. The same paper says larger soil nonlinearity parameters amplify the influence of coupled radial-vertical flow, which means the simplification is less comfortable in highly compressible, strongly nonlinear ground. (mdpi.com) ### How does this change settlement and pore-pressure estimates? The March 9, 2026 article note at MDPI identifies the study as *Water* 2026, volume 18, issue 5, article 645. In the paper’s abstract, the authors link the revised formulation to both average consolidation behavior and the timing of pore-pressure dissipation, rather than only final settlement. (mdpi.com) For design work, that means the model is most useful where prefabricated vertical drains are being applied in very soft ground, reclamation or other cases where large settlement, installation smear and changing permeability are expected. (mdpi.com) In those cases, the paper gives engineers a way to test whether a small-strain, radial-only assumption is likely to understate the time needed for consolidation or misstate early-stage pore-pressure response. ### Where can readers find the paper? MDPI lists the article as open access in *Water* with DOI 10.3390/w18050645. (mdpi.com) The article page and MDPI’s notes page show it was published in 2026 and updated on March 9, 2026. (mdpi.com)