Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading

Semi‐analytical solutions to one‐dimensional (1D) consolidation of the two‐layered soils are developed in this paper that can consider a two‐layered soil system with unsaturated upper soils and saturated lower soils. In this case, the upper soil layer remains the water‐air two‐phase flows, while the lower soil layer only involves the flow of the water phase. Based on the assumptions made in the 1D consolidation framework for saturated and unsaturated soils, the analytical solutions in the transformation space for the consolidation model are derived using a decoupling technique and the Laplace transformation. Subsequently, following the Crump algorithm, the numerical inverse Laplace transformation is carried for the related semi‐analytical results that can analyze the consolidation characteristics of the two‐layered soils in the time domain. Furthermore, two typical cases for saturated soils in the literature are shown to examine the methodology and final solutions. Finally, results of a case study in this paper indicate that the excess pore pressures within the unsaturated soil layer near the interface are significantly affected by the water flow in the saturated soil layer, and that the final primary consolidation settlement of soils would be overestimated if the unsaturated condition of upper soils is ignored.

Section: Mathematical Modelmentioning

confidence: 99%

u_{normalw}^{(1)} false(h_{1}, t false) = u_{normalw}^{(2)} false(h_{1}, t false)

k_{normalw}^{(1)} \frac{\partial u_{normalw}^{(1)} false(h_{1}, t false)}{\partial z} = k_{normalv} \frac{\partial u_{normalw}^{(2)} false(h_{1}, t false)}{\partial z}

…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Semi‐analytical Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi‐analytical solution for one‐dimensional consolidation of a two‐layered soil system with unsaturated and saturated conditions

Qin

Jiang

2021

“…Capillarity arises from surface tension between co‐existing fluid phases in the pore space. It plays a critical role in unsaturated soil mechanics, 19–26 and significantly influences oil recovery predictions 27,28 . The solid deformation is intricately coupled with fluid pressures via nonlinear constitutive laws 29–33 relating the capillary pressure to degree of saturation.…”

Section: Introductionmentioning

confidence: 99%

Preconditioners for multiphase poromechanics with strong capillarity

Camargo

White

Castelletto

et al. 2021

Self Cite

This paper aims to enhance the performance of Newton–Krylov solvers for coupled poromechanical problems with two‐phase flow. In particular, we investigate the impact of capillary pressure on preconditioning strategies. Capillarity complicates the coupling between the solid deformation and fluid pressure degrees of freedom, as well as increases the nonlinearity of the system. Depending on the capillary pressure relation used in the constitutive formulation, the flow equations may exhibit a spectrum of advection‐dominated to diffusion‐dominated behavior. We propose preconditioning approaches that account for this behavior and lead to robust numerical performance within a broad range of regimes.

Time scales in the primary and secondary compression of soils

Liu

Borja

2022

Self Cite

The last several decades have seen a surge of papers dealing with analytical and semi‐analytical solutions to the problem of one‐dimensional consolidation of soils. But rarely has any of these contributions focused on the time scales arising from combined primary and secondary compression. Primary compression has always been attributed to the dissipation of excess pore pressure as fluid is expelled from the soil skeleton to the drainage boundaries. However, there have been several schools of thought when it comes to the process governing the secondary compression. In this paper, we attribute the secondary compression to any of the following processes occurring either individually or in combination: (a) rate‐dependent (viscoplastic) constitutive response of the soil skeleton; (b) existence of a secondary pore scale system that expels fluid from the smaller‐scale pores to the larger‐scale pores; and (c) delayed compression due to creep following Bjerrum's concept of secondary consolidation. Contributions of the present work include closed‐form analytical solutions to the problem of combined primary and secondary compression of soils in one dimension, as well as a quantitative analysis of the time scales involved in such coupled hydromechanical processes.