Poroelastic theory of consolidation for a two-layer system with an upper unsaturated soil and a lower saturated soil under fully permeable boundary conditions

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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.

Section: Introductionmentioning

confidence: 99%

Time scales in the primary and secondary compression of soils

Liu

Borja

2022

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“…The coefficients f𝑛 (𝑝)(𝑛 = 0, 1, 2) in equation ( 15) can be obtained by solving the tri-diagonal matrix system (16). Once f𝑛 (𝑝)(𝑛 = 0, 1, 2) is known, the change in the hydraulic head s𝑛 in Laplace transform space can be obtained based on equation (15).…”

Section: Hydraulic Drawdown and Subsidence Solutionsmentioning

confidence: 99%

“…It is worth noting that there are now analytical models for unsaturated consolidation in the literature. [14][15][16] However, it is beyond the scope of our model to accommodate the effect of variable saturation degree.…”

Section: Effects Of Specific Yieldmentioning

confidence: 99%

“…14,15 semi-analytical solution to a similar two-layered system, with Fredlund and Hasan's model for unsaturated soil adopted in their model. 16 Drawdown-induced consolidation has also attracted considerable attentions. Tseng et al 17 presented a solution for 1-D elastic consolidation of aquitard subjected to a constant drop in hydraulic level.…”

Section: Introductionmentioning

confidence: 99%

“…Li et al. develop a semi‐analytical solution to a similar two‐layered system, with Fredlund and Hasan's model for unsaturated soil adopted in their model 16 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Drawdown‐induced consolidation of aquifer systems considering water‐table decline

Liu

Zhang

2023

Boundary condition is an important factor in estimating land subsidence induced by groundwater withdrawal. In previous analytical studies, the upper boundaries are commonly assumed to be constant‐head, which could fail to reflect the declines in groundwater table during groundwater pumping. A one‐dimensional (1‐D) consolidation model of aquifer systems due to groundwater drawdown is considered in this study, in which the water‐table decline is taken into account. A mathematical model, which incorporates Neuman's model of unconfined flow into Terzaghi's theory of consolidation, is first presented. The analytical solutions for both hydraulic head drawdown and subsidence are developed in the Laplace domain. A more explicit solution to the elastic, single‐layered model is also derived. The validation of the presented solutions is verified by comparing with existing solutions in degenerated cases. The results show that the presented hydraulic drawdown solutions can be used to describe the water table decline. Moreover, the subsidence solutions are notably different from solutions based on the commonly‐used constant‐head boundary, and these previous models could severely underestimate the subsidence. The influences of specific yield, compressibility of the pore water, hydraulic conductivity, and viscosity of soil skeleton on the water table decline and long‐term deformation are also investigated using the presented solutions.

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Lo,

Borja,

Chao

et al. 2023

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We develop an analytical solution to the problem of one‐dimensional consolidation of unsaturated soil subjected to cyclic loads with arbitrary waveforms. The solution predicts the excess pore water and pore air pressures and the accompanying vertical compression in a poroelastic, unsaturated soil material. Cyclic loading occurs in a variety of engineering applications and often generates higher excess pore fluid pressures and larger vertical compression than does a time‐invariant load. In the present study, the loading function is allowed to take on any arbitrary waveform represented by a Fourier trigonometric series. Analytical solution to the boundary‐value problem in one dimension is given in closed form describing the frequency‐independent and frequency‐dependent components of the poroelastic response. We verify the analytical solution through representative examples involving cyclic loads with square and triangular patterns. Apart from the shape of the forcing function, we also investigate the effects of initial water saturation, soil texture, and excitation frequency on the system response.