Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading

Deng, Jiao Hong; Lee, Jhe Wei; Lo, Wei Cheng

doi:10.1016/j.jhydrol.2019.03.087

Cited by 8 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From Equations ( 12), (19), and (29), the complete solutions for triangular waveform loading can also be written in the generic form given by Equation (33), and, more specifically,…”

Section: Triangular Waveformmentioning

confidence: 99%

“…A triangular waveform is given by the Fourier infinite series 33

\begin{eqnarray} \dfrac{f(t)}{p^*}&=&\displaystyle {1\over 2}+\sum _{i=1}^\infty \dfrac{2}{i^2\pi ^2}[1-\cos (i\pi )]\cos (i\omega t)\nonumber \\ &=&{1\over 2}+\sum _{m=1}^\infty \dfrac{4}{(2m-1)^2\pi ^2}\cos [(2m-1)\omega t]\,. \end{eqnarray}

Figure 1B shows a graphical representation of Equation (35) for

\omega = 0.02

Hz and

p^*=0.1

MPa.…”

Section: Oscillatory Waveformsmentioning

confidence: 99%

“…Employing the Laplace transformation and the Fourier representation, Lo et al 16 formulated the analytical solution for the one-dimensional case, and subsequently, Lo et al 32 considered the more general case of time-varying sinusoidal load. Deng et al 33 derived a set of closed-form analytical solutions for the transient and steady-state responses of saturated soils subjected to four types of external time-dependent loading. Lo et al 34,35 investigated the effects of soil texture, stratification, and heterogeneity in water content for a double-layer system with an upper unsaturated soil and a lower saturated soil.…”

Section: Introductionmentioning

confidence: 99%

“…considered the more general case of time‐varying sinusoidal load. Deng et al 33 . derived a set of closed‐form analytical solutions for the transient and steady‐state responses of saturated soils subjected to four types of external time‐dependent loading.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Lo,

Borja,

Chao

et al. 2023

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…From Equations ( 12), (19), and (29), the complete solutions for triangular waveform loading can also be written in the generic form given by Equation (33), and, more specifically,…”

Section: Triangular Waveformmentioning

confidence: 99%

“…A triangular waveform is given by the Fourier infinite series 33

\begin{eqnarray} \dfrac{f(t)}{p^*}&=&\displaystyle {1\over 2}+\sum _{i=1}^\infty \dfrac{2}{i^2\pi ^2}[1-\cos (i\pi )]\cos (i\omega t)\nonumber \\ &=&{1\over 2}+\sum _{m=1}^\infty \dfrac{4}{(2m-1)^2\pi ^2}\cos [(2m-1)\omega t]\,. \end{eqnarray}

Figure 1B shows a graphical representation of Equation (35) for

\omega = 0.02

Hz and

p^*=0.1

MPa.…”

Section: Oscillatory Waveformsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Lo,

Borja,

Chao

et al. 2023

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Wang et al (2017), Liu et al (2018), Zou et al (2018), and Zhao et al (2020), respectively, obtained analytical solutions for the one-dimensional consolidation of clayey soils considering different load and boundary conditions. When considering time-dependent loading, Deng et al (2019) presented closedform solutions for one-dimensional consolidation in saturated soils, Moradi et al (2019) analyzed the one-dimensional consolidation of a multilayered unsaturated soil under partially permeable boundary conditions, and Zhou et al (2020) obtained an analytical solution for a classical one-dimensional thaw consolidation model. However, due to the small sample used in the test, the applicability of this theory in the calculation of deep soft clay could not be verified.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

et al. 2020

Front. Earth Sci.

View full text Add to dashboard Cite

Initial stress and additional effective stress distributions in soil greatly influence the degree of ground consolidation when calculating one-dimensional soft clay ground consolidation in deep soil. The one-dimensional non-linear consolidation governing equations of soft ground under uniform load are derived and solved with the finite difference method. This method is based on the assumptions that the initial stress in soil varies with the ground depth and that the additional effective stress caused by external loads changes with both the ground depth and consolidation time and the hyperbolic model of the soil stress-strain relationship. Formulas for the degree of consolidation and the settlement of the ground are presented. A case study shows that the degree of consolidation in the ground calculated with the finite difference method agrees well with the traditional analytical solution, and the computational efficiency of the finite difference method can be effectively improved when the segmental calculation method is used throughout the consolidation process. The results of another example show that the settlement of the ground calculated with the finite difference method agrees with the in situ data. The suggested method can greatly simplify the consolidation calculation and has a high application value in engineering.

show abstract

A Laboratory Study on Shear Behavior of Biocemented Chlef Sandy Soil

Elroul

Della

Benziane

et al. 2023

Transp. Infrastruct. Geotech.

View full text Add to dashboard Cite

Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading

Cited by 8 publications

References 21 publications

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Poroelastic response of unsaturated soils to cyclic loads with arbitrary waveforms

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

A Laboratory Study on Shear Behavior of Biocemented Chlef Sandy Soil

Contact Info

Product

Resources

About