scholarly journals Semi-analytical solutions to consolidation for unsaturated soils by vertical drains under arbitrary time-dependent loading

2020 ◽  
Vol 794 ◽  
pp. 012057
Author(s):  
Aifang Qin ◽  
Lianghua Jiang ◽  
Tianyi Li ◽  
Weifang Xu
Keyword(s):  
Analytical Solutions ◽  
Unsaturated Soils ◽  
Time Dependent ◽  
Vertical Drains ◽  
Arbitrary Time

Consolidation Theory of Unsaturated Soils with Vertical Drains Considering Well Resistance and Smear Effect under Time-Dependent Loading

2021 ◽  
Vol 147 (9) ◽  
pp. 04021055
Author(s):  
Deqiang Chen ◽  
Pengpeng Ni ◽  
Xinlei Zhang ◽  
Zheng Chen ◽  
Guoxiong Mei ◽  
...  
Keyword(s):  
Unsaturated Soils ◽  
Time Dependent ◽  
Vertical Drains ◽  
Consolidation Theory

scholarly journals Nonlinear Radial Consolidation Analysis of Soft Soil with Vertical Drains under Cyclic Loadings

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Pyol Kim ◽  
Hyong-Sik Kim ◽  
Yong-Gun Kim ◽  
Chung-Hyok Paek ◽  
Song-Nam Oh ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Governing Equation ◽  
Analytical Solutions ◽  
Soft Soil ◽  
Time Dependent ◽  
Vertical Drains ◽  
Consolidation Analysis ◽  
Consolidation Behavior

This paper presents analytical solutions for nonlinear radial consolidation of soft soil with vertical drains under various cyclic loadings. By considering the nonlinear variations of compressibility and permeability expressed by the logarithm relations (e−log σ′ and e−log kh), the governing equation for nonlinear radial consolidation of the soil under equal strain and time-dependent loading is established. The analytical solutions are derived for nonlinear radial consolidation under haversine cyclic loading, trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading. The presented solution is verified through the degeneration into the existing solutions for nonlinear radial consolidation under constant and ramp loadings, which shows the solution proposed in this paper is more general for nonlinear radial consolidation under time-dependent loading. The nonlinear radial consolidation behavior of the soil with vertical drains subjected to various cyclic loadings is investigated using the solutions developed. The proposed solutions can be effectively utilized in the analysis of nonlinear radial consolidation under various cyclic loadings.

scholarly journals Analytical solutions for linearized Richards Equation with arbitrary time-dependent surface fluxes

2001 ◽  
Vol 37 (4) ◽  
pp. 1091-1093 ◽  
Author(s):  
Jiann-Mou Chen ◽  
Yih-Chi Tan ◽  
Chu-Hui Chen ◽  
J.-Y. Parlange
Keyword(s):  
Analytical Solutions ◽  
Surface Fluxes ◽  
Time Dependent ◽  
Richards Equation ◽  
Arbitrary Time

scholarly journals An Equal-Strain Analytical Solution for the Radial Consolidation of Unsaturated Soils by Vertical Drains considering Drain Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Feng Zhou ◽  
Zheng Chen ◽  
Xudong Wang
Keyword(s):  
Analytical Solution ◽  
Unsaturated Soils ◽  
Ground Surface ◽  
Matrix Analysis ◽  
Governing Equations ◽  
Vertical Drains ◽  
Ground Surface Settlement ◽  
Parametric Studies ◽  
Strain Model ◽  
Good Agreement

Developing an analytical solution for the consolidation of unsaturated soils remains a challenging task due to the complexity of coupled governing equations for air and water phases. This paper presents an equal-strain model for the radial consolidation of unsaturated soils by vertical drains, and the effect of drain resistance is also considered. Simplified governing equations are established, and an analytical solution to calculate the excess pore-air and pore-water pressures is derived by using the methods of matrix analysis and eigenfunction expansion. The average degrees of consolidation for air and water phases and the ground surface settlement are also given. The solutions of the equal-strain model are verified by comparing the proposed free-strain model with the equal-strain model, and reasonably good agreement is obtained. Moreover, parametric studies regarding the drain resistance effect are graphically presented.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

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