Abstract
In real practice, the construction of drainage wells is always accompanied by smear effect, whereas it is scarcely discussed in the field of unsaturated soils. In this case, on the basis of the widely-accepted consolidation theory for unsaturated stratum by Fredlund, this paper studies the equal strain consolidation characteristics of unsaturated foundation with drain wells affected by smear effect under time-varying loading (exponential loading as a case). Firstly, with the consideration of corresponding boundary conditions, the governing equations under the equal strain hypothesis are obtained. Afterwards, decoupling process, constant variation method and Fourier series expansion theory are utilized to get the analytical solutions, which are then verified to be credible by means of the finite difference method. Finally, the consolidation patterns of the drainage well foundation modeling in unsaturated soils are studied against hydraulic coefficients, modeling sizes and loading parameter. It reveals that the smear effect can significantly restrain the consolidation process of the foundation by drain wells, while different parameters will lead to various results.
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Abbreviations
- a :
-
The exponential loading parameter
- C a :
-
The air-related interaction constant
- \(C_{{{\rm{v}}_{\rm{r}}}}^{\rm{a}}\) :
-
The air-related consolidation coefficient in the radial direction
- \(C_{{{\rm{v}}_{\rm{z}}}}^{\rm{a}}\) :
-
The air-related consolidation coefficient in the vertical direction
- C w :
-
The water-related interaction constant related to water phase
- \(C_{{{\rm{v}}_{\rm{r}}}}^{\rm{w}}\) :
-
The water-related consolidation coefficient in the radial direction
- \(C_{{{\rm{v}}_{\rm{z}}}}^{\rm{w}}\) :
-
The water-related consolidation coefficient in the vertical direction
- g :
-
The gravitational acceleration
- H :
-
The thickness of the foundation
- \({k_{{{\rm{a}}_{\rm{r}}}}}\) :
-
The air-related permeability coefficient of influenced area in the radial direction
- \({k_{{{\rm{a}}_{\rm{s}}}}}\) :
-
The air-related permeability coefficient of smeared zone
- \({k_{{{\rm{a}}_{\rm{z}}}}}\) :
-
The air-related permeability coefficient of influenced area in the vertical direction
- \({k_{{{\rm{w}}_{\rm{r}}}}}\) :
-
The water-related permeability coefficient of influenced area in the radial direction
- \({k_{{{\rm{w}}_{\rm{s}}}}}\) :
-
The water-related permeability coefficient of smeared zone
- \({k_{{{\rm{w}}_{\rm{z}}}}}\) :
-
The water-related permeability coefficient of influenced area in the vertical direction
- M :
-
The is the air mass molecular
- \(m_1^{\rm{a}}\) :
-
The air-related parameter of net normal stress q0 − ua
- \(m_2^{\rm{a}}\) :
-
The air-related parameter of the net normal stress q0 − ua
- \(m_1^{\rm{w}}\) :
-
The water-related parameter of the net normal stress q0 − ua and suction ua − uw
- \(m_2^{\rm{w}}\) :
-
The water-related parameter of the net normal stress q0 − ua and suction ua − uw
- n :
-
The porosity
- q 0 :
-
The applied external instantaneous loading
- R :
-
The universal air constant
- r e :
-
The largest radius of the influenced region
- r s :
-
The largest radius of the smeared zone
- r w :
-
The radius of the drain
- S r :
-
The saturation
- T :
-
The absolute temperature
- u a :
-
The excess pore-air pressure
- \(u_{\rm{a}}^0\) :
-
The initial excess pore-air pressure
- ū a :
-
The average excess pore-air pressure
- \({u_{{{\rm{a}}_{\rm{s}}}}}\) :
-
The excess pore-air pressure in the smeared zone
- u atm :
-
The atmospheric pressure
- u w :
-
The excess pore-water pressure
- \({u_{{{\rm{w}}_{\rm{s}}}}}\) :
-
The excess pore-water pressure in the smeared zone
- ū w :
-
The average excess pore-water pressure
- \(u_{\rm{w}}^0\) :
-
The initial excess pore-water pressures
- α a :
-
The air-related smear coefficient
- α w :
-
The water-related smear coefficient
- γ w :
-
The water unit weight
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Acknowledgments
This study is supported by the National Natural Science Foundation of China (Grant No. 41807232, Grant No. 41372279 and Grant No. 11672172).
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Huang, Y., Li, T. & Fu, X. Consolidation of Unsaturated Drainage Well Foundation with Smear Effect under Time-Dependent Loading. KSCE J Civ Eng 25, 768–781 (2021). https://doi.org/10.1007/s12205-021-0086-x
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DOI: https://doi.org/10.1007/s12205-021-0086-x