An Analytical Solution for 2D Plane Strain Consolidation in Unsaturated Soils with Lateral and Vertical Semipermeable Drainage Boundaries under Time-Dependent Loading
Publication: International Journal of Geomechanics
Volume 22, Issue 12
Abstract
This paper has proposed a closed-form solution for two-dimensional (2D) plane strain consolidation in unsaturated soils with lateral and vertical semipermeable drainage boundaries under time-dependent loading. By using the eigenfunction expansion technique, the governing equations are expanded into coupled ordinary differential equations, and the final solution of pore pressures is obtained by the integral transform method. The degraded proposed solution is then verified with the existing solution. The results show full agreement with the solutions, which indicates the proposed solution and program are completely correct. Meanwhile, the comparison between the analytical solutions and the finite-element simulations also demonstrates the correctness of the proposed solution. Subsequently, the effect of semipermeable parameters and loading parameters on the consolidation behavior has been investigated through the obtained analytical solution. And the distribution of consolidation profiles along two different directions has also been studied. It can be concluded that time-dependent loading changes the dissipation process obviously compared with constant loading.
Practical Applications
As the soil above the water table line is unsaturated, when constructing structures (e.g., houses and highways) on unsaturated soft soil, assessing the joint deformation of the structure and the foundation soil is essential to prevent excessive settlement and perhaps even cracking of the structures. When constructing on this soil, the foundations are often treated by some measures to avoid settlement and cracking. For example, vertical drains are used to accelerate the consolidation of the foundation soil. However, the presence of factors that impede drainages, such as the well resistance effect and the smear effect, brings some difficulties in calculating the coordinated deformation of the structure and the foundation soil. To integrate the effects of these factors, the research in this paper provides an analytical solution to evaluate the coordinated deformation of buildings and unsaturated soil. The analytical model can provide guidance for the construction of structures on such foundations by taking into account the unsaturated soil, the impeded drainage boundary, and the construction process.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research is supported by the National Key R&D Program of China (Grant No. 2016YFC0800200) and the National Natural Science Foundation of China (Grant Nos. 52078236 and 51878313), and the support is gratefully acknowledged.
Notation
The following symbols are used in this paper:
- g
- gravitational acceleration (= 9.8 m/s2);
- H
- height of the soil sample;
- kwx, kwz/kax, kaz
- parameter of water/air permeability in the x-/ z-direction, respectively;
- L
- length of the soil sample;
- ll, lr, lt, lb
- thickness of the left, right, top, and bottom smear zones, respectively;
- coefficients of water/air volume varies with changes in net normal stress and matric suction, respectively;
- n
- porosity of the soil;
- R
- universal gas constant (= 8.314 J/mol/K);
- Sr
- degree of saturation;
- Sr0
- initial degree of saturation;
- T
- absolute temperature;
- uatm
- absolute pore–air pressure;
- initial excess pore–air and water pressure;
- γw
- unit weight of water (= 9.8 kN/m3); and
- ωa
- molecular mass of air (= 0.029 kg/mol).
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Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Apr 3, 2021
Accepted: Apr 10, 2022
Published online: Sep 26, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 26, 2023
ASCE Technical Topics:
- Consolidated soils
- Continuum mechanics
- Design (by type)
- Domain boundary
- Dynamic loads
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Geomechanics
- Geotechnical engineering
- Lateral loads
- Load factors
- Material mechanics
- Materials engineering
- Mathematics
- Measurement (by type)
- Plane strain
- Soil analysis
- Soil mechanics
- Soil properties
- Soils (by type)
- Solid mechanics
- Static loads
- Statics (mechanics)
- Strain
- Structural design
- Structural dynamics
- Time dependence
- Vertical loads
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