Nonlinear consolidation of thin layers subjected to time-dependent loading

2007 ◽  
Vol 44 (6) ◽  
pp. 717-725 ◽  
Author(s):  
Enrico Conte ◽  
Antonello Troncone
Keyword(s):  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Solution Procedure ◽  
Thin Layers ◽  
Time Dependent ◽  
One Dimensional ◽  
Clay Layers ◽  
Analytical Expressions ◽  
Nonlinear Consolidation

The paper deals with one-dimensional consolidation of saturated clays with variable compressibility and permeability. A formulation is developed to analyse the consolidation of thin clay layers subjected to time-dependent loading. Moreover, a simple solution procedure is presented, which makes use of some analytical expressions derived in this study in conjunction with the Fourier series. Comparisons with other analytical and numerical solutions are shown, and some aspects of the nonlinear consolidation caused by time-dependent loading are highlighted.Key words: one-dimensional consolidation, nonlinear theory, time-dependent loading, excess pore-water pressure, settlement rate.

One-dimensional consolidation of multilayered aquifer systems with viscoelastic properties induced by time-dependent groundwater drawdown

2021 ◽  
pp. qjegh2021-073
Author(s):  
Weitao Yang ◽  
Jin Xu
Keyword(s):  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Time Dependent ◽  
Analytical Models ◽  
Consolidation Process ◽  
One Dimensional ◽  
Groundwater Drawdown ◽  
Aquifer Systems

Most analytical and semi-analytical models for pumping-induced land subsidence invoke the simplifying assumptions regarding characteristics of geomaterials, as well as the pattern of drawdown response to pumping. This paper presents an analytical solution for one-dimensional consolidation of the multilayered soil due to groundwater drawdown, in which viscoelastic property and time-dependent drawdown are taken into account. The presented solution is developed by using the boundary transformation techniques. The validity of the proposed solution is verified by comparing with a degenerated case for a single layer, as well as with the numerical solutions and experimental results for a two-layer system. The difference between the average consolidation degree Up defined by hydraulic head and that Us defined by total settlement is discussed. The detailed parametric studies are conducted to reveal the effects of viscoelastic properties and drawdown patterns on the consolidation process. It is revealed that while the effect of different drawdown response patterns is significant during the early-intermediate stages of consolidation, the viscoelastic properties may have a more dominant influence on long-term consolidation behavior, depending on the values of the material parameters, which are reflected in both the deformation process of soil layers and the dissipation of excess pore-water pressure.

scholarly journals Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Dawei Cheng ◽  
Wenke Wang ◽  
Xi Chen ◽  
Zaiyong Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time Dependent ◽  
Analytic Method ◽  
Partial Differential ◽  
One Dimensional ◽  
Finite Analytic Method ◽  
Nonlinear Consolidation

For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.

Analytical Solution for One-Dimensional Consolidation of Soil Layer Induced by Time-Dependent Groundwater Drawdown

2013 ◽  
Vol 405-408 ◽  
pp. 83-88
Author(s):  
Jian Feng Yao ◽  
Kang He Xie ◽  
Da Zhong Huang
Keyword(s):  
Pore Water Pressure ◽  
Water Pressure ◽  
Separation Of Variables ◽  
Soil Layer ◽  
Time Dependent ◽  
Initial Time ◽  
Total Stress ◽  
One Dimensional ◽  
Factors Influencing ◽  
Groundwater Drawdown

The governing equation was formulated for one-dimensional consolidation of the soil layer induced by time-dependent groundwater drawdown. Using Duhamel's theorem and method of separation of variables, analytical solutions were developed for the problem. Based on the solutions, the consolidation behaviors of the soil layer were studied and the factors influencing the consolidation were investigated. The results show that it is necessary to consider both the changes of total stress and pore water pressure on the boundary. The greater initial time factorTvcis, the slower the rate of the consolidation is.

One-dimensional consolidation under general time-dependent loading

2006 ◽  
Vol 43 (11) ◽  
pp. 1107-1116 ◽  
Author(s):  
Enrico Conte ◽  
Antonello Troncone
Keyword(s):  
Fourier Series ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Simple Calculation ◽  
Time Dependent ◽  
Coefficient Of Consolidation ◽  
One Dimensional ◽  
Practical Applications ◽  
Consolidation Time ◽  
General Time

This paper presents an analytical solution for the analysis of one-dimensional consolidation of saturated soil layers subjected to general time-dependent loading. A simple calculation procedure that makes use of the Fourier series is proposed for practical applications. Both single loads and cyclic loads can be considered by choosing a suitable period for the Fourier series. A number of comparisons with existing theoretical solutions are shown to assess the accuracy of the proposed procedure. Moreover, the experimental results from oedometer tests performed in the present study and from a well-documented case history concerning a large embankment constructed on compressible soils are analysed using this solution to evaluate the coefficient of consolidation of the soil.Key words: one-dimensional consolidation, time-dependent loading, excess pore-water pressure, theoretical solution, Fourier series.

scholarly journals Analytical solution for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading

2020 ◽  
Author(s):  
Pyol Kim ◽  
Hyong-Sik Kim ◽  
Chol-U Pak ◽  
Chung-Hyok Paek ◽  
Gun-Hyang Ri ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Layered Soil ◽  
Time Dependent ◽  
One Dimensional ◽  
Nonlinear Consolidation

Vacuum and surcharge combined one-dimensional consolidation of clay soils

2002 ◽  
Vol 39 (5) ◽  
pp. 1126-1138 ◽  
Author(s):  
E Mohamedelhassan ◽  
J Q Shang
Keyword(s):  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Clay Soils ◽  
Soil Consolidation ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
Consolidation Model ◽  
The One ◽  
Excess Pore

In this study, a vacuum and surcharge combined one-dimensional consolidation model is developed. Terzaghi's consolidation theory is revisited by applying the initial and boundary conditions corresponding to combined vacuum and surcharge loading on a soil. A test apparatus is designed, manufactured, and assembled to verify the model. The apparatus has the capacity of applying designated vacuum and surcharge pressures to a soil specimen, and it allows for the measurement of the excess pore-water pressure, settlement, and volume change during the consolidation process. Two series of tests are performed using the apparatus on two reconstituted natural clay soils, namely, the Welland sediment at water contents close to its liquid limit and the Orleans clay, reconstituted and consolidated under an effective stress of 60 kPa. The former test series mimics the strengthening of a very soft soil, such as the hydraulic fill used in land reclamation. The latter test series is designed to study vacuum–surcharge combined strengthening of a consolidated soil. It is demonstrated from the experiments that the one-dimensional vacuum-surcharge consolidation model describes the consolidation behaviour of both soils well. The consolidation characteristics of the soils show no discrimination against the nature of the consolidation pressure, namely, whether they are consolidated under the vacuum pressure alone, under the surcharge pressure alone, or under a pressure generated by the combined application of vacuum and surcharge. The study concluded that the soil consolidation characteristics obtained from the conventional consolidation tests can be used in the design of vacuum preloading systems, provided that the one-dimensional loading condition prevails.Key words: consolidation, soil improvement, vacuum pressure, surcharge pressure, excess pore-water pressure, soil consolidation parameters.

Simplified Computation of 1D Consolidation for Unsaturated Soil when Air Phase Neglected

2010 ◽  
Vol 168-170 ◽  
pp. 298-302
Author(s):  
Hao Feng Xu ◽  
Kang he Xie
Keyword(s):  
Unsaturated Soils ◽  
Laboratory Tests ◽  
Continuity Equation ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Soil Mass ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
Consolidation Model ◽  
Consolidation Analysis

It is a complicated problem for consolidation analysis of unsaturated soils. Nowadays’ theories are very theoretical, and the parameters in them are so many that it is difficult to solve the equations, i.e., they are not excellently fit for application in engineering. So it is significant to get a simplified theory for consolidation analysis of unsaturated soils. In this paper, according to the phenomena observed in consolidation’s experiments for unsaturated soils, it is assumed that pore-air pressure undergoes an instantaneous dissipation and the consolidation of unsaturated soils can be described as the process of dissipation of excess pore-water pressure. Then a simplified consolidation model is put forward. And based on the principle of the whole soil mass conversation, the continuity equation is founded. Subsequently one- dimensional consolidation equation is derived, which is similar to Terzaghi’s equation for consolidation of saturated soils. Finally, the numerical results from the derived equation are compared with the experimental results from laboratory tests reported in the literature, and the agreement is good. It can be concluded that the hypothesis is rational and the simplified computation is practical in engineering.

Long-wave-induced flows in an unsaturated permeable seabed

2007 ◽  
Vol 586 ◽  
pp. 323-345 ◽  
Author(s):  
PHILIP L.-F. LIU ◽  
YONG SUNG PARK ◽  
JAVIER L. LARA
Keyword(s):  
Diffusion Equation ◽  
Pore Water ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Soil Column ◽  
Seepage Flows ◽  
Dimensional Diffusion ◽  
Special Cases

We present both analytical and numerical solutions describing seepage flows in an unsaturated permeable seabed induced by transient long waves. The effects of compressibility of pore water in the seabed due to a small degree of unsaturation are considered in the investigation. To make the problem tractable analytically, we first focus our attention on situations where the horizontal scale of the seepage flow is much larger than the vertical scale. With this simplification the pore-water pressure in the soil column is governed by a one-dimensional diffusion equation with a specified pressure at the water–seabed interface and the no-flux condition at the bottom of the seabed. Analytical solutions for pore-water pressure and velocity are obtained for arbitrary transient waves. Special cases are studied for periodic waves, cnoidal waves, solitary waves and bores. Numerical solutions are also obtained by simultaneously solving the Navier–Stokes equations for water wave motions and the exact two-dimensional diffusion equation for seepage flows in the seabed. The analytical solutions are used to check the accuracy of the numerical methods. On the other hand, numerical solutions extend the applicability of the analytical solutions. The liquefaction potential in a permeable bed as well as the energy dissipation under various wave conditions are then discussed.

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