scholarly journals One-Dimensional Consolidation of Viscoelastic Soils Incorporating Caputo-Fabrizio Fractional Derivative

2021 ◽  
Vol 11 (3) ◽  
pp. 927
Author(s):  
Minghua Huang ◽  
Chang Lv ◽  
Suhua Zhou ◽  
Shuaikang Zhou ◽  
Jiatao Kang
Keyword(s):  
Fractional Derivative ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Distribution Patterns ◽  
One Dimensional ◽  
Special Cases ◽  
Rectangular Pattern ◽  
Degree Of Consolidation ◽  
The One ◽  
Consolidation Behavior

In this paper, the Caputo-Fabrizio fractional derivative is introduced to investigate the one-dimensional consolidation behavior of viscoelastic soils. Using the Caputo-Fabrizio operator, a novel four-element fractional-derivative model is proposed to capture the viscoelastic properties of the soils, and further the one-dimensional consolidation equation is derived to simulate the consolidation behavior of the soils. Using the techniques of eigenfunction expansion and Laplace transform, a series of analytical solutions are derived to calculate the excess pore-water pressure and the average degree of consolidation of the soils. The total vertical stress in the soil is assumed to change linearly with depth, and its distribution patterns are classified to rectangular pattern, trapezoidal pattern and inverse trapezoidal pattern. Four loading types including instantaneous loading, ramp loading, sinusoidal loading and general cyclic loading are considered. Then, a comparison for several special cases is presented to verify the correctness of the proposed solutions through comparing with existing theories. Moreover, two examples considering ramp and sinusoidal loadings are given to study the consolidation behavior of the viscoelastic soils incorporating the Caputo-Fabrizio fractional derivative.

Analysis of One-Dimensional Consolidation of Non-Homogeneous Layer with Exponential Flow Law

2014 ◽  
Vol 638-640 ◽  
pp. 374-379 ◽  
Author(s):  
Feng Xi Zhou ◽  
Yi Ming He ◽  
Ying Xin
Keyword(s):  
Numerical Solution ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Decisive Role ◽  
Homogeneous Layer ◽  
One Dimensional ◽  
Governing Differential Equation ◽  
Degree Of Consolidation ◽  
Flow Law ◽  
The One

Based on exponential flow law, the analytical solution to the one-dimension consolidation governing differential equation was deduced when the laws of permeability and compressibility coefficients with depth can be expressed as exponential function. By finite difference method, the numerical solution of excess pore water pressure and degree of consolidation was obtained, then the reliability of numerical solution is verified by comparing numerical results with analytical results, and consolidation behavior of non-homogeneous layer with exponential flow law under various parameters is analyzed. The results showed that under the condition of the two-sided drainage, the heterogeneity of foundation consolidation of index of seepage speed depends on the index of the size and the size of the non-uniform parameters. That is when the index m is bigger, increase the permeability coefficient, reduce the compression coefficient, the consolidation is faster, but the inhomogeneous parameters are still play a decisive role.

scholarly journals A One-Dimensional Fractional-Derivative Viscoelastic Model for the Aquitard Consolidation of an Aquifer System

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Ming-hua Huang ◽  
Dun Li
Keyword(s):  
Fractional Derivative ◽  
Land Subsidence ◽  
Water Pressure ◽  
Viscoelastic Model ◽  
Model Parameters ◽  
Consolidation Process ◽  
One Dimensional ◽  
Aquifer System ◽  
Special Cases ◽  
Degree Of Consolidation

Land subsidence resulting from the withdrawal of groundwater is one of the problems of major importance to geosciences and geomechanics. In order to analyze the phenomena of land subsidence, this study attempts to constitute a more reliable prediction model to simulate the consolidation process of the aquifer system under the drawdown of groundwater. A fractional-derivative viscoelastic model is introduced to characterize the rheological properties of the aquitard, and the equation governing the consolidation process is established on the basis of the one-dimensional consolidation theory. The semianalytical solutions for the pore-water pressure, the settlement of aquitard, and the degree of consolidation are deduced using both finite sine transform and Laplace transform. Then, the comparisons of two special cases are performed to validate the correctness of the proposed model. The variations in the degree of consolidation and settlement of the aquitard are simulated to analyze the consolidation behavior of the aquifer system, and the influences of model parameters and the drawdown speed of groundwater are investigated.

Numerical estimation of the one-dimensional consolidation behavior of clay

2020 ◽  
Vol 17 (2) ◽  
pp. 16-25
Author(s):  
Firdevs Uysal ◽  
Osman Sivrikaya
Keyword(s):  
Experimental Study ◽  
Numerical Modeling ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Soft Soil ◽  
Log P ◽  
One Dimensional ◽  
Creep Models ◽  
The One ◽  
Consolidation Behavior

The consolidation behavior of clayey soils is traditionally evaluated in the laboratory using the one-dimensional consolidometer test. A new oedometer cell design with a ring of 60 mm in height, 75 mm in diameter was made to measure the excess pore-water pressure at the undrained base of the specimen and the friction between the soil and the ring, and to determine the ε – log p curve. This study deals with numerical modeling of the one-dimensional consolidation test and comparing the data obtained from the experimental study with the data from the modeling. In the modeling, the Soft Soil and Soft Soil Creep models were used for the clay proposed in this study. The results show, as a general trend, that the data from the numerical modeling are compatible with those from the experimental study.

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.

scholarly journals Analytical Solution for One-Dimensional Consolidation of Soil with Exponentially Time-Growing Drainage Boundary under a Ramp Load

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ming Sun ◽  
Meng-fan Zong ◽  
Shao-jun Ma ◽  
Wen-bing Wu ◽  
Rong-zhu Liang
Keyword(s):  
Analytical Solution ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
The One ◽  
Interface Parameters ◽  
Ramp Load ◽  
Excess Pore

By introducing the exponentially time-growing drainage boundary, this paper investigated the one-dimensional consolidation problem of soil under a ramp load. Firstly, the one-dimensional consolidation equations of soil are established when there is a ramp load acting on the soil surface. Then, the analytical solution of excess pore water pressure and consolidation degree is derived by means of the method of separation of variables and the integral transform technique. The rationality of this solution is also verified by comparing it with other existing analytical solutions. Finally, the consolidation behavior of soil is studied in detail for different interface parameters or loading scheme. The results show that the exponentially time-growing drainage boundary can reflect the phenomenon that the excess pore water pressure at the drainage boundaries dissipates smoothly rather than abruptly from its initial value to the value of zero. By adjusting the values of interface parameters b and c, the presented solution can be degraded to Schiffman’s solution, which can compensate for the shortcoming that Terzaghi’s drainage boundary can only consider the two extreme cases of fully pervious and impervious boundaries. The significant advantage of the exponentially time-growing drainage boundary is that it can be applied to describe the asymmetric drainage characteristics of the top and bottom drainage surfaces of the actual soil layer by choosing the appropriate interface parameters b and c.

The theory of one-dimensional consolidation of saturated clays. II. Finite nonlinear consolidation of thick homogeneous layers

1981 ◽  
Vol 18 (2) ◽  
pp. 280-293 ◽  
Author(s):  
Robert E. Gibson ◽  
Robert L. Schiffman ◽  
Kenneth W. Cargill
Keyword(s):  
Pore Water Pressure ◽  
Water Pressure ◽  
Excess Pore Pressure ◽  
Conventional Theory ◽  
One Dimensional ◽  
Consolidation Settlement ◽  
Finite Strain Theory ◽  
Effective Stress Analysis ◽  
The One ◽  
Excess Pore

The one-dimensional consolidation of a thick clay layer, initially consolidated fully under its own weight, is considered. Account is taken of the variation of the coefficients of permeability and compressibility as consolidation proceeds. To render the theory consistent finite strains are permitted. Comparisons with conventional theory, in a practical example, show that nonlinear finite strain theory predicts the progress of consolidation settlement to be substantially swifter than indicated by conventional theory, although the dissipation of excess pore pressure may be slower. The consequences of this indicate that conventional consolidation theory has the potential to seriously underestimate the excess pore water pressure in a soft layer. As a result, the estimated shear strength would, if an effective stress analysis were used, be overestimated; a potentially unsafe design could emerge.

scholarly journals Analytical solution for one-dimensional consolidation of double-layered soil with exponentially time-growing drainage boundary

2018 ◽  
Vol 14 (10) ◽  
pp. 155014771880671 ◽  
Author(s):  
Wenbing Wu ◽  
Mengfan Zong ◽  
M Hesham El Naggar ◽  
Guoxiong Mei ◽  
Rongzhu Liang
Keyword(s):  
Analytical Solution ◽  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Soil Layer ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
Present Solution ◽  
The One ◽  
Excess Pore

In this article, the exponentially time-growing drainage boundary is introduced to study the one-dimensional consolidation problem of double-layered soil. First, the one-dimensional consolidation equations of soil underlying a time-dependent loading are established. Then, the analytical solution of excess pore water pressure and average consolidation degree is obtained by utilizing the method of separation of variables when the soil layer is separately undergone instantaneous load and single-stage load. The validity of the present solution is proven by the comparison with other existing analytical solution. Finally, the influence of soil properties and loading scheme on the consolidation behavior of soil is investigated in detail. The results indicate that, the present solution can be degraded to Xie’s solution utilizing Terzaghi’s drainage boundary by adjusting the interface parameter, that is to say, Xie’s solution can be regarded as a special case of the present solution. The interface parameter has a significant influence on the excess pore water pressure of soil, and the larger interface parameter means the better drainage capacity of the soil layer.

Analysis of One-Dimensional Thermal Consolidation for Saturated Soil Considering Different Permeabilities

2014 ◽  
Vol 919-921 ◽  
pp. 641-644
Author(s):  
Cai Xia Guo ◽  
Rui Qian Wu
Keyword(s):  
Pore Water ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Saturated Soil ◽  
Excess Pore Water Pressure ◽  
One Dimensional ◽  
Consolidation Theory ◽  
Thermal Consolidation ◽  
The One ◽  
Excess Pore

Based on the analytical solutions of pore-water pressure and settlement. Problems of the one-dimensional thermal consolidation of saturated soil considering three different permeabilities were analyzed. Aiming at each permeability of thermal consolidation theory, compared with the corresponding Terzaghis consolidation theory, the one-dimensional thermal consolidation behaviour of saturated soil was analyzed in terms of excess pore-water pressure, the settlement. The results show that the permeability plays an important role in the thermal consolidation. The more permeability, the quicker pore-water pressure dissipation and the rate of settlement. Settlement of ground is more sensitive to temperature condition than the excess pore-water pressure. The behaviour of excess pore-water pressure in the process of thermal consolidation is very similar to the corresponding Terzaghis theory.

scholarly journals Influence of pore water pressure change on consolidation behavior of saturated poroelastic medium

2020 ◽  
Vol 382 ◽  
pp. 375-379
Author(s):  
Chao-Lung Yeh ◽  
Wei-Cheng Lo ◽  
Cheng-Wei Lin ◽  
Chung-Feng Ding
Keyword(s):  
Pore Water ◽  
Pore Water Pressure ◽  
Saturated Porous Medium ◽  
Water Pressure ◽  
Soil Layer ◽  
Pressure Change ◽  
Clay Layer ◽  
Poroelastic Medium ◽  
Total Settlement ◽  
Consolidation Behavior

Abstract. There are many factors causing land subsidence, and groundwater extraction is one of the most important causes of subsidence. A set of coupled partial differential equations are derived in this study by using the poro-elasticity theory and linear stress-strain constitutive relation to describe the one-dimensional consolidation in a saturated porous medium subjected to pore water pressure change due to groundwater table depression. Simultaneously, the closed-form analytical solutions for excess pore water pressure and total settlement are obtained. To illustrate the consolidation behavior of the poroelastic medium, the saturated layer of clay sandwiched between two sand layers is simulated, and the dimensionless pore water pressure changes with depths and the dimensionless total settlement as function of time in the clay layer are examined. The results show that the greater the water level change in the upper and lower sand layers, the greater the pore water pressure change and the total settlement of the clay layer, and the more time it takes to reach the steady state. If the amount of groundwater replenishment is increased, the soil layer will rebound.

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.

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