One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.

Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

This paper presents an analytical solution for one-dimensional consolidation of soft soil under some common types of cyclic loading such as trapezoidal cyclic loading, based on the assumptions proposed by Davis and Raymond （1965） that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of the soil and that the distribution of initial effective stress is constant with depth the solution obtained, some diagrams are prepared and the It is verified by the existing analytical solutions in special cases. Using telex ant consolidation behavior is investigated.

One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient

Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.

Analytical solution to one-dimensional consolidation in unsaturated soils

This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.

Study on one-dimensional consolidation of soil under cyclic loading and with varied compressibility

This paper presents a semi-analytical method to solve one dimensional consolidation problem by taking consideration of varied compressibility of soil under cyclic loading. In the method, soil stratum is divided equally into n layers while load and consolidation time are also divided into small parts and time intervals accordingly. The problem of one-dimensional consolidation of soil stratum under cyclic loading can then be dealt with at each time interval as one-dimensional linear consolidation of multi-layered soils under constant loading. The compression or rebounding of each soil layer can be judged by the effective stress of the layer. When the effective stress is larger than that in the last time interval, the soil layer is compressed, and when it is smaller, the soil layer rebounds. Thus, appropriate compressibility can be chosen and the consolidation of the layered system can be analyzed by the available analytical linear consolidation theory. Based on the semi-analytical method, a computer program was developed and the behavior of one-dimensional consolidation of soil with varied compressibility under cyclic loading was investigated, and compared with the available consolidation theory which takes no consideration of varied compressibility of soil under cyclic loading. The results showed that by taking the variable compressibility into account, the rate of consolidation of soil was greater than the one predicted by conventional consolidation theory.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING

Based on the layered visco-elastic soil model, according to the Terzaghi's one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained. The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. According to the results of several numerical examples, the consolidation of visco-elastic soils logs behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.

Semi-analytical solution to one-dimensional consolidation in unsaturated soils

In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy＇s law, and Fick＇s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

Analytical solution to one-dimensional consolidation in unsaturated soils under sinusoidal cyclic loading

An analytical solution was presented to the unsaturated soil with a finite thickness under confinement in the lateral direction and sinusoidal cyclic loading in the vertical direction based on Fredlund's one-dimensional consolidation equation for unsaturated soil. The transfer relationship between the state vectors at the top surface and any depth was gained by applying the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy's law and Fick's law. The excess pore-air and pore-water pressures and settlement in the Laplace-transformed domain were obtained by using the Laplace transform with the initial and boundary conditions. The analytical solutions of the excess pore-air and pore-water pressures at any depth and settlement were obtained in the time domain by performing the inverse Laplace transforms. A typical example illustrates the consolidation characteristics of unsaturated soil under sinusoidal loading from analytical results. Finally, comparisons between the analytical solutions and results of the numerical method indicate that the analytical solution is correct.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED SOILS WITH IMPEDED BOUNDARIES UNDER TIME-DEPENDENT LOADINGS

On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.

Study of measurements of air velocity transducer deriving average air velocity of roadway based on one-dimensional linear regression

One-dimensional linear regression equation between measured value of air velocity transducer and the average air velocity was established by experimental data. The effect is to be evaluated. Through judging the parameters, one-dimensional linear equation established is valid. Regression equation can approximately put the measurements of air velocity transducer into the value of average air velocity. The distribution of air velocity field is simulated using Comsol in the conditions of the same length of roadway, the same air velocity and different sections.

NONLINEAR AND ELASTO-PLASTICITY CONSOLIDATION MODELS OF UNSATURATED SOIL AND APPLICATIONS

The non-linear constitutive model suggested by the authors and the Alonso's elasto-plasticity model of unsaturated soil modified by the authors are introduced into the consolidation theory of unsaturated soil proposed by CHEN Zheng-han, and the non-linear and the elasto-plasticity consolidation models of unsaturated soil are obtained. Programs related to the two consolidation models are designed, and a 2-D consolidation problem of unsaturated sail is solved using the programs, the consolidation process and the development of plastic;one under multi-grade bad are studied. The above research develops the consolidation theory of unsaturated soil to a new level.

Energy-efficient virtual machine consolidation algorithm in cloud data centers

Cloud data centers consume a multitude of power leading to the problem of high energy consumption. In order to solve this problem, an energy-efficient virtual machine(VM) consolidation algorithm named PVDE(prediction-based VM deployment algorithm for energy efficiency) is presented. The proposed algorithm uses linear weighted method to predict the load of a host and classifies the hosts in the data center, based on the predicted host load, into four classes for the purpose of VMs migration. We also propose four types of VM selection algorithms for the purpose of determining potential VMs to be migrated. We performed extensive performance analysis of the proposed algorithms. Experimental results show that, in contrast to other energy-saving algorithms, the algorithm proposed in this work significantly reduces the energy consumption and maintains low service level agreement(SLA) violations.

Exact Solution of Terzaghi’s Consolidation Equation and Extension to Two/Three-Dimensional Cases

The differential equation by Terzaghi and Fr?hlich, better known as Terzaghi’s one-dimensional consolidation equation, simulates the visco-elastic behaviour of soils depending on the loads applied as it happens, for example, when foundations are laid and start carrying the weight of the structure. Its application is traditionally based on Taylor’s solution that approximates experimental results by introducing non-dimensional variables that, however, contradict the actual behaviour of soils. The proposal of this research is an exact solution consisting in a non-linear equation that can be considered correct as it meets both mathematical and experimental requirements. The solution proposed is extended to include differential equations relating to two/three dimensional consolidation by adopting a transversally isotropic model more consistent with the inner structure of soils.

Solution to 1-D consolidation of non-homogeneous soft clay

In this work, semi-analytical methods were used to solve the problem of 1-D consolidation of non-homogeneous soft clay with spatially varying coefficients of permeability and compressibility. The semi-analytical solution was programmed and then verified by comparison with the obtained analytical solution of a special case. Based on the results of some computations and comparisons with the 1-D homogeneous consolidation (by Terzaghi) and the 1-D non-linear consolidation theory (by Davis et al.) of soft clay, some diagrams were prepared and the relevant consolidation behavior of non-homogeneous soils is discussed. It was shown that the result obtained differs greatly from Terzaghi’s theory and that of the non-linear consolidation theory when the coefficients of permeability and compressibility vary greatly.

One-dimensional Chain Topology in [Ag(C_6H_6NCl)_2](ClO_4), Generated through Weak Interaction between Molecules

The mononuclear complex [Ag(C6H6NCl)2](ClO() has been prepared and structurally analyzed by single-crystal X-ray diffraction. The complex crystallizes in the monoclinic system, space group C2/c with unit cell parameters: a=15.5314(2), b=8.0247(8), c=15.3701(2)?.β=118.832(2)°, V=1678.2(3)?3, Z=4, Mr=462.46, Dc=1.830Mg/m3, F(000)=912, μ(MoKα) = 1.694cm-1. The final R and wR are 0.0472 and 0.1272 for 1484 observed reflections with I≥3σ(I). The Ag atom is coordinated by two nitrogen atoms of 4-chloromethyl-pyridine in a linear coordination geometry. Each molecule is further linked by the weak interaction between the Cl and Ag atoms to form a one-dimensional chain structure with Ag－Cl distance of 3.240?.

Sea surface temperature retrieval based on simulated microwave polarimetric measurements of a one-dimensional synthetic aperture microwave radiometer

Compared with traditional real aperture microwave radiometers,one-dimensional synthetic aperture microwave radiometers have higher spatial resolution.In this paper,we proposed to retrieve sea surface temperature using a one-dimensional synthetic aperture microwave radiometer that operates at frequencies of 6.9 GHz,10.65 GHz,18.7 GHz and 23.8 GHz at multiple incidence angles.We used the ERA5 reanalysis data provided by the European Centre for Medium-Range Weather Forecasts and a radiation transmission forward model to calculate the model brightness temperature.The brightness temperature measured by the spaceborne one-dimensional synthetic aperture microwave radiometer was simulated by adding Gaussian noise to the model brightness temperature.Then,a backpropagation(BP)neural network algorithm,a random forest(RF)algorithm and two multiple linear regression algorithms(RE1 and RE2)were developed to retrieve sea surface temperature from the measured brightness temperature within the incidence angle range of 0°-65°.The results show that the retrieval errors of the four algorithms increase with the increasing Gaussian noise.The BP achieves the lowest retrieval errors at all incidence angles.The retrieval error of the RE1 and RE2 decrease first and then increase with the incidence angle and the retrieval error of the RF is contrary to that of RE1 and RE2.

Coefficient of consolidation by end of arc method

One of the most important issues in geotechnical engineering is excess pore pressure caused by clay soil loading and consolidation. Regarding uncertainties and complexities, this issue has long been the subject of attention of many researchers. In this work, a one-dimensional consolidation apparatus was equipped in a way that pore water pressure and settlement could be continuously read and recorded during consolidation process under static loading. The end of primary consolidation was obtained using water pressure changes helping to present a new method for determining the end of primary consolidation and consolidation coefficient. This method was then compared with two classical theory methods of lg t and t. Using Terzaghi's theory, the way of pore pressure dissipation for lg t, t and the new method was found and compared with experimental results. It is concluded that the new method has better results.

One-dimensional nonlinear consolidation of soft clay with the non-Darcian flow

Based on the non-Darcian flow law described by exponent m and threshold gradient i 1 under a low hydraulic gradient and the classical nonlinear relationships e-lgσ′ and e-lgk v (Mesri and Rokhsar, 1974), the governing equation of 1D nonlinear consolidation was modified by considering both uniform distribution of self-weight stress and linear increment of self-weight stress. The numerical solutions for the governing equation were derived by the finite difference method (FDM). Moreover, the solutions were verified by comparing the numerical results with those by analytical method under a specific case. Finally, consolidation behavior under different parameters was investigated, and the results show that the rate of 1D nonlinear consolidation will slow down when the non-Darcian flow law is considered. The consolidation rate with linear increment of self-weight stress is faster than that with uniform distribution one. Compared to Darcy's flow law, the influence of parameters describing non-linearity of soft soil on consolidation behavior with non-Darcian flow has no significant change.