Solution For Consolidation Research Articles

A closed-form solution for axisymmetric electro-osmotic consolidation considering smear effects

A closed-form solution for axisymmetric electro-osmotic consolidation considering smear effects

Analytical Solutions for Consolidation of Unsaturated Soil with Time-Dependent Boundary Conditions

Unsaturated soil is widely distributed in geotechnical projects, of which the consolidation and settlement are of great importance. Based on the consolidation theory of unsaturated soil, proposed by Fredlund and Hansan, this paper deals with one-dimensional consolidation of single-layer unsaturated soil with six types of boundary conditions, which can be denoted by arbitrary specified time-dependent functions. The analytical solutions in the time domain are provided directly, by homogenization of nonhomogeneous boundary conditions and the eigenfunction expansion method. Until then, the solutions for excess pore-water pressure and excess pore-air pressure in the single-layer unsaturated soil with all possible Dirichlet or Neumann boundary conditions are provided. Finally, the analytical solutions in this paper are validated against published results, and responses of excess pore-water pressure and excess pore-air pressure in the soil layer subjected to different time-dependent boundary conditions are investigated.

Evaluation of a Thermal Consolidation Process for the Production of Enhanced Technical Fabrics

Fiber reinforced composites are increasingly used in high value applications. A novel technology (NanoWeld®) enhancing the structural integrity of the interlayer has demonstrated promising results; however, manufacturing issues related to scalability need to be overcome. The developed technology relies on consolidating thermoplastic nanofiber nonwoven veils onto technical dry fabrics through roll-to-roll ultrasonic welding. The enhanced technical dry fabrics can be further processed as any other technical fabrics for the composites industry. An alternative solution for consolidation is proposed here, based on a thermo-compressive approach to address the scalability issue. A finite element model has been employed to simulate the operating conditions and provide information for optimization of the process. Its results demonstrate that consolidation is achieved rapidly, indicating that the production rate could be accelerated. The quality of enhanced technical dry fabrics produced using the proposed consolidation assembly has been evaluated using scanning electron microscopy as well as mechanical testing of fiber reinforced composites. The mechanical response of such manufactured composites has been compared against benchmark NanoWeld® composites, demonstrating superior performance.

A General Analytical Solution for Axisymmetric Consolidation of Unsaturated Soil with Impeded Drainage Boundaries

The consolidation of soil is one of the most common phenomena in geotechnical engineering. Previous studies for the axisymmetric consolidation of unsaturated soil have usually idealized the boundary conditions as fully drained and absolutely undrained, but the boundaries of unsaturated soil are actually impeded drainage in most practical situations. In this study, we present a general analytical solution for predicting the axisymmetric consolidation behavior of unsaturated soil that incorporates impeded drainage boundary conditions in both the radial and vertical directions simultaneously. The impeded drainage boundary is modeled using the third kind boundary, and it can also realize fully drained and absolutely undrained ones by changing the drainage parameter. A general analytical solution is developed to predict the excess pore-air and pore-water pressures as well as the average degree of consolidation in an unsaturated soil stratum using the common methods of eigenfunction expansion and Laplace transform. The newly developed solution is expressed in the product of the terms of time, depth, and radius, which are derived using Laplace transform, usual Fourier, and Fourier-Bessel series, respectively. The eigenfunctions and eigenvalues are evaluated from the impeded drainage boundaries in both radial and depth dimensions. Then, the correctness of the proposed analytical solution is verified against the existing analytical solution for the case of traditional boundaries and against the finite difference solution for the case of general impeded drainage boundaries, and excellent agreements are obtained. Finally, the axisymmetric consolidation behavior of unsaturated soil involving impeded drainage boundaries is demonstrated and analyzed, and the effects of the drainage parameters are discussed. The results indicate that the larger drainage parameter generally expedites the dissipations of the excess pore pressures and further promotes the soil settling process. As the drainage parameter increases, its influence gradually diminishes and even can be neglected when it is larger than 100. The general analytical solution and findings of this study can help for better understanding the axisymmetric consolidation behavior of the unsaturated soil stratum in the ground improvement project with vertical drains as well as the gas-oil gravity drainage mechanism in the naturally fractured reservoirs.

Innovative solutions in construction of deep industrial brine, oil and gas wells in deformable fractured reservoirs

The paper deals with the methodological features of drilling and completion of wells in the fractured natural reservoirs containing oil and gas accumulations with different reservoir pressures of fluid-pressure systems from abnormally high to abnormally low. The authors had studied the fluid-pressure systems of industrial lithium-bromine brines, oil and gas fields and accumulations in the south of the Siberian platform for the period from 1983 to 2019. The article summarizes the main results, including new technical solutions protected by the Russian Federation patents. The authors proposed and patented a series of new technical solutions for the immediate consolidation of natural permeable fractures during the primary opening of the reservoir by drilling, as applied to a fractured reservoir. The main task of the study is to preserve the permeability of the fractured system in the bottomhole formation zone under the action of compressive stresses (rock mass) that increase with the formation of a drawdown cone, primarily in the bottomhole formation zone with the increase in the drawdown (ΔP) above critical values. Such an area is the bottomhole formation zone within a radius of the first meters around the well that penetrated the fractured reservoir. Practice has proved that the use of innovative solutions through the advanced consolidation of permeable fractures in the bottomhole formation zone (of fluid-producing oil- and gas-bearing, water-bearing reservoir) in the open (initial natural) state ensures the preservation of natural permeability of natural filtering fractures of the reservoir with the fluid system reservoir pressure from anomalously low to abnormally high. The solution ensures constant permeability of the fractured filtration system throughout the cleaning cycles of the bottomhole formation zone rocks from drilling mud, obtaining of the true calculated hydrodynamic parameters based on the results of well testing in the modes of the “steady-state production method” and well flow rate (productivity) stabilization under further well operation.

Semianalytical Solution of One-Dimensional Consolidation of Multilayered Unsaturated Soils

Abstract This study is devoted to deriving a semianalytical solution to one-dimensional consolidation of multilayered unsaturated soils subjected to an instantaneous loading. The proposed multilaye...

Green’s function analytical solution for free strain consolidation of soft soil improved by stone columns subjected to time-dependent loading

This paper proposes an analytical solution in terms of Green’s function formulations for axisymmetric consolidation of a stone column improved soft soil deposit subjected to time-dependent loading under free strain condition. The mathematical derivations incorporate the pore water flows in radial and vertical directions in stone column and soft soil synchronously. The capabilities of the proposed analytical solution are evaluated via worked examples investigating the influences of three common time-dependent external surcharges (namely step, ramp and sinusoidal loadings) on consolidation response of the composite ground. The examples show that a faster increase of load from an initial surcharge to an expected loading might generate more significant excess pore water pressure to be dissipated during the early stages of consolidation, but the dissipation rate in soft soil would speed up significantly afterwards. The column and soil settlements along with the differential settlement between them also proceed faster corresponding to the acceleration of loading – unloading processes. Finally, the proposed analytical solution is employed to evaluate the excess pore water pressure dissipation rate at an investigation point in soft clay of a case history foundation. The calculation results exhibit a reasonable agreement with field measurement data when various constant values of stress concentration ratio are substituted into the solution to reflect the increase of stress concentration ratio with consolidation time in real practice.

Semianalytical Solution for One-Dimensional Consolidation in a Multilayered Unsaturated Soil System with Exponentially Time-Growing Permeable Boundary

AbstractThis paper proposes new semianalytical solutions to one-dimensional consolidation of unsaturated soils with a multilayered system under the partially permeable boundary condition, in which ...

Consolidation of Viscoelastic Soil With Vertical Drains for Continuous Drainage Boundary Conditions Incorporating a Fractional Derivative Model

In geotechnical engineering, vertical drainage is the most economical method for accelerating the consolidation of a large area of soft ground. In this study, we analyze the viscoelasticity of the soil and the actual drainage conditions on the top surface of the soil, and then we introduce continuous drainage boundary conditions and adopt a fractional derivative model to describe the viscoelasticity of the soil. With the use of a viscoelasticity model, the governing partial differential equation for vertical drains under continuous drainage boundary conditions is obtained. With the application of the Crump numerical inversion method, the consolidation solution for vertical drains is also obtained. Further, the rationality of the proposed solution is verified by several examples. Moreover, some examples are provided to discuss the influence of interface drainage parameters on the top surface of soil and the viscoelasticity parameters of soil on the consolidation behavior of vertical drains. The proposed method can be applied in the fields of transport engineering to predict the consolidation settlement of a foundation reinforced by vertical drains.

Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions

Analytical solutions for 1D consolidation of unsaturated soils with mixed nonhomogeneous boundary conditions

Consolidation theory of homogeneous multilayer treatment by air-boosted vacuum preloading

Air-boosted vacuum preloading, composed of anticlogging vertical drains and an outer booster system, is a new foundation treatment method that is beneficial to accelerating soil consolidation by applying different pressures between soil and vertical drains. Based on the assumption of equal strain, the present paper has simplified the calculation model of the air-boosted vacuum preloading method. Combined with the Newman-Carroll equation, the analytical solution for the consolidation of the double-layer soil foundation is proposed using separation of variables. Moreover, the theoretical solutions of consolidation without well resistance and ideal wells were given, and a chart convenient for engineering practice was acquired. Results show that the setting of well diameter ratio should not be more than 10 in engineering practice. At present, the consolidation theory of air-boosted vacuum preloading is imperfect and only focuses on the reinforcement mechanism of single-layer foundation. Therefore, it is of great significance to perfect the consolidation theory of air-boosted vacuum preloading with multiple layers.

Two-dimensional consolidation analysis of geotextile tubes filled with fine-grained material

In this study, a two-dimensional consolidation solution for geotextile tubes filled with fine-grained material was presented. The solution is based on a combination of various methods that were modified or extended to take into account the change in tube shape, the nonlinear interaction between the soil and geotextile, and the water content distribution of the tube during consolidation. Using the proposed solution, the effect of various necessary input parameters was investigated. Thereafter, numerous dewatering and consolidation properties of various combinations of geotextiles and fill materials were obtained from several tests such as the half cross-section test, hanging bag tests, and geotextile tube demonstration test. Results of the study have shown that the method presented in this study can well-represent the consolidation behavior of geotextile tubes filled with fine-grained material.

Theoretical Study on One-Dimensional Consolidation of Underconsolidated Marine Clay Induced by Ramp Loading

The position of maximum excess pore water pressure is found to be a critical indication in the design of horizontal drainage systems for saturated soil, controlled by the drainage capacity at the boundaries and the self-weight of soil both of which are often ignored. In sea reclamation works, however, the dredged clay used is mostly under consolidated and will undergo the self-weight consolidation. In this paper, an exponentially time-growing drainage boundary condition is adopted, based on which the analytical solution of one-dimensional consolidation of underconsolidated soil under a ramp loading is obtained by using the eigenfunction expansion technique. The obtained solution is verified and a parameter analysis is later carried out. It turns out that when considering the self-weight of the soil subjected to the ramp loading, the variation of the position of maximum excess pore water pressure over time depends heavily on the symmetry of the boundary conditions. The smaller the over consolidation ratio (OCR<1), the shorter the distance of the plane of maximum excess pore water pressure to the bottom surface of the soil layer. Moreover, the larger the loading rate, the higher the plane of maximum excess pore water pressure at the loading stage.

One-Dimensional Consolidation Analysis Considering Non-Darcian Flow and Self-Weight Based on Continuous Drainage Boundary

The one-dimensional consolidation problem of soft soil with self-weight and non-Darcian flow is studied by introducing continuous drainage boundary. A numerical solution is derived by using finite difference method and its correctness is proved by comparing with existing analytical and numerical solutions. Based on the present solution, the consolidation behavior of soil is detailedly analyzed by adjusting the different parameters. The results show that, the soil consolidation rate increases with the increase of interface parameters or external loading rate. The difference between the average consolidation degree obtained by the solution with continuous drainage boundary and that with traditional boundary is mainly in the early stage of consolidation, but in the late stage of consolidation, the difference between these two solutions becomes smaller. Compared with the soil consolidation solution considers non-Darcian flow, the soil consolidation rate with Darcy flow is faster.

An analytical solution for self-weight consolidation based on one-dimensional small-strain consolidation wave theory

Terzaghi's consolidation theory neglects inertial effects on the consolidation of saturated soils. To quantify the inertial effects, in this paper an original one-dimensional small-strain consolidation wave (C-wave) theory is developed, based upon a proposed modified Darcy's law with relaxation time and the equation of motion for soil ensemble. The one-dimensional governing equations were first formulated for self-weight consolidation, followed by a closed-form solution employing the method of separation of variables. The proposed model was then validated against wave velocity measurements and verified against finite-difference analysis. The half-closed self-weight consolidation behaviour was subsequently investigated, compared with Terzaghi's theory, Fillunger–Heinrich's dynamic theory and the u–p form of Biot's wave theory. This research indicates that: (a) superior to conventional models under comparison, the C-wave model enhances the predictability of the C-wave velocity; (b) the dimensionless C-wave coefficient (Cw) dominates the fundamental consolidation behaviour; (c) a wave-diffusion duality underlying the consolidation mechanism contributes qualitatively to the spatial bottom-up pattern and temporal response delay in consolidation observations; and (d) Terzaghi's theory can afford a practically accurate solution provided the Cwand time factor are below and above approximately 0·01, respectively. The C-wave theory may enrich the understanding of consolidation-related phenomena involving an appreciable Cw.

Extension of ALE method in large deformation analysis of saturated soil under earthquake loading

This article develops an Arbitrary Lagrangian Eulerian (ALE) finite element program for liquefaction dynamic analysis of saturated sand based on the updated Lagrange finite element program in U-P form. Based on the operator splitting technique, this method adopts the displacements of boundary points and Radial Basis Function (RBF) method to optimize the mesh, and employs super-convergence elements patch and Radial Basis Function (RBF) method to reconstruct variable fields and project variables between old and new configurations. The analytical solutions and numerical solutions of one-dimension consolidation are compared to verify the accuracy of the ALE method. Three typical dynamic liquefaction problems of saturated sand are implemented to measure the applicability of UL method and ALE method. The results show that both methods can provide similar results in the case of small earthquakes. Under strong earthquakes, the UL method fails for large-scale or local mesh distortion, while the proposed ALE can still maintain the health of the mesh and provide satisfactory results.

A hydro-mechanical coupled solution for electro-osmotic consolidation in unsaturated soils considering the decrease in effective voltage with time

For electro-osmotic consolidation in unsaturated soils, coupled deformation, inconsistent changes in hydraulic conductivity and electro-osmotic permeability with matric suction, and a decrease in effective voltage with time occur simultaneously. To consider all of these processes, an analytical solution was proposed. The time-stepping method was adopted in the calculation of the solution to depict the nonlinear change in shrinkage deformation with matric suction. The accuracy of the proposed analytical solution was validated by comparison with results from laboratory tests and from a previously presented solution without considering coupled deformation. Then, a parametric study was conducted. The results indicate that the dissipation of the pore water pressure is slow when considering coupled deformation, but a large volume of water is discharged in the end, especially for soils with a large volumetric shrinkage index Cm. A larger final negative pore water pressure and discharged water can be predicted by considering the inconsistent changes in hydraulic conductivity and electro-osmotic permeability. Finally, with the consideration of the decrease in effective voltage over time, both the maximum negative pore water pressure and final drainage decrease, which is consistent with field observations.

TRACTOR: Traffic‐aware and power‐efficient virtual machine placement in edge‐cloud data centers using artificial bee colony optimization

SummaryTechnology providers heavily exploit the usage of edge‐cloud data centers (ECDCs) to meet user demand while the ECDCs are large energy consumers. Concerning the decrease of the energy expenditure of ECDCs, task placement is one of the most prominent solutions for effective allocation and consolidation of such tasks onto physical machine (PM). Such allocation must also consider additional optimizations beyond power and must include other objectives, including network‐traffic effectiveness. In this study, we present a multi‐objective virtual machine (VM) placement scheme (considering VMs as fog tasks) for ECDCs called TRACTOR, which utilizes an artificial bee colony optimization algorithm for power and network‐aware assignment of VMs onto PMs. The proposed scheme aims to minimize the network traffic of the interacting VMs and the power dissipation of the data center's switches and PMs. To evaluate the proposed VM placement solution, the Virtual Layer 2 (VL2) and three‐tier network topologies are modeled and integrated into the CloudSim toolkit to justify the effectiveness of the proposed solution in mitigating the network traffic and power consumption of the ECDC. Results indicate that our proposed method is able to reduce power energy consumption by 3.5% while decreasing network traffic and power by 15% and 30%, respectively, without affecting other QoS parameters.

Nonlinear consolidation theory for prefabricated vertical drains with elliptic cylindrical assumption

Based on the influence of the non-linear change in the consolidation process of permeability coefficient and compressibility of soft soils and the theory of elliptic cylinders, derived the control equation of the nonlinear consolidation of the vertical foundation of the strip plastic drainage board. Further, according to the complete orthogonal space theory, the equivalent polynomial analytical expression of the nonlinear term is given. Then, the analytic solutions of the nonlinear consolidation are given, and through numerical calculation and verification analysis, it is considered that the Indrarantna (2005) approximation has a relatively small error at Cc/Ck (close to 1) and Nu (&lt;4), but when Cc/Ck (difference from 1) and Nu are large (&gt;4), the error is large.

A general analytical solution for two-dimensional plane strain consolidation of unsaturated soil incorporating lateral and vertical impeded drainage boundaries

In most practical consolidation problems, impeded drainage boundaries are a great concern. By simultaneously introducing the impeded drainage boundaries in the horizontal and vertical directions, this study attempts to constitute a general two-dimensional (2D) plane strain consolidation system of unsaturated soil. A newly analytical solution is developed to calculate the excess pore-air and pore-water pressures and average degree of consolidation. On the basis of the eigenfunction expansion method, the developed analytical solution is given as a product of three functions, including one variable of time, horizontal and vertical dimensions only. For the impeded drainage boundaries, the eigenfunctions and eigenvalues are derived in the horizontal and vertical dimensions. The Laplace transform technique is further adopted to solve the ordinary differential system in the time domain. The developed analytical solution is verified with the existing analytical/semi-analytical solutions and finite difference solution for several typical cases. Excellent agreements are obtained so that the correctness of the developed analytical solution is validated. Moreover, two worked examples are presented to show the superiority of the developed analytical solution and to assess the influences of the drainage parameters on the 2D plane strain consolidation behavior of unsaturated soil.