Three-dimensional Consolidation Research Articles

Численное моделирование цунами оползневого типа

The article proposes mathematical models and stable numerical algorithms for solving problems of deformation and flow of water-saturated porous materials. This class of problems arises in many engineering and applied fields, from field development to biomechanics. Of particular interest are the problems of the collapse of the banks of rivers, lakes and bays of the seas due to their catastrophic impact on possible consequences, for example, blocking the riverbed, the occurrence of a tsunami on the water surface of a reservoir, etc. For the mathematical description of the stress-strain state of saturated porous media, the Biot theory of three-dimensional consolidation is used, supplemented by the kinetics of damage accumulation in the medium and the Drucker-Prager yield conditions. After the formation of the main yield surface (or crack) in the material at the moment of the beginning of the collapse, its rheological properties are presented in the form of a Bingham model with a mathematical description similar to the Navier-Stokes equations with effective viscosity. A characteristic hydrodynamic feature of the problem under consideration is the presence of a free surface. Numerical modeling of the considered problems is carried out by the finite element method. The evolution of the free surface and the occurrence of a tsunami generated by a landslide are investigated.

Analysis of Undrained Shear Characteristics and Structural Damage of Granite Residual Soil

Three-dimensional consolidation testing, scanning electron microscopy, and undrained triaxial testing of granite residual soil (GRS) in Shenzhen, China, were conducted. The effect of the structural strength of GRS was quantitatively analyzed using the method of comprehensive structure potential parameter description. The failure strength ratio of the soil decreases with increasing confining pressure, and it is approximately 1 when the confining pressure is higher than the yield stress (σs). The undrained shear strength (Su) of the undisturbed soil varies in stages with confining pressure σ3. The relationship between Su and σ3 for the reconstituted soil is approximated as a straight line through the origin. The soil's comprehensive structure potential parameters (the structural contribution rates of the tangential shear modulus, mE, and the deviatoric stress, md) decrease linearly with increasing σ3. The mE and md sample values are similar under the same confining pressure. It is reasonable to use structure potential parameters to quantitatively evaluate the structure contribution rate of GRS. The microstructure is constantly adjusted, and the soil microstructure form for different confining pressures strongly correlates with its shear characteristics.

Prediction of Three-Dimensional Consolidation Settlement: Observational Method and Its Applicability

This paper presents a closed form of the simplified three-dimensional (3D) (vertical and radial) consolidation solution, which has negligible errors for practical cases. Based on the simplified solution, two observational methods (namely, 3D modified curve fit and linear rule methods) that could predict the actual 3D consolidation settlement behaviors by reflecting the effect of sampling range were newly developed. The appropriateness of the proposed methods was verified by using 3D and two-dimensional (2D) theoretical data. Then, the proposed methods were applied to three case records. Back-analyzed results (i.e., the end of consolidation settlement S100 and consolidation coefficient ch(n)) were slightly affected by the differently approached methods and the inputted value of vertical consolidation coefficient (cv). S100 and ch(n) values obtained from the 3D modified methods were close to those secured from the 2D modified methods due to the insignificant effect of vertical drainage for the cases. Owing to incomplete measurement (93%–98% of S100, i.e., no consideration of sampling range effect), an existing 3D method and the original 2D Asaoka and exponential methods predicted a lower S100 and higher ch(n) than those predicted by the 3D or 2D modified curve fit methods. Therefore, the proposed 3D methods can be recommended for practical applications.

Nonlinear Analysis of the Thaw Settlement in Ice-Rich Embankments

In this paper, the law of ice-rich permafrost embankment thaw consolidation is studied based on three-dimensional nonlinear large strain thaw consolidation theory. To avoid problems associated with numerical simulation efficiency and stability when a nonlinear stress-strain relationship is employed, a segment interpolation function is used to implement the nonlinear relationship between the compression modulus and the void ratio, and the corresponding simulation strategy is proposed. Through a comparison of the monitoring and calculated results, it is indicated that the calculation accuracy on ice-rich embankment thaw settlement can be notably improved after nonlinear theory is implemented with the proposed numerical simulation method. A further analysis of the calculated results indicates that the interactive effects between the thermal and mechanical fields can be more reasonably described by nonlinear theory than by linear theory. It is also determined that the postthaw pore water in the shallow embankment dissipates in the early operation period, while in the following long operation period, the development of the permafrost embankment thaw settlement is mainly due to the dissipation of newly postthaw pore water at the thaw depth or the permafrost table. This is one of the main differences in the law of permafrost embankment thaw settlement compared with that of unfrozen embankments.

Statistical and hydro-mechanical coupling analyses on groundwater drawdown and soil deformation caused by dewatering in a multi-aquifer-aquitard system

Groundwater withdrawn in a multi-aquifer-aquitard system (MAAS) may cause vertical cross-flow supplement and result in groundwater drawdown and soil deformation in both aquifers and aquitards. This study investigates the responses of groundwater and deep soils to dewatering in the MAAS through statistical and numerical analyses. Field data of ten pumping tests conducted in the MAAS, in Shanghai urban area are collected, and a statistical analysis for groundwater drawdown and ground settlement is performed. Field measurements indicate that the drawdowns are distributed linearly along radial distance in logarithmic coordinates. However, the ground settlements are disproportional to the drawdowns and show a trilinear distribution along the radial direction. To examine the inconsistent distributions of the groundwater drawdown and the ground settlement, representative dewatering models are developed numerically and solved explicitly by the coupled Biot’s three-dimensional consolidation theory. Numerical results of dewatering in MAAS are compared to those obtained by a non-coupling formula. Moreover, effect of a micro-confined aquifer on drawdown and soil deformation is discussed. It is found that soil compression in each stratum is closely related to the decline of the pore pressure, whilst small expansions are observed in early dewatering stages. Due to the hydro-mechanical coupling effect, the ground surface settlement near the pumping well obtained by the coupled numerical method is significantly smaller than that by the non-coupling formula. Owing to horizontal and vertical cross-flow supplement, an additional aquifer embedded in aquitard above the pumping aquifer can relief both the groundwater drawdown and ground surface settlement significantly.

Three-Dimensional Modeling of Wave-Induced Seabed Response Around a Semi-Buried Pipeline: A Small-Scale Case

Abstract In this paper, a three-dimensional integrated numerical model for a small-scale case of wave-induced oscillatory soil response around a semi-buried pipeline (PORO-WSSI-PIPE 3D) is proposed. In this model, we combine the Reynolds-averaged Navier–Stokes (RANS) equations for the 3D wave motions and the Biot’s consolidation equations for a porous elastic seabed foundation through pressure continuity at common boundaries, with pipeline being an elastic and impermeable medium. The computational results are validated through comparison with previous analytical solutions and laboratory wave flume tests, obtaining good agreement. Following validation, the numerical model is applied to simulate wave-seabed-pipeline interaction with different obliquities between pipeline and incident wave, varying from 30 deg to 90 deg. Snapshots of wave-seabed-pipeline interaction, as well as dynamic pore pressure distributions at typical locations in the vicinity of a semi-buried pipeline, are obtained and analyzed. The three-dimensional consolidation process of seabed under gravitational forces including the body forces of a pipeline is also discussed.

Coefficient of Consolidation and Volume Change for 3-D Consolidation

The settlement is the most serious problem of fine soil. This settlement is caused by a phenomenon called soil consolidation. Most previous studies were concerned with studying one (1-D) and two-dimensional (2-D) consolidation. That in some cases does not give a simulation of reality representation. It was necessary to study the three-dimensional (3-D) consolidation to simulate what happens to the fine soil in nature. Therefore, the consolidation behavior of four fine soils was studied in this paper. The studied soil samples were collected at the foundation levels of four different sites in El-Qalubia governorate, Egypt. A series of laboratory consolidation tests were carried out as one, two and three dimensional consolidation by using manufactured Oedometer apparatus. So, the effect of consolidation conditions (1-D, 2-D and 3-D) on consolidation coefficient (Cv) and volume change coefficient (mv) was investigated. Also, an empirical equation was correlated the relationship between Cv and mv.

Coefficient of Consolidation and Volume Change for 3-D Consolidation

The settlement is the most serious problem of fine soil. This settlement is caused by a phenomenon called soil consolidation. Most previous studies were concerned with studying one (1-D) and two-dimensional (2-D) consolidation. That in some cases does not give a simulation of reality representation. It was necessary to study the three-dimensional (3-D) consolidation to simulate what happens to the fine soil in nature. Therefore, the consolidation behavior of four fine soils was studied in this paper. The studied soil samples were collected at the foundation levels of four different sites in El-Qalubia governorate, Egypt. A series of laboratory consolidation tests were carried out as one, two and three dimensional consolidation by using manufactured Oedometer apparatus. So, the effect of consolidation conditions (1-D, 2-D and 3-D) on consolidation coefficient (Cv) and volume change coefficient (mv) was investigated. Also, an empirical equation was correlated the relationship between Cv and mv.

Multi-dimensional consolidation analysis of transversely isotropic viscoelastic saturated soils

Based on the extended precise integration method, we investigate the multi-dimensional consolidation problem of transversely isotropic viscoelastic saturated soils. Firstly, we introduce extended precise integration solutions of multi-dimensional such as axisymmetric and three-dimensional Biot's consolidation. Then the Merchant model is applied to simulate the viscoelasticity of soils. Through the elastic-viscoelastic correspondence principle, the corresponding conversion between elastic parameters and viscoelastic parameters is achieved in the Laplace transformed domain. Finally, by a numerical inversion we obtain the solution of axisymmetric and three-dimensional consolidation of viscoelastic transversely isotropic saturated soils. Two numerical examples are conducted to verify this proposed method. Furthermore, several examples are presented to study the effect of viscoelasticity on the consolidation behavior of transversely isotropic viscoelastic saturated soils.

Departure of soft rock mass from undrained response in drilled shaft and plate load tests

The average degree of consolidation of soft rock mass in the immediate vicinity of the base of drilled shaft or plate load tests was evaluated using the Biot Three-Dimensional Consolidation Theory. The compressibility parameters of soft rock mass were estimated using the contact pressure and displacement relationships obtained from the in situ drilled shaft and plate load tests. It was found that typical drilled shaft and plate load tests on soft rocks are drained to partially drained, with the average degree of consolidation dependent on the rock type and weathering condition, foundation diameter, and the loading stage. It was also determined that drained behavior is observed under service conditions due to the low compressibility of soft rocks in the early stages of loading.

Development of a model to predict consolidation of tailings

Understanding tailing consolidation behaviour is critical for proper management of tailing impoundments. Extensive research has been conducted in order to resolve the economic and environmental considerations of tailing management facilities. Many researchers have developed numerical solutions which explain the difference between the behaviours of soft soils, such as tailings, and natural soils with respect to one-dimensional (1D), two-dimensional and three-dimensional consolidation theories. In this study, a fully implicit model was developed by introducing a new compressibility equation to predict the long-term 1D consolidation behaviour of tailings. This study also presents the numerical development of the model and subsequent validation by comparing the model’s predictions to previously published field and laboratory test data. Finally, a case study was carried out for tailings from two different tailing impoundments to predict the consolidation behaviour. The case study consisted of statistical analysis followed by numerical modelling. The statistical analysis indicated that the newly developed model has a better goodness of fit with the initial studies’ results compared with other widely used functions. The model was then used to generate settlement, void ratio, excess pore pressure and effective stress profiles.

Study of leaching scenarios for the application of incineration bottom ash and marine clay for land reclamation

Green technology for utilizing incineration bottom ash (IBA) and marine clay (MC) using chemical-physical combined method (CPCM) for land reclamation has been proposed for Singapore. The formed filled material was termed as MC-IBA matrix. This proposed technology is an attractive proposition for solving twin problems of finding space for disposal of incineration ash and finding sustainable and low-cost resource as filled material for reclamation. Modeling simulation experiments of land reclamation employing this technology were conducted using the in-house three-dimensional consolidation cells to assess its geotechnical and environmental feasibility. The shear strength of MC-IBA matrix was found to improve significantly under the CPCM treatment and attained 26–30 kPa within around 2 wk. It demonstrated the geotechnical effectiveness of the technology. From environmental aspect, heavy metal contamination through any possible on-site effluents discharge must be considered and evaluated. Effluent generations through self-weight consolidation process (SWC) and vacuum pre-loading (VP) during reclamation construction period were studied, including those of IBA storage and transportation period were simulated. The results were analyzed and compared with the relevant regulation standards. It was found that metal concentrations of all the effluents met the public sewer discharge standard. In regards to the allowable limits for trade effluent discharge into watercourse, VP effluent complied with the standard, while SWC effluent generated during construction period and soaked rainwater generated during IBA transportation and storage period failed to meet the requirements as Cu and Ba concentrations were higher than the limits. As such, an inorganic coagulant was proposed to remove excess Cu and Ba from effluent.

Effect of Vertical Pressure on Horizontal and Vertical Permeability of Soil and Effect of Surcharge Pressure on 3D Consolidation of Soil

Permeability and consolidation of soil are known as the most variable soil properties. The values of permeability and consolidation of soil may vary with depth even in case of homogeneous soil layers, and because of that, the determination of appropriate values of permeability and consolidation is a complex and complicated engineering task. In this study, horizontal and vertical permeability apparatus and a 3D (three‐dimensional) consolidation apparatus are developed to determine the effects of vertical pressure on horizontal and vertical permeability and the effects of vertical surcharge pressures on three‐dimensional consolidation of soil. A series of horizontal and vertical permeability tests of soil under different vertical pressures and a series of 3D consolidation tests under different surcharge pressures are performed. From the study, it is observed that the horizontal and vertical permeability of soil changes with the changes in vertical pressures, and 3D consolidation of soil also changes with the changes in surcharge pressures. The horizontal and vertical permeability values obtained from the newly developed horizontal and vertical permeability apparatus are used in Terzaghi’s one‐dimensional consolidation theory to find out the consolidation characteristics of the soil, and it is compared with the results obtained from the newly developed 3D consolidation apparatus.

Transient Solutions of an Isotropic Thermostatic Pervious Half Space Subjected to a Point Hot Fluid Injection

Elastic transient deformation of a half space due to a point of hot fluid injection at constant rate is studied in this paper. The half space ground surface is modelled as a thermostatic pervious boundary. Biot’s three-dimensional consolidation theory with thermal effect is introduced to derive the analytical solutions of the transient consolidation deformation due to a point of hot fluid injection. The stratum is modelled as a saturated isotropic poroelastic half space. Using Laplace and Hankel integral transforms, closed-form solutions of the horizontal and vertical displacements are obtained. The maximum ground surface horizontal displacement can be exactly derived, and it is around 30% of the maximum ground surface vertical displacement. Moreover, the golden ratio appears in the maximum ground surface horizontal displacement and corresponding vertical displacement of a half space. The study concludes that golden ratio emerges in this phenomenon, and the horizontal displacement should be properly considered in the prediction of vertical displacement induced by a hot fluid injection. The study can provide better understanding of the hot fluid injection induced responses of an isotropic porous elastic half space.

Hydro-mechanical Behaviors of the Three-dimensional Consolidation of Multi-layered Soils with Compressible Constituents

Compressibility and permeability are two major coupled factors for the engineering properties of soils. Such hydro-mechanical behaviors of soil greatly rely on the composition and the structure of soil which is often expressed in terms of porosity. In this paper, the effect of soil porosity on the soil mechanisms is studied in the research of Biot's consolidation for soft soil. Assuming a constant porosity in a finite layer, the drained bulk modulus and the permeability are porosity-dependent, and the fluid and the soil skeleton of highly saturated soil are assumed to be compressible. The expressions of displacement, stress and pore pressure are obtained with the aid of Laplace-Hankel transforms for the axisymmetric problem. The continuity of multilayered soil yields the global stiffness matrix in the transformed domain. Meanwhile, by introducing the stiffness matrix of the soil base, the compressible and permeable boundary conditions are more acceptable in practical engineering and the global stiffness matrix is then solved in the transformed domain. Taking the inverse of the Laplace-Hankel transforms gives the real answers for Biot's consolidation. The results show that the increase in porosity leads to a higher compressibility and permeability of soil, and consequently, causes a higher settlement and accelerates the process of consolidation. However, the assumption of the constant porosity of soil has some limitations due to ignoring the nonlinear development of soil structure during consolidation and the further works about the variation modes of porosity need to be done for a better understanding of soil consolidation.

Investigation of the Effects of Anisotropic Flow of Pore Water and Multilayered Soils on Three-Dimensional Consolidation Characteristics

Many practical engineering problems are seriously different from the assumptions which are considered for one-dimensional consolidation test and need to concentrate on three-dimensional consolidation of soil under different boundary conditions. In this study three-dimensional consolidation tests are performed with four different anisotropic flow conditions of pore water and fifteen different combinations of horizontal layered soils. Twelve different three-dimensional consolidation tests are also performed with different soils, surrounded by anisotropic vertical soil layers on two opposite sides. From these studies, it is observed that the anisotropic flow of pore water does not have any effect on initial and final surface settlement of soil but has a significant effect during the consolidation process. The anisotropic flow of pore water during the consolidation process has an immense effect on the coefficient of consolidation. Horizontal layered soil has a great effect on both surface settlement and the rate of settlement. Vertical soil layers on two opposite sides of consolidative soil have an immense effect on the horizontal movements of consolidating soil, finally affecting the resultant vertical settlement of soil. Vertical anisotropic surrounding soil layers also have an effect on the rate of consolidation settlement.

Combined Vertical and Radial Consolidation under Time-Dependent Loading

AbstractCombined vertical and radial consolidation drainage under linear time-dependent loading is presented with varying loading-dependent coefficients of vertical and radial consolidation determined analytically and experimentally. The convolution integral of viscoelasticity theory with variable time was first used to separately predict the average degree of consolidation under time-dependent loading for individual vertical and radial directions. The predicted average degree of combined vertical and radial consolidation was then determined using Carrillo's approach. Four different loading rates were applied in consolidation tests on three types of remolded clay with various plasticity indices to estimate the effects of loading rate on the consolidation settlement. Furthermore, two different spacing ratios of well drain were investigated. The findings indicated that Carrillo's approach for the present three-dimensional consolidation is valid. Furthermore, the viscoelastic settlement prediction in terms o...

A Study with a New Device on Compression Properties of Fine-Grained Reconstituted Soils

For the purpose of examining the settlement behavior of fine-grained soils, a sufficient number of one- and three-dimensional consolidation tests on ten different reconstituted soils were performed in the study. A three-dimensional consolidation test apparatus, which is considered to be a modified form of standard oedometer test apparatus and permits lateral strains to occur, was designed. The consolidation tests were carried out both with standard oedometer and with the new test device so that the effect of different displacement conditions on the test results could be compared. Oedometer tests, by using both the conventional one-dimensional and the new test apparatus, were also carried out with the purpose of understanding the effect of test apparatus on the results. According to the plasticity indexes of the samples, it was found that three-dimensional settlements were greater than one-dimensional settlements at the vertical pressures of 200–300 kPa and higher. The slopes of three-dimensional settlements’ curves were found to be steeper than those determined from standard oedometer curves at the pressures of over 150–200 kPa. When comparing the calculated compression moduli for each group of test results, it was found that the three-dimensional moduli values were 50–75 % of the one-dimensional moduli values. On all of the three-dimensional test results, performed, while the central part was being loaded incrementally, small settlements on the surrounding part were observed. During the removal of the applied loads from the central part, the small settlements reached on the surrounding part approximately remained constant.

Consolidation analysis of transversely isotropic layered saturated soils in the Cartesian coordinate system by extended precise integration method

A general solution for three-dimensional consolidation of transversely isotropic layered saturated soils is presented as an extension to the extended precise integration solution for consolidation in the cylindrical coordinate system. Starting with the governing equations of Biot's consolidation of transversely isotropic saturated soils in the Cartesian coordinate system, an ordinary differential matrix equation is deduced with the aid of Laplace–Fourier transforms. Based on the precise integration method for two-point boundary value problems, an extended precise integration solution of multilayered systems subjected to internal loads or dislocations is presented and then used to solve the above ordinary differential matrix equation, the actual solution in the physical domain is obtained by taking a numerical inversion. The feasibility of the proposed method is proved by three examples, and the influence of transverse isotropy of the soil skeleton on the consolidation behavior is analyzed.

Deduction of three-dimensional electro-osmotic theory

When a solar energy supply system was used in the electro-osmotic ground improvement procedure, soil nearby the anode and cathode was found to have metal ion dissipation and consolidation according to the energy dispersive spectrometer before and after the electro-osmosis. This phenomenon is different from those that use accumulators as a power supply system. Soil only nearby the anode had ion consolidation because accumulators could not supply stable power. This study found that owing to the metal ion consolidated clay under solar energy electro-osmosis, the soil strength at the anode and cathode increases. Moreover, the ion consolidation diffusion was similar to three-dimensional consolidation behaviour. Therefore, this study used excess pore water pressure of the three-dimensional consolidation behaviour to deduce the three-dimensional electro-osmotic equation under solar energy electro-osmosis. The results can serve as a reference for subsequent studies on solar energy electro-osmosis.