One-dimensional Consolidation Research Articles

Method for calculating cyclic load induced 1D and PVD unit cell consolidation deformations

Consolidation deformation induced by low frequency cyclic loads was investigated by finite element analysis (FEA) and some available test data. Both one-dimensional (1D) consolidation and the consolidation of a prefabricated vertical drain (PVD) unit cell were considered. With theoretical reasoning and using the results of FEA, it has been established that the amount and the rate of consolidation deformation induced by a continuous cyclic load with a maximum load increment of q, can be calculated using the consolidation result of a static load with a magnitude of q/2. Providing the compression increment (ΔS) near the drainage boundary where the effective stress increment is larger than q/2 is taking into account. The magnitude of ΔS is cyclic load frequency dependent and a method for evaluating it has been proposed. Further, it has been proposed that during the cyclic loading period, the creep deformation induced by sustained static load on a soil layer should be included into the total deformation. The proposed method was applied to two 1D and one PVD unit cell laboratory tests of cyclic load induced consolidations. Good agreement between the measured and the calculated settlement – time curves was obtained.

Analytical Investigation of Electroosmotic Consolidation in Unsaturated Soils Considering the Coupling Effect and a Nonuniform Initial Water Content

Electroosmosis often dewaters soil into unsaturated conditions. Due to the shrinkage deformation and decrease of effective voltage that occur during the electroosmotic consolidation as the soil changes from the saturated to unsaturated state, an analytical solution with the consideration of the coupled deformation and time-decreasing effective voltage was developed for one-dimensional (1D) electroosmotic consolidation in unsaturated soils. The effect of nonuniform distribution of the initial water content was also considered. To validate the effectiveness of the proposed analytical solution, a laboratory test was conducted. Thereafter, the proposed solution was used in a parametric study to investigate the effects of the coupled deformation, distribution pattern of the initial water content, and decrease rate of the effective voltage. The results indicated that the coupling effect increases with a decrease in the desaturation coefficient, and the coupling effect is significant for soft soils with high retention capability and compressibility. The nonuniform distribution of initial water content also had a great influence on the consolidation rate. When the initial water content increased from the anode to the cathode, the consolidation rate was fast in that direction but slow in the other direction. Finally, with the consideration of time-decreasing effective voltage, the calculated maximum matric suction and drainage decreased and the completion time of electroosmotic consolidation was shortened. In summary, the analytical solution developed in this study could capture the actual problems for electroosmosis consolidation in field applications to some extent.

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...

Interpreting temperature effects in soils using thermally-enhanced viscoplastic model

The goal of this work is to show that the thermomechanical behaviour of soils can be interpreted as rate processes that are controlled by temperature-dependent viscous properties. A simple thermally-enhanced viscoplastic model is proposed that combines critical state soil mechanics and overstress viscoplasticity, and includes the dependence of viscosity parameters on environmental temperatures in a way consistent with the well-established Arrhenius law of chemical reactions. This modelling approach is shown to be able to reproduce many well-observed patterns of the temperature effects on the volumetric and distortional characteristics of soils. The application of the thermally-enhanced viscoplastic model in boundary value problems is demonstrated by analysing one-dimensional consolidation of saturated soils subjected to coupled mechanical and thermal loading. The connection between temperature-sensitive viscous properties and experimentally observed transient acceleration of secondary consolidation in soils subjected to heating is highlighted.

Effect of Matric Suction and Density on Yield Stress, Compression Index and Collapse Potential of Unsaturated Granite Soil

Residual granite soil from Malaysia shows some problematic features such as: high void ratio, low natural dry density, and loose of apparent cohesion of the soil immediately after rain due to wetting. This study is aimed to evaluate the influence of suction and density on unsaturated behavior of the residual granite soil e.g., the yield stress (σc), compression and swelling indices (Cc, Cr), and collapse potential (CP). To do that, a modified oedometer was fabricated on the basis of the axis translation technique (ATT). Then, one-dimensional consolidation tests were performed under different suctions using the modified oedometer. The results showed a negligible increase in σc when the applied suctions were less than the air entry value. The σc values of dense soil samples were higher than that of loose soil samples regardless of the matric suction. Besides, the values of Cc appeared in three zones: saturation, desaturation and residual zones, while, Cr was independent of the matric suction. The difference of CP under similar matric suction indicated a hydraulic hysteresis behavior of the residual granite soil. However, the hydraulic hysteresis effect on the maximum CP was negligible.

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 ...

Possibilistic Uncertainty Quantification in One-Dimensional Consolidation Problems

Abstract In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional (1D) consolidation problems. A possibility distribution is the one-point coverage function of a random set and is viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on the transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problem.

Laboratory Investigation on the Stress-Dependent Anisotropic Shear Wave Velocity (Vs) and Coefficient of Lateral Earth Pressure at Rest (K0) of Granular Materials

The stress-dependent K0, Vs, and Vs anisotropy and their correlations with sand for 1D consolidation stress were tested with a custom-designed floating-wall consolidometer-type Bender Element (BE) testing apparatus. K0 of a soil sample was calculated using stress measurements through soil pressure transducers installed at the midsection of the consolidometer. The Vs and Vs anisotropy were measured by the bender elements installed in three orthogonal directions in the consolidometer, i.e., vh, hv, and hh. Granular soils with different sizes and shapes were tested. The effects of the stress level, overconsolidation ratio (OCR), particle size and shape on the Vs anisotropy, and K0 of the granular soils during one-dimensional consolidation were investigated. The laboratory investigations suggested (1) the K0 showed a constant value during loading, while it increased as the OCR increased during unloading, (2) soils with smaller particle sizes, rough surfaces, and angular geometry tended to have a lower value of K0, and vice versa, (3) both the anisotropic stress state and the anisotropic fabric (geometry) could lead to the Vs anisotropy, but the Vs anisotropy was manifested due to the horizontal stress-lock during unloading stage, and (4) the published correlation between Vs and K0 was modified by introducing the influence of the OCR, which could effectively reduce the variation and improve the prediction accuracy. Therefore, the modified correlation could be used as a robust approach to estimate K0 for both normally consolidated and highly overly consolidated granular soils.

Empirical Compressibility Index Equations for Artificial Remolded Clay Mixtures

A series of one-dimensional consolidation tests was conducted on reconstituted soil mixtures with different mineral compositions. Test groups were prepared by mixing various proportions of kaolinite, quartz, and montmorillonite in which the initial water contents were equal to the liquid limits of the soils. The focus was on the compression behavior of reconstituted clay mixtures, including the rarely reported triple mixtures, as well as establishing a link between the liquid limit and the clay mineral ratio of the specimens. The intrinsic compression indexes of the soils were highly dependent on the composition of the soils and the initial water contents. New equations were proposed to estimate the compression index based on the clay mineral content, liquid limit, plasticity index, and initial void ratio. A triangular chart was proposed to estimate the compression indexes of reconstituted soils. A simple way to determine the virgin compression lines of reconstituted specimens is described.

Experimental study on the one-dimensional nonlinear consolidation and seepage of saturated clay considering stress history under ramp loading

Experimental study on the one-dimensional nonlinear consolidation and seepage of saturated clay considering stress history under ramp loading

Anisotropic elastoplastic response of double-porosity media

We present a continuum framework to simulate fluid flow through anisotropic elastoplastic media with double porosity. Two effective stress measures σ′ and σ′′ emerge from the thermodynamic formulation, which are energy-conjugate to the elastic and plastic components of strain, respectively. Both effective stress measures can be expressed as a combination of the total Cauchy stress σ and the average pore pressure p¯ in the two pore scales. In the effective stress for elasticity, p¯ is scaled with a rank-2 Biot tensor, whereas the effective stress for plasticity follows the Terzaghi form in which p¯ is scaled by the Kronecker delta. The Biot tensor and storage coefficients are derived as functions of elasticity parameters and porosities. A mixed finite element formulation is introduced to discretize the domain and solve initial boundary-value problems. A stabilization scheme is employed on equal-order interpolation for both displacement and pressure fields throughout the entire range of drainage responses. Numerical simulations reproduce the hydromechanical response of Opalinus shale in one-dimensional consolidation tests throughout the range of primary and secondary consolidation under different external loads. Numerical simulations of the consolidation of a rectangular domain subjected to a strip load demonstrate the efficacy of the proposed stabilization scheme, as well as illustrate the impacts of stress history, mass transfer, and different pore systems on the hydromechanical response.

Irreversibility of soil skeletal deformations: The Pedagogical Limitations of Terzaghi’s celebrated model for soil consolidation

The paper examines the role of irreversibility of skeletal deformations of a consolidating soil and its role in the pedagogy for explaining the development of pore fluid pressures in saturated soils subjected to loading and unloading. The role of irreversibility is demonstrated through the consideration of a one-dimensional consolidation model with an elasto-plastic skeletal response.

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.

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 large-strain model for soft soil consolidation induced by vacuum-assisted prefabricated horizontal drain

Prefabricated horizontal drain (PHD) assisted by vacuum pressure has been used in practice to accelerate the consolidation process of dredged soft mud. However, very few studies have investigated the large-strain nonlinear consolidation caused by vacuum-assisted PHD. Therefore, based on the piecewise-linear method, this study proposes a one-dimensional consolidation model (called VCS herein) for the soft soil consolidation induced by vacuum-assisted PHD. The proposed VCS model has the capability to consider the large strain, PHD assisted by time-dependent vacuum pressure, soil self-weight, time-dependent surcharge loading and nonlinear changes of the geotechnical parameters and is thus superior to the existing models in the literature. The VCS was validated by comparing with the analytical and semi-analytical solutions reported in the literature. In addition, model test of PHD-vacuum preloading consolidation was designed and performed to further verify the proposed model, and excellent agreement was observed. Based on this model, a parametric study was performed to investigate the effect of several relevant parameters on the vacuum preloading consolidation. Moreover, the differences between PHD-vacuum consolidation and PVD-vacuum radial consolidation were investigated. The results indicate that the initial soil height, vacuum pressure and boundary condition considerably influence the performance of vacuum preloading (e.g., time rate of consolidation and final settlement), whereas the time-dependent vacuum preloading affects only the time rate of the vacuum preloading consolidation and not the final settlement magnitude. For the same soil layer, the final settlement of PHD-vacuum consolidation and PVD-vacuum radial consolidation is relatively close. However, the consolidation rate of PHD-vacuum consolidation is obviously faster than that of PVD-vacuum consolidation.

Piecewise-Linear Model for One-Dimensional Consolidation Considering Non-Darcian Flow under Continuous Drainage Boundary

Abstract Based on the piecewise-linear consolidation model, this paper presents a consolidation model that considers the drainage conditions and non-Darcian flow of clayey soils. In the proposed mo...

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.

Numerical simulation of forerunning fracture in saturated porous solids with hybrid FEM/Peridynamic model

In this paper, a novel hybrid FEM and Peridynamic modeling approach proposed in Ni et al. (2020) is used to predict the dynamic solution of hydro-mechanical coupled problems. A modified staggered solution algorithm is adopted to solve the coupled system. A one-dimensional dynamic consolidation problem is solved first to validate the hybrid modeling approach, and both δ-convergence and mr-convergence studies are carried out to determine appropriate discretization parameters for the hybrid model. Thereafter, dynamic fracturing in a rectangular dry/fully saturated structure with a central initial crack is simulated both under mechanical loading and fluid-driven conditions. In the mechanical loading fracture case, fixed surface pressure is applied on the upper and lower surfaces of the initial crack near the central position to force its opening. In the fluid-driven fracture case, the fluid injection is operated at the centre of the initial crack with a fixed rate. Under the action of the applied external force and fluid injection, forerunning fracture behavior is observed both in the dry and saturated conditions.

Measurement and Investigation on 1-D Consolidation Permeability of Saturated Clay considering Consolidation Stress Ratio and Stress History

To study the influence of consolidation stress ratio and stress history on 1-D consolidation permeability of saturated clay, one-dimensional consolidation permeability tests were carried out with GDS triaxial device. The results indicated that the permeability coefficient and void ratio of normally and overconsolidated saturated clay decreased with the increase of consolidation stress ratio under different consolidation stress ratios but the same stress history. And the amount of final sample’s compression increased with the increase of the consolidation stress ratio. Under the condition of the same consolidation stress ratio but different stress history, the amount of final compression of the overconsolidated saturated clay was smaller than that of the normally consolidated saturated clay. Besides, the stress difference σdv between consolidation pressure σ and gravity stress σ c z was fitted to the amount of the final sample’s compression, and a good linear relationship between the stress difference σ d v and the amount of the final sample’s compression under each consolidation pressure was obtained. The results showed that it is necessary to consider the influence of consolidation stress ratio and stress history simultaneously on 1-D consolidation permeability of saturated clay. Meanwhile, it can accurately predict the amount of the final sample’s compression after knowing the gravity stress. Moreover, a model prediction analysis was conducted on the saturated clay and recommended to use the modified Kozeny-Carman’s equation to predict the permeability coefficient of Luochuan saturated clay during one-dimensional consolidation.

Microstructure Evolution of Saturated Clay Under Cyclic Shearing

Abstract Changes in soil microstructure are important for understanding the macro-behavior of soil. Studies in the past have mainly focused on analysing variations under isotropic and one-dimensional consolidation. The present study aims to investigate the microstructure evolution of saturated clay under cyclic shearing. Cyclic triaxial tests are carried out under different magnitudes of effective confining pressure, cyclic deviator stress, and overconsolidation ratio (OCR). The soil microstructure is determined through the scanning electron microscope and mercury intrusion porosimetry tests. It is observed that there is a threshold cyclic deviator stress, above which the soil specimens show significant plastic strain and eventually fail. The threshold value is found to increase almost linearly with the increase of effective confining pressure and OCR. On the other hand, when the cyclic deviator stress is higher than the threshold value, some large pores appear even though the total pore volume is kept constant (undrained condition under cyclic loads). With the appearance of some larger pores, the soil skeleton becomes weaker and eventually fails.