One-dimensional Consolidation Research Articles

1923–2023: One Century since Formulation of the Effective Stress Principle, the Consolidation Theory and Fluid–Porous-Solid Interaction Models

In 1923, Karl Terzaghi developed the theory of soil consolidation in which he introduced the concept of effective stress (ES). Over the past century, various theoretical aspects have been unraveled regarding the Effective Stress Principle (ESP) and the fluid–porous-medium interaction in deformable permeable media; nevertheless, some aspects have been debated for a long time, and some perplexities are still perceived among scientists and professionals. By way of example, in the study of flow in deformable permeable media, particularly in fractured porous systems, some problems are still open. This review is aimed at providing an overview of the progress achieved over the past century in the theoretical and experimental treatment of ESP—with particular reference to saturated porous media—and of the geomechanical aspects of fluid flow and fluid–rock interaction, trying to answer to some common questions among professionals, such as what is the correct expression for the ES to be used in applications and why there are various formulations? Additionally, we try to answer questions related to the modeling of fluid flow in fractured porous media. Therefore, this review paper is divided into two main sections, “Effective Stress Principle” and “Fluid Flow, Consolidation, and Fluid–Rock Interaction”. In the first section, the basic concepts and the theory underlying the ESP are preliminarily illustrated, with a simple but rigorous theoretical proof, and, subsequently, historical remarks are provided. The second illustrates the different adopted theoretical approaches to fluid flow, starting from Terzaghi’s theory of one-dimensional consolidation up to the recent dual- and multiple-porosity models.

Characterization of large strain consolidation parameters of soft materials with time-variant compressibility at low effective stress

The one-dimensional (1D) large strain consolidation (LSC) of saturated soft materials that are deposited at very low-density usually exhibit time-variant compressibility (void ratio vs vertical effective stress (e-σv′)) relation. The 1D column-like model test serves as an effective approach for characterizing this consolidation characteristic if all the physical parameters (including the settlement rate, pore pressure and density) are measured. Unfortunately, the density measurement is not always realistic due to its high cost (e.g., with X-rays) and the time-effect must be roughly neglected by using an average compressibility relation. This can further lead to erroneous estimations of the materials’ permeability (k) relation (permeability vs void ratio (k-e)) in the LSC analysis. This paper presents two modifications on two conventional equations for compressibility and permeability, respectively. The first one describes the compressibility curve’s movement in the lne-lnσv′ plane, and the other quantifies the ratio between the permeability calibrated by neglecting time-effect and its true value. These modifications originate from deep comparative analyses of several physical parameters between the column test and numerical prediction. Meanwhile, a simple hand-calculation procedure is proposed to estimate the new constants.

Mechanical properties and microscopic characterization of cement stabilized calcareous sand modified by nano SiO2

The accessible crushing property of calcareous sand leads to poor mechanical properties. Cement is usually used for solidification treatment in engineering. Nano-SiO2 (NS) can further improve the strength of cement-stabilized calcareous sand (CCS). In this study, the mechanical research of NS modified CCS is carried out through unconfined compression strength (UCS) test, split tensile strength (STS) test, and one-dimensional consolidation (ODC) test. The results show that when the CCS was solidified with 4.5‰ NS, the unconfined compressive strength reaches the maximum after 7–14 days of solidification, and the strengthening effect of NS is reflected in the early hydration stage. The addition of NS increased the splitting tensile strength at 7 days and 14 days by 100% and 48%,respectively. The ratio of splitting tensile strength to unconfined compressive strength was about 0.11, which was consistent with the curing law of solidified soil. Moreover, the addition of NS can reduce the compression coefficient of the sample, improve the compression modulus, and improve the compressive deformation resistance of CCS. The scanning electron microscopy (SEM) was used to study the microscopic mechanism. SEM test showed that the addition of NS produced more needle-like hydrates, and the nucleation effect of NS made the hydrates more tightly cemented. The porosity was obtained after the binary processing of SEM images, and the relationship model between the microstructure parameter porosity and UCS was established.

One-Dimensional Solar Energy Thermal Consolidation Model Testing and Analytical Calculation for Marine Soft Clays

There are significant energy and financial expenditures associated with the current thermal drainage consolidation approach used to treat the marine soft clay foundation. Especially for some reclaimed lands in remote areas where a large amount of stable electricity is not readily available. In view of the problem, this paper aims to investigate a novel treatment method by using solar energy thermal consolidation. The model testing was conducted to assess the treatment effect of the foundation. Results from two groups of one-dimensional surcharge preloading consolidation model experiments, conducted under conditions of both solar heating and ambient temperature, were presented. The advantage of the solar heating approach was demonstrated by a comparison of the two tests. An analytical calculation method was proposed for predicting the consolidation behavior on the basis of the temperature variation caused by solar energy in the marine soft clays, and good agreement was observed. The outcomes reveal that solar heating can improve the consolidation effect of soil deep in the foundation. The foundation temperature can be raised by 15 °C in winter, and the variation range can exceed 10 °C. The settlement increases by 16% compared with the ambient temperature group.

Analytical Solution for One-dimensional Electro-osmosis Consolidation of Low Permeability Soil in the Recessed Chamber Filter Press

Analytical Solution for One-dimensional Electro-osmosis Consolidation of Low Permeability Soil in the Recessed Chamber Filter Press

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils under continuous drainage boundary conditions

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils under continuous drainage boundary conditions

One dimensional normal consolidation line equation

Abstract Many empirical equations have been proposed in the past to predict the parameters of the one-dimensional normal consolidation line (1D-NCL) for soils. However, applications of these equations are limited to specific range of pressure and plasticity soils. General empirical equations for 1D-NCL for large range of pressure and plasticity soils are presented in this study. It is assumed that the 1D-NCL has up to three slopes and these slopes start at different stresses depending on liquid limit (LL) of soils. The 1D-NCL of 59 different soils for a large range of LL (19–520%) was used to establish the initial part of 1D-NCL. The soils were categorized based on their LL into two groups: (i) LL < 110% and (ii) LL > 110%. The equations for initial part of 1D-NCL were compared with the previous empirical 1D-NCL equations. The comparisons showed that the new 1D-NCL equations have a better agreement with tests results, especially for highly plastic soils. Moreover, two soils with different plasticity were used to verify the new 1D-NCL equations. The verifications showed a good agreement between the experimental and the predicted results.

Assessment of soil parameters during post-liquefaction reconsolidation of loose sand

Saturated deposits of loose sand may suffer liquefaction under earthquake shaking. Liquefaction-induced damage occurs during the earthquake loading and may continue during the post-liquefaction reconsolidation stage in which excess pore pressures gradually dissipate. An accurate evaluation of soil parameters is of great significance for the full depiction of this process. Consolidation-related problems are typically investigated using Terzaghi's one-dimensional consolidation theory, assuming a constant permeability, one-dimensional stiffness, and consolidation coefficient throughout this process. Some studies based on physical model tests suggest that an assumption of a single and constant value of soil parameter is not appropriate to study the reconsolidation of liquefied sand. This paper presents the results of three geotechnical centrifuge experiments to contribute to the current understanding of this phenomenon. The centrifuge data is combined with oedometer and fluidization test data, producing several empirical relationships to estimate the soil parameters related to the reconsolidation of liquefied sand. A simplified method is adopted to reproduce the time histories of excess pore pressure dissipation and ground surface settlement using the estimated soil parameters as the input. It is shown that the coefficient of consolidation and one-dimensional stiffness vary as a function of effective stress or excess pore pressure ratio, markedly increasing during the reconsolidation of liquefied sand. The predictions of the proposed methodology appear to match the experimental measurements reasonably well as long as appropriate soil parameters are used.

One-dimensional consolidation of unsaturated–saturated soil system considering pervious or impervious drainage condition induced by time-dependent loading

Since the ground with unsaturated soil layer and saturated soil layer is very common in most areas, a more comprehensive analytical solution is essential for the accurate prediction of ground consolidation behavior. In this paper, the one-dimensional consolidation theories for unsaturated and saturated soils are introduced to simulate the consolidation characteristics of the different soil layers, and the hypothetical soil interface of two layers that only allows pore water to flow is supposed in this model. After using the decoupling and Laplace transformation techniques to the coupled governing equations, the general Laplace-domain solutions are proposed under the permeable or impermeable surface for ground consolidation that an unsaturated–saturated ground with finite thickness subject to arbitrary time-dependent loading. The results in the temporal domain for the excess pore pressures and soil settlement are numerically obtained by Crump’s algorithm. The methodology and proposed solution are validated by some published solutions in the literature. Based on the proposed solutions under the three representative boundary conditions, the temporal behavior of ground subjected to ramp loading is explored. The results show that boundary condition would significantly affect the evolutions of excess pore pressures and further change the ground settlement.

Geotechnical Evaluation of Crushed Sandstone Waste Materials from Amasiri Quarries, Southeastern Nigeria for Use in Civil Engineering Projects

This paper presents the study of crushed sandstones wastes (CSW) aiming at their utilization as main materials for the base layer of flexible pavements with series of geotechnical laboratory tests contained in American Society for Testing and Materials adopted for their evaluations. The tests conducted included particle size distribution, Atterberg limits, compaction characteristics, California bearing ratio, unconsolidated undrained compressive strength, free swell index and one-dimensional consolidation tests. Statistical analyses using proprietary computer software were used to investigate the spatial variations of the geotechnical data, and degrees of relationships that exist among the tested parameters. From the results, the Atterberg limits tests revealed intermediate plasticity with less than 35% fines (percentage passing No. 200 British Standard sieve) in majority of the samples; an indication of good highway materials. The relatively high maximum dry density, low optimum moisture content and high shear strength recorded by the tested CSW materials proved their usability in most road projects such as sub-base and subgrade. The strength indicators adopted to evaluate the validity of the CSW as pavement materials showed relatively high shear strength as the undrained cohesion values satisfy the requirement of greater than 103 kN/m2 values specified for base course materials. The empirical correlations analyses verified the influence of moisture on the strength parameters and gave a general overview of the geotechnical behaviors of the examined quarry wastes. Therefore, CSW materials are adjudge suitable but in order to achieve long term strength gain and stability especially in high volume applications, stabilizations will be required.

Investigation of One-dimensional Consolidation of Fractional Derivative Model for Viscoelastic Saturated Soils Caused by the Groundwater Level Change

The Fractional calculus theory is introduced into the Merchant model to study the mechanical characteristics of saturated soils. Laplace transform is applied to the 1D consolidation and the fractional derivative Merchant model constitutive equations of saturated soils. In the transform domain, the analytical solutions of effective stress and settlement are obtained by solving the simultaneous equation. The Crump's method is used to the numerical inversion of Laplace transform, and the semi-analytical solution of the one-dimensional consolidation is obtained. A series of parameters, such as the fractional order, compression modulus, coefficient of viscosity, permeability coefficient and the variation models of groundwater level, are studied. Considering the continuity conditions, the 1D consolidation equation of single-layer saturated soil is generalized to multi-layer soils, and then the influence of different boundaries on several kinds of consolidation behavior was analyzed.

Compressibility of Fly Ash and Fly Ash-Bentonite Mixtures

Environmental protection, one of the most important issues nowadays, forces civil engineers to look for alternative solutions to the known ones. The use of substitute materials as an embankment fill or a ground material under the embankment instead of natural soil follows these trends. A great amount of fly ash is disposed of in landfills. It is a cost-effective material that can be used in construction instead of natural soil. The geotechnical properties of fly ash as a construction material in place of soil need to be examined. It includes laboratory tests to determine the chemical composition and geotechnical characteristics. In the present work, one-dimensional consolidation tests have been conducted to examine the compressibility behaviour of compacted fly ash and fly ash-bentonite mixtures used in the earth structures like road embankments. The analysis of the consolidation phenomenon is useful for predicting the magnitude and rate of settlement of the structure. Materials compacted at OMC to their MDD, according to Standard Proctor, were tested in Rowe-Barden type consolidometer on saturated and non-saturated samples. Coefficients of consolidation have been compared between values derived from log-time and square-root-of-time methods and direct hydraulic conductivity tests. Bentonite amount in fly ash-bentonite mixtures influences the vertical deformation of the sample.

IMPROVING THE CONSOLIDATION CHARACTERISTICS OF SALINE SABKHA SOIL BY ADDING BITUMEN

The rapid economic and population growth, increase in constructions, and a small selection of appropriate soil resources in Kuwait have made it necessary to research soil stabilization methods because the existing soils are currently unsuitable in their natural conditions. In this study, the consolidation characteristics of sabkha soil samples in southern Kuwait mixed with 0%, 4%, 8%, and 10% bitumen with respect to soil dry weight were investigated. For this purpose, an experimental program, including soil characterization tests, modified Proctor compaction test, one-dimensional consolidation test, and collapsibility test, was executed. Results indicate that increasing the bitumen percentage improves the compressibility characteristics of sabkha soil. Upon the addition of 10% bitumen, the yield stress increased from 25 to 34 kPa, compression index slightly increased from 0.02774 to 0.03145, and swelling index decreased from 0.0119 to 0003. Further, there was a considerable reduction in the collapse potential from 1.192 to 0.301 upon the addition of 10% bitumen. Thus, it is evident that the disadvantageous characteristics of sabkha soil can be mitigated. The results support the possibility of recycling the sabkha soil, thereby contributing toward addressing the environmental issues associated with the disposal of excavated sabkha soil.

Some remarks on the pore water pressure dissipation patterns from the one-dimensional consolidation test

Some remarks on the pore water pressure dissipation patterns from the one-dimensional consolidation test

General analytical solutions for one-dimensional large strain consolidation of soft soils under electro-osmosis–surcharge preloading

In this study, the governing equation for one-dimensional large strain consolidation of soft soils under electro-osmosis–surcharge preloading is derived with some assumptions, and the general analytical solution is proposed for the first time by using the methods of algebraic transformation and separation variable. The expressions for the specific analytical solutions under several common cases in foundation treatment are developed. Besides, the correctness of the proposed analytical solutions is verified by comparing them with the existing analytical solutions and finite difference solution. Finally, based on the proposed analytical solutions, the effects of effective voltage Vm, the ratio of electro-osmosis (EO) conductivity to hydraulic conductivity ke/kv and volume compressibility coefficient mv1 on the consolidation behaviors are analyzed. It is found that the increase of Vm increases the absolute values of excess pore water pressure (EPWP) and hence the settlement increases. Furthermore, the increasing ratio of ke/kv leads to larger absolute values of EPWP generated in the soil, resulting in an increase of settlement. The consolidation degree Us defined by settlement based on small strain and large strain models decreases with the increase of mv1, and both the differences of Us and settlement between the two consolidation theories increase with the increase of mv1. In conclusion, the proposed analytical solution is simple in form and practical, which can be adopted to analyze the one-dimensional large strain consolidation behaviors under electro-osmosis–surcharge preloading.

One-Dimensional Consolidation for Unsaturated Soils under Depth-Dependent Stress Induced by Multistage Load

One-Dimensional Consolidation for Unsaturated Soils under Depth-Dependent Stress Induced by Multistage Load

One-Dimensional Consolidation of Multilayered Soil with Continuous Drainage Boundaries and Under Time-Dependent Loading

One-Dimensional Consolidation of Multilayered Soil with Continuous Drainage Boundaries and Under Time-Dependent Loading

Performance Evaluation of Lateritic Subgrade Soil Treated with Lime and Coir Fibre-Activated Carbon

The subgrade layer’s stability considerably influences the long-term performance of pavement systems. This study investigates the influence of lime as a traditional stabiliser and activated carbon with coir fibre (ACF) as waste materials and an environmentally friendly binder to stabilise lateritic subgrade soil. Experiments, including the one-dimensional consolidation and unconfined compressive strength (UCS) tests, have been conducted to investigate the geotechnical properties of stabilised soil in various percentages of additives 3%, 6%, 9%, and 12% lime and 1%, 2%, and 3% ACF. The results demonstrate that 3% ACF and 12% lime can significantly improve the strength parameters and decrease the void ratio and permeability in the stabilised soil. Furthermore, microstructural analysis was performed before and after stabilisation for optimum content. The microstructural analysis proves that AC and lime particles fill soil voids, and gel formation binds the soil particles in the stabilised soil matrix. The results show that 3% ACF stabilised soil is comparable with 12% lime in UCS value and decreasing void ratio. Furthermore, both are suitable for subgrade of low-volume road stability according to Malaysian standards.

Thermal Effect in Nonlinear One-Dimensional Consolidation of Cold Region Soil

The thermal effect can significantly influence the consolidation of the soil, especially in the cold region. Previous studies have established to research that the drops in the ambient temperature would slow down the consolidation process, resulting in the slow dissipation of excess pore water pressure. In addition, the previous studies neglect the final settlement because consolidation is also influenced by thermal effect. In this paper, a closed-form solution to the one-dimensional nonlinear consolidation of soil considering the thermal effect is proposed. In the mathematical framework, the influences of the thermal effect on the compression index, the permeability, and the elastic modulus of the soil are considered. The solution is fully verified by comparing it with the FDM solution neglecting the thermal effect and the classic Terzaghi’s solution. An analysis has been carried out to assess the influence of temperature, stress ratios, consolidation time, the ratio of compression index to permeability index, and the interface parameters on the consolidation process. Different from many previous studies overlooking the thermal effect on the modulus of the soil, a model has been developed which points out that the final settlement due to consolidation would vary significantly with the ambient temperature. Therefore, the thermal effect must be considered in the consolidation calculation of the freeze–thaw cycle soil in the cold region.

Experimental study of one-dimensional nonlinear consolidation of an aquitard under multistage loading

• Design of experimental instrument for simulating consolidation of aquifer system. • Monitor the parameters of aquitard and characterize their nonlinear distribution. • Conduct multistage loading to simulate complex and realistic loading conditions. • Reverse pore water pressure fluctuations occur in the thicker aquitard. • Calculate the curves of pore water pressure base on different hydraulic conductivities. Aquifer heterogeneity is critical for predicting processes involved in the dissipation of pore water pressure, consolidation, and rebound. The consolidation and rebound of aquifer systems should consider the spatiotemporal variation in the hydraulic and mechanical parameters of the aquifer and aquitard. In this study, a series of laboratory experiments was conducted to characterize the consolidation and rebound of the aquifer system and estimate the hydraulic conductivity of the aquitard. The experimental results revealed that under multistage loading, the compression in the upper part of the aquitard tended to decrease, while the compression in the lower part of the aquitard tended to increase. In addition, the variation in hydraulic conductivity and deformation of the aquitard were closely related and reasonably matched at each stage. Moreover, a one-dimensional consolidation model was developed to simulate the variation in pore water pressure and compare it with the experimental pore water pressure. Reverse pore water pressure fluctuations occurred within a part of the aquitard away from the drainage boundary. Compared to the theoretical curves, the experimental curves of the pore water pressure calculated from the initial and asymptotic hydraulic conductivities exhibited delayed and advanced effects. These findings can help elucidate the characteristics of consolidation and rebound of aquifer systems and the spatiotemporal variation in hydraulic conductivity.