One-dimensional Consolidation Theory Research Articles

Experimental study on soil deformation caused by overexploitation of groundwater.

Due to the overexploitation of deep groundwater, the largest cone of depression in the world has formed in the North China Plain. This led to severe geological hazards, including land subsidence and ground fissures, and also caused economic losses. The prevention and treatment of subsidence needs to rely on the accurate prediction of subsidence amount. According to the one-dimensional consolidation theory and effective stress principle, combined with stratum structure, groundwater flow, stress distribution, and so forth, the high-pressure consolidation test results of 569.6m deep borehole soil samples are adopted; with a specific focus on stress and deformation parameters under exploitation of groundwater condition, the soil-water coupling prediction model of groundwater level lowering depth and land subsidence has been established. Verification with measured subsidence data near the study sites demonstrated that the predicted curve is consistent with the measured one and the differences between them are acceptable. The model can be applied in different areas after making adjustment based on different regional stratigraphic structures. Its key advantage lies in the ability to provide land subsidence prediction for areas lacking monitoring data, making it highly valuable for widespread application. PRACTITIONER POINTS: There is a compressible stratum structure; it is the internal factors of land subsidence. The groundwater level decline causes the soil body stress to change. It is land subsidence of the external factors. Based on the one-dimensional consolidation theory and by combining stratigraphic structures, groundwater flow, and stress distribution, a ground settlement prediction model was established.

SETTLEMENT IN THE NOTHERN PART OF BEKASI REGENCY, WEST JAVA PROVINCE, BASED ON CONE PENETRATION TEST DATA

In the nothern part of Bekasi Regency, the soil layers are dominated with alluvial deposit, especially clay and silt deposit. It makes the potential of the settlement in this area is getting higher. In this research, Cone Penetration Test (CPT) have been done to determine the soil layers from the surface till the 20 meters depth and to identify other soil properties, such as unit weight, compression index, swelling index, void ratio, etc. This research aims to analyze the total settlement in the northern part of Bekasi Regency based on CPT data. The total settlement is calculated by using the theory of One-Dimensional Primary Consolidation based on CPT data. The research area shows that the highest result of total settlement calculation is in the northern part of research area which directly adjacent to the Java Sea. It can be happened because the clay layers in northern part is way thicker than the other area.

Consolidation analyses of PVD-improved marine clay considering long-term natural sedimentation

An analytical solution is derived to calculation the consolidation of marine clay improved by vertical drains under long-term natural sedimentation conditions based on Gibson's one-dimensional consolidation theory and Barron's free-strain theory. The model tests are conducted to verify the accuracy of the proposed theoretical model. Fair agreements between the results from laboratory tests and proposed theory verified it accuracy. Parametric studies are also conducted to investigate the effects of the clay deposition properties and time-dependent sedimentation rates on the consolidation of the marine clay. Under the selected parameter conditions in this article, for the deposition rate of clay deposition layer, k/(2Ch)=1, the maximum of excess pore water pressure keeps stable and is close to 6 kPa. The maximum difference in excess pore water pressure at the bottom of clay deposition layer is approximately 40.1 kPa under two conditions of deposition rate of 0.5 and 10. The average degree of consolidation U of the soil layer after 100 and 200 days of sedimentations are 86 % and 97 %, respectively.

Study on the Factors Affecting the Performance of a Pressure Filtration–Flocculation–Solidification Combined Method for Mud Slurry Treatment

A pressure filtration–flocculation–solidification combined treatment possesses great potential for the reutilization of the waste mud slurry generated from diverse construction projects as filling material due to its versatility and high efficiency. However, very limited existing studies have focused on the factors affecting pressure filtration’s efficiency. In this paper, a calculation model for compression filtration is established based on laboratory pressure filtration model tests and one-dimensional large-strain consolidation theory. The influence of various parameters on pressure filtration’s efficiency is analyzed, and favorable values for these parameters are recommended. The results show that an increased initial mud cake thickness significantly increases the dewatering time and reduces the treatment’s efficiency. A lower dewatering time and higher efficiency can be achieved by increasing the filtration pressure, but the efficiency improvements become limited after reaching the critical pressure threshold. For the mud slurry used in this study, the optimal values for the initial mud slurry bag thickness, filtration pressure, and dewatering time are 240 mm, 1.0 MPa, and 30 min, respectively, yielding a final mud cake water content of 58.7% after filtration.

Analytical Solution for Negative Skin Friction in Offshore Wind Power Pile Foundations on Artificial Islands under the Influence of Soil Consolidation

The construction of offshore wind power pile foundations on artificial islands is a challenging task due to soil consolidation and additional loads that result in negative skin friction (NSF). In this study, a comprehensive pile–soil interaction model is established to investigate the development of NSF in artificial islands under the action of self-weight consolidation of fill soil and surcharge load. The one-dimensional consolidation theory and an ideal elastoplastic load transfer model are employed to obtain the analytical solution for skin friction and axial force of the pile with respect to time and depth. The predicted results are in good agreement with the field tests and finite element methods. Finally, a parametric study is conducted to investigate the effect of pile installation time, surcharge load, and pile head load on the development of NSF.

Improved analysis and design for surcharging

Surcharging or preloading is one of the oldest and most widely used in situ ground improvement techniques to strengthen weak compressible clays and to remove undesirable settlements prior to erection of permanent infrastructure. Recently, the ground improvement technique has been adopted in combination with many other techniques. The current design methodology for surcharging based on the concept of average degree of consolidation is inadequate, as all the primary consolidation settlement to be induced by the permanent load is not eliminated by the surcharging process. The problem is quantitatively analysed using Terzaghi's one-dimensional consolidation theory. The proportion of residual primary consolidation settlement is quantified, and the starting time of the re-occurrence of primary consolidation on exertion of the permanent load is determined. The effect of a change in surcharging duration on the proportion of residual settlement is quantified. The results are presented in design charts to facilitate application of the results by practicing geotechnical engineers.

Determination of hydraulic parameters of non-linear consolidation clay layers by type curve method

The consolidation of clay layers is of great significance for groundwater environmental protection, groundwater storage utilization, and land subsidence. In this study, the governing equation for the excess pore water pressure during the non-linear consolidation process of clay layers under load conditions is obtained based on the one-dimensional non-linear consolidation theory. Analytical solutions are then derived for clay layers with single or double drainage caused by the dissipation of the excess pore water pressure. With these analytical solutions, the groundwater dynamics and deformation of the clay layer are analyzed. Correspondingly, a type curve method is proposed to calculate the hydraulic parameters of the clay layer through laboratory experiments, which verifies the reliability of the analytical solutions. The study results show that the deformation of the clay layer predicted by the non-linear consolidation theory is smaller than that predicted by the linear consolidation theory. The deformation of the clay layer increases with the increase in the thickness of the clay layer, the compressive index, and the overburden load, while it decreases with the increase in the initial void ratio and the initial effective stress. The stable time, at which the consolidation of the clay layer is completed, increases with the increase in the compression index and the thickness of the clay layer, while it decreases with the increase in the initial void ratio, the initial effective stress, and the initial hydraulic conductivity. It does not vary with the load pressure. Conclusively, the deformation prediction based on the non-linear consolidation theory is more accurate and applicable to further load pressures.

Large-deformation consolidation models of saturated–unsaturated materials under self-weight and evaporation

This paper develops the one-dimensional large-deformation consolidation theory for the porous medium under alternating saturated–unsaturated conditions, through a former generalization of the well-established Gibson’s nonlinear theory from saturated to unsaturated regime. With the differential relations between the coordinate systems, the equations governing the momentum\\mass balances in the unsaturated porous stratum are transported from the moving current to the initial Lagrangian coordinate system. Without loss of generality, the collective forms of various incremental constitutive laws are then incorporated for unsaturated materials, indicating that any particular constitutive law has been embraced. Two forms of final governing equations are derived depending on the primary independents: σv-uw (total vertical stress - pore fluid pressure) and w (gravimetric water content); which are solved by two distinct finite-element codes on the initial fixed configuration. Numerical examples demonstrate that the two resulting Total Lagrangian formulations are equivalent, yield virtually identical predictions and agrees well with an existing finite-differential code that solves the equations in the convective configuration. The dynamical consolidation process evolving from a weight-driven saturated stage to an evaporation-driven unsaturated stage is quantitatively captured very well by the predictions. The impacts of evaporation, material’s compressibility, and permeability in these two distinct stages are independently explored through several parametric analyses on the consolidation/dewatering rates and the penetration of drying front. Through one factor must affect, in concert with the others, such a hydro-mechanical coupling process, these results can provide a profound understanding of the entire consolidation process of a porous stratum under large deformations.

Semi-analytical solutions to the one-dimensional consolidation for double-layered unsaturated ground with a horizontal drainage layer

In order to accelerate the consolidation rate of double-layered unsaturated ground with poor hydraulic conductivity, the sand blanket is always set between two adjacent unsaturated soil layers to produce drainage paths along the horizontal direction in practical engineering. Based on the one-dimensional consolidation theory of unsaturated soil proposed by Fredlund and Hassan(1979), the semi-analytical solutions of excess pore-air and pore-water pressures, and settlement of the double-layered unsaturated ground with the horizontal drainage blanket are obtained by Laplace transform technique in this paper. Additionally, the current solutions can degenerate into those under the single-layered unsaturated model, which are then utilized to compare with existing solutions in literature, the significant agreement indicates that the present solutions are reliable and general. At last, a case study is adopted to investigate the influence of the vertical position of the drainage blanket, and permeability coefficients ratio of two adjacent soil layers on the consolidation of the double-layered unsaturated ground. Results show that the horizontal drainage layer will effectively accelerate the consolidation process, and the setting depth of 0.7H works best. Moreover, the smaller the ratio of the permeability coefficient of the upper layer to that of the lower layer (with the permeability coefficient of the upper layer remaining constant), the faster consolidation will develop.

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.

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.

Study on the Treatment Technology of Silty Clay in Reconstruction and Expansion Project

<p>According to different geological conditions and different soft foundation thicknesses, this paper uses Terzaghi's one-dimensional consolidation theory, finite element simulation condition calculation and combined with code requirements to analyze the effects of replacement, cement mixing piles, and prestressed pipe piles on the foundation treatment of silty silty clay, and finally through the comparison and selection of plans, from the perspective of economic and technical rationality, determines the specific treatment method used.</p>

Evaluation of hydro-mechano-chemical behaviour of bentonite-sand mixtures

Bentonite-sand mixtures are widely used in engineering barrier of deep geological disposal of high-level radioactive nuclear waste and anti-seepage barrier of civil geotechnical engineering. Under the action of groundwater solution infiltration and external stress, the hydro-mechanical (HM) behaviour of bentonite-sand mixtures, i.e. the swelling characteristics and permeability, will change. Once the anti-seepage and filtration effect is weakened or lost, the pollutants will spread to the biosphere. Therefore, it is necessary to study the swelling characteristics and permeability of bentonite-sand mixtures under coupled mechano-chemical (MC) effect and to establish corresponding prediction model. For this reason, swelling tests under salt solution with different concentrations are conducted on pure bentonite and its mixtures with 30%, 70% and 90% sand contents, the compression tests are carried out on saturated samples, and the saturated permeability coefficient k of the sample under each load is calculated by Terzaghi's one-dimensional consolidation theory. The concepts of true effective stress p e , montmorillonite void ratio e m and critical sand content α s are introduced to determine the e m - p e relationship and finally the k - e m relationship of bentonite-sand mixtures. It is found that when the sand content α ≤ α s , the e m - p e relationship of the mixture is linear and independent of the salt solution concentration, and when α > α s , the e m - p e relationship of bentonite-sand mixture is bi-linear with the true effective deviatoric stress p esα as the intersection. In addition, the e m - k relationship also shows the linear trend when α ≤ α s , and the slope of the line increases with the increase of the salt solution concentration. When α > α s , the k - e m relationship will deviate from the linear relationship. Moreover, the larger the sand content is, the farther the deviation is. On the basis of summing the regularity, a model for predicting the HM behaviour of bentonite-sand mixture under the coupled MC effect is proposed. By comparing the swelling and permeability test results with model prediction results of different types of bentonite and its sand mixtures, the predictive model is verified. The study on the HM behaviour of bentonite-sand mixtures under salt solution infiltration and the model establishment can provide experimental and theoretical basis for the design and construction of anti-seepage engineering by bentonite-sand mixtures.

One-dimensional consolidation of unsaturated soils considering self-weight: Semi-analytical solutions

For the newly deposited soil, the consolidation will occur under the self-weight and external load jointly if the soil is treated by the stack pre-pressure method. The soil stress caused by self-weight has a significant influence on its consolidation process no matter the soil is either saturated or unsaturated. However, the soil’s self-weight is ignored in the one-dimensional (1D) consolidation theory for unsaturated soils (Fredlund and Hasan, 1979). In this paper, we derived the semi-analytical solutions for excess pressures and normalized settlement in 1D dimensional consolidation of unsaturated soils considering self-weight. The analytical solutions were obtained by Crump’s method (Crump, 1976), through a computing program coupling the calculation of initial excess pore pressures with the inverse Laplace transform of the obtained solutions. Then, the proposed solutions are verified through a degradation case. Several 2D charts are presented to visualize the solutions, and various examples are employed to discuss the key factors that affect one-dimensional consolidation behavior of unsaturated soils when self-weight is considered. It can be found that the relative excess pore pressure will be restrained for the one-dimensional consolidation when considering self-weight.

The effect of thermal consolidation on bearing characteristics of static drilling rooted energy pile

Static drilling rooted energy pile is a new type of energy pile technology recently developed and promoted in soft soil areas. This technology has the advantages of green, low-carbon and good heat exchange effect. But its related basic theoretical research is still lacking. Therefore, the physical model of the static drilling rooted energy pile is deduced. The thermal consolidation settlement process of the soil around the pile is analyzed firstly based on one-dimensional thermal consolidation theory. And, the load transfer method is combined to derive the pile circumference under the coupling effect of load and temperature variation. The governing equations for frictional resistance and pile deformation are deduced and solved with numerical programs. Then an actual engineering case with static drilling rooted energy pile in soft soil area is calculated and analyzed. The results show that the temperature increase of the surrounding soil increases the relative displacement of pile and soil, which resulting in a decrease in the upper side friction resistance and an increase in the lower side friction resistance; and this effect will be enlarged during the cooling stage. The maximum axial addition stress caused by the temperature variation reaches 75.4% of the stress by load, so the influence of temperature changes on the bearing capacity of the pile foundation cannot be ignored. The research laid a theoretical foundation for the analysis and popularization of the static drilling rooted energy pile in coastal soft area.

Investigation of the coefficient of consolidation of fine-grained soils using combined apparatus

The scope of this investigation is to compare the coefficient of consolidation (cv) values defined by the Taylor's Square Root of Time Fitting Method, which is obtained from the conventional oedometer tests, with the cv values calculated by Terzaghi's One-Dimensional Consolidation Theory, which is obtained from the permeability-consolidation tests performed with a combined apparatus specifically designed for this study. In addition, an empirical relation is developed to determine cv using the coefficient of permeability (k) and index properties of the soils. The cv values obtained from the permeability-consolidation tests using the combined apparatus were found to be larger than the cv values defined by the Taylor's Method, which is one of the oedometer tests. The findings showed that the difference was more prominent in the soil samples with a high plasticity. It was also found that the cv calculated by the Taylor's Method exhibited a distribution in a wide range with the increased load depending on the degree of plasticity of the soil. The cv obtained from the combined apparatus it decreased with low load values and increased with higher loads levels. The cv obtained by the proposed empirical relationship showed good agreement with the cv defined by permeability-consolidation relationships.

General Analytical Solution to Consolidation of Unsaturated Soil with Vertical Drain considering Drain Resistance

This paper presented a general analytical solution to consolidation of unsaturated soil with vertical drain considering drain resistance. Based on Fredlund’s one-dimensional consolidation theory and the equal-strain assumption, the coupled governing equations of excess pore-water and pore-air pressures are first decoupled by introducing two new variables. the method of eigenfunction and undetermined coefficients are then used to obtain the general solution under the drain resistance condition. Moreover, the good agreement between the equal-strain results and the typical free-strain results confirms the validity of the proposed solution. The consolidation behaviours, concluding average excess pore-air and pore-water pressures, are investigated against the drain resistance and the ratio of influence radius to vertical drain radius.

One-dimensional non-linear consolidation theory of soft ground coupled with thermal effect

Temperature has an important effect on the consolidation of soft soil. Considering current experimental data, a compression model for soft soil considering the influence of temperature is discussed. At the same time, a new expression for the permeability of soft soil considering the effect of temperature is presented. On the basis of the two models, a one-dimensional non-linear consolidation equation considering the effect of temperature on soft ground is established. Following the classical solution method of Davis and Raymond, the equation is solved analytically. After that, the influence of temperature on the consolidation process of soft ground is analysed. The results show that the higher the temperature, the faster will be the consolidation rate; the influence of temperature on consolidation rate is not a simple linear relationship.

A One-Dimensional Fractional-Derivative Viscoelastic Model for the Aquitard Consolidation of an Aquifer System

Land subsidence resulting from the withdrawal of groundwater is one of the problems of major importance to geosciences and geomechanics. In order to analyze the phenomena of land subsidence, this study attempts to constitute a more reliable prediction model to simulate the consolidation process of the aquifer system under the drawdown of groundwater. A fractional-derivative viscoelastic model is introduced to characterize the rheological properties of the aquitard, and the equation governing the consolidation process is established on the basis of the one-dimensional consolidation theory. The semianalytical solutions for the pore-water pressure, the settlement of aquitard, and the degree of consolidation are deduced using both finite sine transform and Laplace transform. Then, the comparisons of two special cases are performed to validate the correctness of the proposed model. The variations in the degree of consolidation and settlement of the aquitard are simulated to analyze the consolidation behavior of the aquifer system, and the influences of model parameters and the drawdown speed of groundwater are investigated.

One-dimensional nonlinear consolidation theory for soft ground considering secondary consolidation and the thermal effect

Based on the assumption that the change of the void ratio is caused by effective stress, creep effect and temperature, a one-dimensional nonlinear consolidation theory considering the thermal effect is established that contains the heat balance equation and the continuity equation. Verification and calculation examples are performed. The results show that the dissipation rate obtained using the present method is slower than that obtained using the traditional method. The pore water dissipation rate or consolidation rate considering the secondary consolidation and temperature is higher than that when only considering secondary consolidation. Heating accelerates the dissipation rate of pore water, especially in the early stage of consolidation.