Consolidation Theory Research Articles

A physics-informed data-driven approach for consolidation analysis

Identifying governing equations from data and solving them to acquire spatio-temporal responses is desirable, yet highly challenging, for many practical problems. Data-driven modelling has shown significant potential to influence knowledge discovery in complex geotechnical processes. To demonstrate feasibility, in this study a physics-informed data-driven approach is developed to automatically recover Terzaghi's consolidation theory from measured data and obtain the corresponding solutions. This process incorporates several algorithms including sparse regression and prior information-based neural network (PiNet), transformed weak-form partial differential equations (PDEs) (to reduce sensitivity to noisy measurement) and Monte Carlo dropout to achieve a measure of prediction uncertainty. The results indicate that consolidation PDEs can be accurately extracted using the proposed approach, which is also shown to be robust to noisy measurements. PDEs solved by PiNet are also shown to provide excellent agreement with actual results, thus highlighting its potential for inverse analysis. The proposed approach is generic and provides an auxiliary method to verify heuristic interpretations of data or to directly identify patterns and obtain solutions without the need for expert intervention.

Research on prevention and control methods of land subsidence induced by groundwater overexploitation based on three-dimensional fluid solid coupling model—a case study of Guangrao County

Land subsidence is an environmental geological phenomenon with slowly decreasing ground elevation, The North China Plain is one of the areas with the most serious land subsidence in China, and Guangrao County is one of the subsidence centers. This paper is based on the hydrogeological and engineering geological data of Guangrao County, the groundwater monitoring data for many years and the land subsidence monitoring data, systematically analyzes the dynamic characteristics of groundwater, the distribution and evolution of land subsidence, and the correlation between groundwater exploitation and land subsidence development in different layers of this area. Based on Biot porous medium consolidation theory, establishes a three-dimensional fluid solid coupling numerical model of land subsidence in Guangrao County, restores the development process of land subsidence, predicts and analyzes the subsidence evolution law under different groundwater exploitation schemes, and proposes targeted prevention and control measures. The research results show that: the shallow groundwater forms a cone of depression with Guangbei Salt Field as the center, and the deep groundwater forms an elliptical regional cone of depression with the urban area as the center. The ground is gradually formed two small settlement areas with the urban area of Guangrao County and Guangbei Salt Field as the settlement center, and there is a trend of interrelated expansion. The three-dimensional fluid solid coupling model of land subsidence accurately restored the development process of land subsidence in the study area, predicted that under the current groundwater exploitation conditions, by 2040, the settlement of Guangrao urban settlement center will increase to 1,350 mm, forming a large regional funnel centered around the urban area, and gradually developing and expanding around. Prohibition of groundwater exploitation in the main funnel area is a more reasonable and effective exploitation plan to prevent the development of land subsidence.

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.

Numerical analysis of metro station pit dewatering and its influence

The underground water level in Xi’an city is generally shallow, and the excavation of the deep foundation pit mainly needs underground water dewatering. The ground deformation due to the dewatering and its influences should be fully analyzed. The empirical formula estimates the water inflow of the foundation pit, and the process of dewatering and metro station construction is simulated via the finite element method and the theory of soil consolidation according to the field investigation and survey data of the natural geological and hydrological environment. The time of water level falling and recovery, ground settlement, and strata deformation caused by pit dewatering and excavation are predicted. The analysis results of the ground settlement are within reasonable limits and close to the previous metro projects. Finally, the influence of groundwater dewatering on Xi’an Metro Line 14 is discussed. The settlement induced by dewatering for constructing a metro station in the sandy stratum is relatively small, and the loess stratum has the most significant dewatering settlement. The proportion of settlement due to dewatering of the station construction in the loess stratum is nearly 1/3 versus the total land subsidence.

Developing a theory of full democratic consolidation: Exploring the links between democracy and digital transformation in developing eastern European countries

This paper analyzes the impact of the adoption of an information system on the consolidation process of a fully democratic system for eastern European countries. The interactions between the adoption of e-management policies and democracy are examined as a strategic approach to managing future, dynamic organizations. Fuzzy-set qualitative comparative analyses (fsQCA) were conducted to assess the combined effect of the conditions. The fsQCA analysis considered a sample of 26 case studies of eastern European countries with post-communist, in transition regimes as the unit of analysis.During the research the factors that were necessary or sufficient to consolidate a full democratic system in developing countries were detected, analyzed, and explained. The output is presented as a result of applying the strategic approach given by the current sociotechnical transition based on improving the management of societies through information technology capabilities. The objective is to consolidate the output in developing countries given the institutionalization of a society’s e-management core value system. As a response to the current crisis and detected anomalies (IS, Globalization and Power Concentration) in democratic consolidation theory this research empirically demonstrates the need to create a technology-based system with the goal of presenting high performance and capability to support the heavy processing of economic, societal, and political challenges among businesses, citizens, and governments as the main actors in a democratic system. As a result of the research a ‘Theory for Full Democratic Consolidation through IS’ is proposed based on the ‘magic’ pathway or model developed using a qualitative, comparative analysis methodology.The novelty of this research lies in the fact that in contrast to the current academic literature, it turns the consolidation of the democratic system and its components into a result while the process’s approach is offered by the strategic approach offered by the transformative discourse of information technologies.

Displacement analysis of single pile in soft soil with ground load

The pile will have a large lateral displacement in soft soil under the role of heaped load. Based on Biot consolidation theory, combined with a certain highway project, a three-dimensional FEM model was established, the process that the soil lateral load deformation lead to the pile side displacement was simulated. On the ground of the former result, the influence factors for the displacement of pile top and the pile displacement field distribution are analysed. The results shows that, the building load area, load grade and the distance from loading area to pile have a major influence on the pile side displacement. On the other hand, the load on pile top have a very small contribution for stability of anti-side displacement. The buildings nearby the area of pile foundation should be given attention in practical engineering.

Dynamic analysis of beams vibrating on nonlinear poroelastic multi‐layered continuum

AbstractThe paper presents a framework for analysis of beams interacting with nonlinear‐poroelastic, layered continuums (e.g., clayey soils) when subjected to time‐dependent loads. The poroelastic layered continuum is characterized by a nonlinear‐elastic constitutive relationship that relates the secant shear modulus to the induced shear strain. The Biot's theory of consolidation is combined with a dynamic beam‐continuum interaction model to develop the analysis. The vertical consolidation settlement of the beam and the excess pore pressure in the porous continuum are assumed to be products of separable functions, and the extended Hamilton's principle of least action is applied to obtain the differential equations governing the inertial consolidation motion of the beam‐continuum system and the dissipation of excess pore pressure. An iterative numerical algorithm is used to solve these coupled differential equations following one‐dimensional finite element analysis in which the implicit Wilson‐Θ time integration scheme is used to obtain the time history of beam and continuum responses. The novelty of the framework is that it rigorously takes into account the nonlinear poroelastic soil‐structure interaction within a dynamic time‐integration framework with minimal computational resources. The characteristics of this newly developed model are illustrated through examples.

Study of Energy Dissipation in a Two-Phase Soil System

The dependence of energy dissipation coefficient on filtration properties and on creep characteristics of soil skeleton is examined. The study was carried out on the basis of the general solution of the joint task of creep and consolidation theory for a two-phase soil system obtained on the basis of the generalized model of bulk forces, taking into account the interaction of soil phases, changes over time in the general stress state at any point of the soil and additional pressures in pore water, and incomplete transfer of external pressure to the pore water. Interactions between phases are taken into account in the solution of the one-dimensional joint task of the theory of creep and consolidation, and the creep kernel is taken in the form of an exponential function. The formula for the deformation of two-phase soils is presented as the sum of two syllables due to primary and secondary consolidation of the soil. The strain formula uses experimentally obtained values of filtration characteristics and creep parameters of the soil skeleton. Using the formulas obtained, hysteresis loops under sinusoidal stress changes can be plotted and the energy expended per deformation cycle and the dissipation coefficient for two-phase soil can be obtained.

ANALISIS DERAJAD KONSOLIDASI PADA PERBAIKAN TANAH DENGAN METODE PRE-FABRICATED VERTICAL DRAIN (PVD) PADA PROYEK PEMBANGUNAN JALAN TOL SEMARANG – DEMAK PAKET 2

Soft soil is a type of soil that has low shear strength, small coefficient of permeability, compressibility and low soil bearing capacity. 1-D consolidation theory by Terzaghi (1925), assumes that during the consolidation process the value of the consolidation coefficient (Cv) is constant. Flow is only vertical direction. The analysis carried out is to know magnitude of decline and time required to achieve 90% consolidation. Quantitative data is used to analysis numerical data and calculated using existing formulas. Value of settlement using Terzaghi method and principle of normal consolidation is 1.68834 m. To achieve a degree of consolidation of 90% without PVD is 274350 days with a decrease of 1.5196 m. With triangular pattern PVD installation on distance of 0.9 m is 75 days with a large reduction of 1.523 m. Based on the result, time required to achieve a degree of 90% consolidation using PVD is onliy 75 days, while on same day without using PVD consolidation results are around 0.017%. This shows that PVD can speed up the time required for soil consolidation.

Simplified mathematical modeling to plane strain consolidation considering unsaturated and saturated conditions for ground with anisotropic permeability

Road embankment where the unsaturated soil layer lies above the saturated soil layer is often encountered in geotechnical engineering, but the analytical models for evaluating the plane stain consolidation characteristics of an unsaturated–saturated ground are limited. With a combination of the consolidation theories for saturated and unsaturated soils, this paper thus develops a plane strain consolidation model for exploring the transient behavior of unsaturated–saturated soils subjected to instantaneous loading. A semi-analytical solution, which is a simple tool for assessing unsaturated–saturated soil consolidation, is proposed by making use of decoupling strategy, Fourier expansion as well as Laplace transformation. Further, the proposed solution in this paper is validated by the published analytical or semi-analytical solutions in some specific cases. By implementing the proposed solution into a computation, the consolidation behavior of an unsaturated–saturated subgrade is presented, and the effects of important factors, including the anisotropic permeability ratio and interlayer permeability ratio, are studied. The anisotropic permeability ratio and interlayer permeability ratio are significant indexes to change the consolidation rate of lower soils so that the prefabrication of lateral drainage boundary on both sides of the unsaturated–saturated subgrade would accelerate its consolidation.

Excess pore water pressure and seepage in slopes induced by breaking internal solitary waves

Internal solitary waves (ISWs) can induce the dynamic response of the seabed when they propagate over the seabed. In particular, the interaction between ISWs and the seabed is complex on slopes. In our study, the breaking of ISWs was simulated by Large Eddy Simulation (LES), and the pressure induced by ISWs was analyzed. In addition, the excess pore water pressure in the seabed was calculated based on Biot's consolidation theory. We found that the ISW-induced pressure changed the polarity when they propagated over the slope. The change rate of polarity increased with an increase in slope angle. However, the change of polarity was not obviously related to the breaking mechanisms of ISWs. Two distinct seepage fields existed in the whole seabed with sloping topography. In the flat region and near the foot of the slope, pore water flowed upward under the action of the ISW-induced negative pressure. The pore water near the top of the slope flowed downward because the ISW-induced pressure turned positive. Then, the two different parts of the seabed faced different failure risks. This study provides a basis for evaluating the seabed stability influenced by ISWs and contributes to researching the transformation of seabed topography induced by ISWs.

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.

Has the concept of systems consolidation outlived its usefulness? Identification and evaluation of premises underlying systems consolidation.

Systems consolidation has mostly been treated as a neural construct defined by the time-dependent change in memory representation from the hippocampus (HPC) to other structures, primarily the neocortex. Here, we identify and evaluate the explicit and implicit premises that underlie traditional or standard models and theories of systems consolidation based on evidence from research on humans and other animals. We use the principle that changes in neural representation over time and experience are accompanied by corresponding changes in psychological representations, and vice versa, to argue that each of the premises underlying traditional or standard models and theories of systems consolidation is found wanting. One solution is to modify or abandon the premises or theories and models. This is reflected in moderated models of systems consolidation that emphasize the early role of the HPC in training neocortical memories until they stabilize. The fault, however, may lie in the very concept of systems consolidation and its defining feature. We propose that the concept be replaced by one of memory systems reorganization, which does not carry the theoretical baggage of systems consolidation and is flexible enough to capture the dynamic nature of memory from inception to very long-term retention and retrieval at a psychological and neural level. The term "memory system reorganization" implies that memory traces are not fixed, even after they are presumably consolidated. Memories can continue to change as a result of experience and interactions among memory systems across the lifetime. As will become clear, hippocampal training of neocortical memories is only one type of such interaction, and not always the most important one, even at inception. We end by suggesting some principles of memory reorganization that can help guide research on dynamic memory processes that capture corresponding changes in memory at the psychological and neural levels.

From cognitive maps to spatial schemas.

A schema refers to a structured body of prior knowledge that captures common patterns across related experiences. Schemas have been studied separately in the realms of episodic memory and spatial navigation across different species and have been grounded in theories of memory consolidation, but there has been little attempt to integrate our understanding across domains, particularly in humans. We propose that experiences during navigation with many similarly structured environments give rise to the formation of spatial schemas (for example, the expected layout of modern cities) that share properties with but are distinct from cognitive maps (for example, the memory of a modern city) and event schemas (such as expected events in a modern city) at both cognitive and neural levels. We describe earlier theoretical frameworks and empirical findings relevant to spatial schemas, along with more targeted investigations of spatial schemas in human and non-human animals. Consideration of architecture and urban analytics, including the influence of scale and regionalization, on different properties of spatial schemas may provide a powerful approach to advance our understanding of spatial schemas.

Theoretical analysis and experimental verification of large deformation electro-osmosis consolidation treatment of dredged slurry

Electro-osmosis (EO) can be used to rapidly treat large areas of dredged slurry. At present, the theory of electro-osmosis consolidation (EOC) needs to be further developed to fit actual dredged slurry treatment scenarios. In this study, governing equations of EOC considering the large deformation constitutive relationship were derived with excess pore water pressure (EPWP) as a variable, and a concise EOC model was established for dredged slurry. Together with boundary conditions and initial conditions, the numerical method was adopted to obtain the finite difference solution for the EOC model. Then, EO experiments with different voltage stages were conducted using a self-designed and large-diameter EOC device, where the variations in current, drainage volume, EPWP, water content and vane shear strength were measured. Moreover, the phenomena of soil cracks, heat release, and electrode corrosion as well as the formation of Fe(OH)3 were recorded during the EO process. Additionally, nonlinear variation laws for effective stress, hydraulic permeability coefficient (HPC) and electro-osmosis permeability coefficient (EOPC) with void ratio of dredged slurry were obtained through indoor tests, in which a self-designed device for testing EOPC was used. Finally, the correctness of the proposed EOC model was verified by comparison with the results of the experiments and Esrig's analytical solution considering the small-strain constitutive relationship, where the consolidation characteristics were analyzed. In conclusion, the large deformation EOC model deduced in this paper could provide a more accurate prediction of the consolidation behavior of dredged slurry.

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.

Numerical investigation of solute transport into deformable marine sediments driven by ocean waves

Most existing studies do not consider the effect that the deformability of submarine sediments may have on solute transport under the action of ocean waves. In this study a two-dimensional numerical model based on Biot’s poro-elastic consolidation theory and an advection–dispersion equation is established to investigate the transport of non-reactive solute into a deformable porous seabed under the influence of ocean waves. The numerical model is then validated against experimental and analytical results in order to demonstrate its accuracy and robustness. The simulation results indicate that ignoring the deformability of seabed soil and associated seepage force due to ocean waves may lead to a significant underestimation of the rate of solute transport in shallow layers of marine sediment, particularly fine sand or silt. The effects of parameters such as the shear modulus, non-dimensional mechanical dispersion coefficient (related to particle size and permeability), dimensionless sediment thickness, wave steepness and the relative water depth have on solute transport into deformable sediments were investigated. The results indicate that the ratio of the longitudinal coefficient of mechanical dispersion between deformable and non-deformable sediments that can represent the enhancement of solute migration due to soil deformation may reach up to 85. This becomes more pronounced as the shear modulus and permeability of sediments decrease and the depth of water increases when the sediment thickness is less than 0.8 times the wavelength. The rate of solute transport in deformable sediments reaches its maximum when the sediment thickness is about 0.2 times the wavelength. In fact, as the relative water depth increases from 0.1 to 0.3, the enhancement of solute migration due to wave-induced soil deformation increases by about 60%-80%. In comparison to linear waves, shallow water waves, e.g., the first-order cnoidal waves, can increase the transport of solute more due to its strong non-linear behaviour, particularly in deformable seabed.

Semianalytical Model of Unloading-Induced Pore-Water Pressure and Consequent Consolidation Settlement of Surcharge Preloading Railway Subgrade

Surcharge preloading is a suitable foundation treatment for high-speed railways in soft soil regions. As a temporary preload on the foundation, the surcharge load must be removed before track construction. In this process, rebound deformation of the foundation and variation in the pore-water pressure have been widely observed. These phenomena significantly influence the further evolution process of foundation consolidation. Although Biot’s consolidation theory is suitable for unloading-induced soil consolidation, the conventional Laplace transform method for solving Biot’s equations entails a time-consuming procedure and cannot reflect the time-dependent characteristics of the preloading and unloading process. To address these issues, a time difference method is proposed in this work. The ordinary differential equation in the transformation domain is obtained using the backward two-step difference method, and a physical analytical solution of the plane strain problem of overloaded subgrade is obtained via the Fourier inverse transform method. The proposed solution is validated through a comparison with existing literature data and actual engineering practices. Finally, based on this calculation method, the influence of the surcharge preloading amount, loading time, and soil properties on pore-water pressure dissipation and distribution after surcharge preloading removal is investigated.

Nonlinear consolidation analysis of multilayered soil with coupled vertical-radial drainage using the spectral method

The nonlinear variation of soil compressibility and permeability with void ratio (i.e., e-log σ′ and e-log k) has been included in the consolidation theory to accurately predict the behavior of soft soil stabilized by vertical drains. However, most current nonlinear consolidation models incorporating the coupled radial-vertical flow are based on some simplified assumptions, while including some features such as the complex implementation of multilayered computations, time-dependent loading and stress distribution with depth. This study hence introduces a novel approach where the spectral method is used to analyze the nonlinear consolidation behavior of multilayered soil associated with coupled vertical-radial drainage. In addition, time- and depth-dependent stress and soil properties at each soil layer are incorporated into the proposed model. Subsequently, the solution is verified against experimental and field data with comparison to previous analytical solutions. The results show greater accuracy of the proposed method in predicting in-situ soil behavior. A parametric study based on the proposed solution indicates that the ratio between the compression and permeability indices (ω = Cc/Ck) has a great impact on the consolidation rate, i.e., the greater the ω, the smaller the consolidation rate. Increasing the load increment ratio and the absolute difference between unity and ω (i.e., |ω − 1|) can exacerbate prediction error if the conventional simplified methods are used.

A model of autonomous interactions between hippocampus and neocortex driving sleep-dependent memory consolidation

How do we build up our knowledge of the world over time? Many theories of memory formation and consolidation have posited that the hippocampus stores new information, then "teaches" this information to the neocortex over time, especially during sleep. But it is unclear, mechanistically, how this actually works-How are these systems able to interact during periods with virtually no environmental input to accomplish useful learning and shifts in representation? We provide a framework for thinking about this question, with neural network model simulations serving as demonstrations. The model is composed of hippocampus and neocortical areas, which replay memories and interact with one another completely autonomously during simulated sleep. Oscillations are leveraged to support error-driven learning that leads to useful changes in memory representation and behavior. The model has a non-rapid eye movement (NREM) sleep stage, where dynamics between the hippocampus and neocortex are tightly coupled, with the hippocampus helping neocortex to reinstate high-fidelity versions of new attractors, and a REM sleep stage, where neocortex is able to more freely explore existing attractors. We find that alternating between NREM and REM sleep stages, which alternately focuses the model's replay on recent and remote information, facilitates graceful continual learning. We thus provide an account of how the hippocampus and neocortex can interact without any external input during sleep to drive useful new cortical learning and to protect old knowledge as new information is integrated.