Consolidation Theory Research Articles

Study on the Deformation Characteristics of Railway Subgrade Structures Induced by Groundwater Level Changes

The groundwater extraction will lead to a drop in water level, causing a change in the distribution of additional stress in the strata. This phenomenon leads to uneven settlement of the railway subgrade. In severe cases, this could threaten the safe operation of trains. Therefore, the degree and main factors influencing groundwater extraction in the settlement of the railway subgrade need to be determined through research. Based on railway subgrade engineering, the first step involved monitoring the settlement resulting from groundwater extraction during the spring irrigation period. Following this, the settlement characteristics of the subgrade structure were analysed. Subsequently, based on the Biot consolidation theory of the soil, a numerical simulation model was established to study the threshold parameters of the groundwater extraction on site. Finally, the primary and secondary relationships of the influencing factors must be clarified. The research results show that: (1) According to the monitoring data, groundwater extraction resulted in a subgrade subsidence of 15.2 mm, exceeding the prescribed threshold, affecting the engineering quality. (2) By the numerical simulation results, the distance parameter of the wells is the most significant factor affecting the deformation of the subgrade, followed by the quantity of extraction. So, the distance between the wells and the tracks should be kept at more than 150 m; the pumping volume should not exceed 1500 m3/day. (3) Using horizontal jet grouting piles to reinforce the subgrade can reduce the maximum uneven deformation from 18.14 to 7.86 mm, an effective settlement control measure.

One-dimensional consolidation analysis of layered foundations with continuous drainage boundaries considering soil structure and physical properties

IntroductionMany theories of consolidation for soils have been proposed in the past, but most of them have ignored the structural characteristics of clay, yet the natural layered soils are widely distributed around the world.MethodsA theoretical model is established to analyze the one-dimensional consolidation behavior of layered soils, in which a time-dependent drainage boundary and the structural characteristics of the soil are taken into account. Using the integral transform and characteristic function methods, the analytical solution is derived, the effectiveness of which is evaluated against the degradation of solutions and the numerical results calculated using the finite element method.Results and discussionFinally, the influences of interface parameter, soil permeability coefficient and soil compressibility on consolidation behaviors are discussed. Results show that in structured soils, early dissipation of excess pore water pressure and consolidation rates are predominantly influenced by interface parameters, permeability, and volume compression coefficients. Higher values of these parameters accelerate early stages of consolidation, which is especially evident in the upper soil layers. Over time, the distinct effects of interface and permeability coefficients on consolidation diminish. Higher volume compression coefficients, while initially beneficial, eventually slow down the consolidation process, indicating an interaction with the ongoing soil structural changes.

Phase transition in porous materials: effects of material parameters and deformation regime on mass conservativity

AbstractPhase transition in porous materials is relevant within different engineering applications, such as freezing in saturated soil or pancake sea ice. Mathematical descriptions of such processes can be derived based on Biot’s consolidation theory or the Theory of Porous Media. Depending on parameters such as density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. Numerical solution procedures for the general, finite deformation case, suffers from instabilities and high computational costs. Simplifications, assuming small deformations, increases stability and computational efficiency. Within this work shortcomings of simplified theories based on Biot and linearisations of the Theory of Porous Media (TPM) are systematically studied. In order to determine the interaction of the different model parameters a non-dimensional model for poro-elasticity is presented. Based on a characteristic test-case including phase-transition and consolidation, the simplified models are compared to the fully non-linear TPM, focusing on mass errors as well as the time behaviour of the solution. Taking further into account the efficiency of discretisation based on different primal variables and finite-element-spaces, a guideline for selecting an appropriate combination of model, kinematic assumption and discretisation scheme is presented.

Study on drainage mechanism of complete path for vacuum preloading based on thermodynamics theory

Vacuum preloading has been a widely used consolidation method for soft clay ground improvement since the 1980s. Consolidation theory only explains the radial drainage process from soil to prefabricated vertical drains (PVD); however, the complete drainage path mechanism by which water drains vertically through PVD to the upper horizontal sand drainage layer and eventually to vacuum pumps is still unclear, resulting in controversies about vacuum preloading. A large oedometer test was performed to study the complete drainage-path mechanism for vacuum preloading. During vacuum preloading, the soil’s average internal temperature decreased to 5 °C below initial temperature, with the lowest temperate occurring near the PVD, which was 2 °C lower than the outskirt. A complete drainage path mechanism is proposed based on the phenomenon of internal temperature decreases. Water evaporates only in the PVD, and the vertical movement of water in the PVD is caused by a density difference between the gas molecules that is independent of gravity. Finally, the proposed mechanism was used to explain the controversy about vacuum preloading. For example, vacuum should not decay along the PVD, vacuum acting elevation at the top or bottom of the PVD has no effect on the final vacuum preloading effectiveness, there is no unsaturated zone formed, and the groundwater level does not drop during vacuum preloading.

A simplified interpolation algorithm for the numerical simulation of the consolidation in composite foundation containing group of stone columns

Based on Biot consolidation theory, a simplified interpolation algorithm under the finite element method and a corresponding modeling method for group of stone columns are proposed to solve the consolidation simulation problem of composite foundation containing group of stone columns. The correctness of the modeling method and computational program is confirmed by comparing the results from the unit cell model with those from axisymmetric model and analytical solution. Subsequently, the composite foundation model is used to verify the accuracy of this method in calculating the settlement change and consolidation time under load for composite foundation containing group of stone columns. Compared to detailed modeling, this method gets satisfactory results with simpler modeling and less computation time. In comparison to homogenization method, this method offers better computational accuracy and enables the stress analysis of stone column. Additionally, discussions on mesh sensitivity, number of stone columns and the influence of the upper structure provide guidelines for the application of this method in practical engineering projects.

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. To address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parametrized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Large strain consolidation analysis of dredged sludge treated with multilayer PHDs combined with vacuum pressure

Multilayer PHDs combined with vacuum pressure for the treatment of dredged sludge yards are effective in avoiding the bending effect of drainage bodies during consolidation. However, the existing theory of self-weight consolidation cannot reflect the actual consolidation properties of dredged sludge treated with multilayer PHDs combined with vacuum pressure. In this study, the nonlinear large-strain consolidation model of dredged sludge treated with multilayer PHDs combined with vacuum pressure was established, considering the nonlinear compressibility and permeability of dredged sludge, self-weight stress of dredged sludge and the variation of dredged sludge height with time. The reliability of the model is verified by comparison with existing consolidation theory, indoor test, and field test data. By researching the effect of the PHDs laying ratios, the height of each dredged sludge layer, and the stacking process time on the consolidation rate of dredge sludge, it is found that if the total height of the treated dredged sludge is 9.0 m and the 5.0 m high yard is designed with double-layer PHDs, the optimal PHDs laying ratios is 20%, the optimal location of the 2nd layer PHDs is at half of the total height of dredged sludge and the optimal stacking time is 140 days.

Integration of overlapping sequences emerges with consolidation through medial prefrontal cortex neural ensembles and hippocampal-cortical connectivity.

Systems consolidation theories propose two mechanisms that enable the behavioral integration of related memories: coordinated reactivation between hippocampus and cortex, and the emergence of cortical traces that reflect overlap across memories. However, there is limited empirical evidence that links these mechanisms to the emergence of behavioral integration over time. In two experiments, participants implicitly encoded sequences of objects with overlapping structure. Assessment of behavioral integration showed that response times during a recognition task reflected behavioral priming between objects that never occurred together in time but belonged to overlapping sequences. This priming was consolidation-dependent and only emerged for sequences learned 24 hr prior to the test. Critically, behavioral integration was related to changes in neural pattern similarity in the medial prefrontal cortex and increases in post-learning rest connectivity between the posterior hippocampus and lateral occipital cortex. These findings suggest that memories with a shared predictive structure become behaviorally integrated through a consolidation-related restructuring of the learned sequences, providing insight into the relationship between different consolidation mechanisms that support behavioral integration.

Axisymmetric consolidation behavior of multilayered unsaturated soils with transversely isotropic permeability

Time-dependent consolidation behavior of unsaturated soils is a vital problem in the geotechnical engineering. With the aid of the Fredlund consolidation theory, this work further assumes the total stress of soils skeleton freely change, and extends the Fredlund consolidation theory to a Biot-type theory, establishing the fully-coupled equation model of multilayered unsaturated poroelastic media with transversely isotropic permeability. To convert the partial differential governing equation into ordinary differential equations, the integration transform technology is applied. Subsequently, the precise integration method is used to acquire the time-dependent consolidation solution of multilayered unsaturated media with transversely isotropic permeability in the transformed domain, which is further solved in the actual domain by the inverse Hankel transform. A verification examples is provided to compare the present results with the existing work in the literature, showing a great coincidence and proving the feasibility of the present solution. Finally, numerous numerical examples are presented to investigate the evolution of excess pore pressure and settlement under quasi-static loads, revealing the consolidation behavior of unsaturated soils. The results demonstrates that the ramping time, stratification, permeability, depth and m1w have a significant effect on the consolidation behavior.

Analytical Solutions for Composite Foundations Reinforced by Partially Penetrated Stone Columns and Vertical Drains

ABSTRACTWhen stone columns or vertical drains are applied to improve soils, it is common to face situations where the soft soil layer is too thick to be penetrated completely. Although consolidation theories for soils with partially penetrated vertical drains or stone columns are comprehensive, consolidation theories for impenetrable composite foundations containing both two types of drainage bodies have been few reported in the existing literature. Equations governing the consolidation of the reinforced zone and unreinforced zone are established, respectively. Analytical solutions for consolidation of such composite foundations are obtained under permeable top with impermeable bottom (PTIB) and permeable top with permeable bottom (PTPB), respectively. The correctness of proposed solutions is verified by comparing them with existing solutions and finite element analyses. Then, extensive calculations are performed to analyze the consolidation behaviors at different penetration rates, including the total average consolidation degree defined by strain or stress and the distribution of the average excess pore water pressure (EPWP) along the depth. The results show that the total average consolidation rate increases as the penetration rate increases; for some composite foundations with a low penetration rate, the consolidation of the unreinforced zone cannot be ignored. Finally, according to the geological parameters provided by an actual project, the obtained solution is used to calculate the settlement, and the results obtained by the proposed solution are in reasonable agreement with the measured data.

Long-term effect of soil settlement on lateral dynamic responses of end-bearing friction pile

This paper presents a closed-form solution to evaluate the lateral dynamic responses of pile foundation adjacent to superficial surcharge. The equilibrium equation of soil is analyzed using continuum solutions, and the Euler-Bernoulli beam theory is employed to model the pile. The consolidation settlement of surrounding soil induced by the superficial surcharge is determined by Terzaghi's consolidation theory. The lateral soil resistance is formulated using potential functions, and the dynamic responses of the end-bearing friction pile are subsequently obtained by considering the vertical load and skin friction. Our results are compared with analytical approaches from previous literature to validate the effectiveness of the present solution. The evolutions of lateral dynamic responses of pile foundation are systematically analyzed. It is suggested that the superficial surcharge influences the distribution of skin friction of the pile foundation, thereby altering its lateral dynamic responses. This phenomenon does not manifest immediately but demonstrates significant long-term effects during the consolidation settlement of surrounding soil.

Modeling pore fluid pressure and deformation in unsaturated soils under gravitational compaction and cyclic loading

Cyclic loading of fluid-bearing soils often induces excess pore water pressure, leading to accumulation of strain in the solid matrix. Additionally, variations in material density and volumetric fraction due to gravitational effects generate momentum forces, which subsequently cause deformation in the soil. In this paper, we present a mathematical framework of poroelasticity that generalizes the simultaneous action of gravitational body forces and cyclic loading to analyze solid deformation and fluid pressure dissipation in partially-saturated porous media. To account for the effect of gravity, the gradient of the vertical displacement needs to be treated as an additional dependent variable alongside pore air and water pressures.We numerically solve a mixed strain-controlled and pressure-prescribed boundary-value problem using a finite difference scheme as a representative example to quantify the impact of gravitational forces. Our results show that gravitational compaction affects both total settlement and excess pore water pressure, with its influence being particularly significant at lower water saturations, regardless of excitation frequency, soil depth, or type. The effect of gravity is more pronounced in soils with higher compressibility but appears insensitive to excitation frequency. Notably, the gravitational effect correlates linearly with the depth of the soil deposit and, therefore, should be well integrated into the consolidation theory of poroelasticity.

Hippocampus supports long-term maintenance of language representations: Evidence of impaired collocation knowledge in amnesia

Traditional systems consolidation theories of memory suggest that the role of the hippocampus in maintaining memory representations diminishes over time, with learned information eventually becoming fully independent of the hippocampus. Knowledge of collocations in one’s native (L1) language are acquired during development and are solidly acquired by adulthood. Remote semantic knowledge of collocations might therefore be expected to be resistant to hippocampal pathology. Patients with hippocampal damage and severe anterograde amnesia completed two tasks testing English collocation knowledge originally designed for use with English language learners. Patients with hippocampal damage demonstrated impairments in recognition of common English collocations, despite a lifetime of language experience (including postsecondary education) prior to sustaining this damage. These results suggest the hippocampus contributes to the long-term maintenance of linguistic representations and provides a challenge to traditional consolidation views of memory and an extension of newer theories to include a role for the hippocampus in maintaining semantic memory.

Music cue during slow wave sleep improves visuospatial memory consolidation.

The active system consolidation theory assumes that sleep between encoding and retrieval promotes memory consolidation. In the present study, we cued new memories during slow-wave (SWS) or rapid eye movements (REM) sleep stages by presenting an instrumental music stimuli that had been previously presented during a learning session. In a within-subjects design, 18 participants slept for three nonconsecutive nights (cue during SWS, cue during REM, and no cue during control night) and were trained in a visuo-spatial memory task. The administration of cue during SWS produced better memory accuracy in comparison with REM and the control condition.

Fully coupled finite strain consolidation analysis for soft clay treated by prefabricated horizontal drain with vacuum and heat preloading

This paper established a one-dimensional fully coupled finite strain consolidation analysis for soft clay treated by thermal prefabricated horizontal drain under vacuum and heat preloading with the consideration of thermal elastic viscoplastic (TEVP) behaviors of soft clay. Firstly, the governing equations for finite strain consolidation, heat conduction, and heat convention process have been carefully derived based on the well-established Gibson’s large strain consolidation theory and TEVP constitutive model. Secondly, the accuracy and reliability of the numerical method have been verified with benchmark cases and three physical model tests. Then, improvement of consolidation efficiency rate (IER) was defined and used to study the effect of three variables on consolidation efficiency. Last but not least, a graphical user interface (GUI) was provided to support researchers and engineers in utilizing the proposed numerical method for conducting consolidation analysis of soft soil treated in the same or similar fashion.

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.

Does slow oscillation-spindle coupling contribute to sleep-dependent memory consolidation? A Bayesian meta-analysis.

The active system consolidation theory suggests that information transfer between the hippocampus and cortex during sleep underlies memory consolidation. Neural oscillations during sleep, including the temporal coupling between slow oscillations (SO) and sleep spindles (SP), may play a mechanistic role in memory consolidation. However, differences in analytical approaches and the presence of physiological and behavioral moderators have led to inconsistent conclusions. This meta-analysis, comprising 23 studies and 297 effect sizes, focused on four standard phase-amplitude coupling measures including coupling phase, strength, percentage, and SP amplitude, and their relationship with memory retention. We developed a standardized approach to incorporate non-normal circular-linear correlations. We found strong evidence supporting that precise and strong SO-fast SP coupling in the frontal lobe predicts memory consolidation. The strength of this association is mediated by memory type, aging, and dynamic spatio-temporal features, including SP frequency and cortical topography. In conclusion, SO-SP coupling should be considered as a general physiological mechanism for memory consolidation.

Consolidation Theory Selection of Dredger Fill

Consolidation Theory Selection of Dredger Fill

Wave–Induced Soil Dynamics and Shear Failure Potential around a Sandbar

Sandbars are commonly encountered in coastal environments, acting as natural protections during storm events. However, the sandbar response to waves and possible shear failure is poorly understood. In this research, a two–dimensional numerical model is settled to simulate the wave-induced sandbar soil dynamics and instability mechanism. The model, which is based upon the Reynolds-averaged Navier–Stokes (RANS) equations and Biot’s consolidation theory, is validated using available experiments. Parametric studies are then conducted to appraise the impact of the wave parameters and soil properties on soil dynamics. Results indicate that the vertical distribution of the maximum vertical effective stress in the sandbar is different from that in the flat seabed, which decreases rapidly along the soil depth and then increases gradually. The impact of soil permeability and saturation on the vertical effective stress distribution around the sandbar also differ from that in the flat seabed. Unlike the flat seabed, the vertical distribution of shear stress in the sandbar increases with an increasing wave period. The sandbar soil shear failure potential is discussed based upon the Mohr–Coulomb criterion. Results show that the range of shear failure around the sandbar is wider and the depth is deeper when the wave trough arrives.

Large strain consolidation of soft soils with partially penetrating PVDs: Analytical solutions incorporating variable well resistance

The large-strain geometric assumptions and nonlinear compressibility and permeability have significant effects on the consolidation of soft soils with high compressibility. However, analytical solutions for large-strain nonlinear consolidation of soft soils with partially penetrating PVDs have been rarely reported in the literature. A double logarithmic model is adopted to describe the nonlinear compressibility and permeability of soft soils with high compressibility, and a large-strain consolidation model for soft soils with partially penetrating PVDs under the condition that the excess pore water pressure at the interface between the improved and unimproved layers is equal is established based on Gibson’s large-strain consolidation theory. The analytical solution for the large-strain nonlinear consolidation model for soft soils with partially penetrating PVDs is obtained. The reliability of the analytical solution obtained in this study is verified by comparing it with the existing solutions under different conditions, and the maximum deviation between the two methods does not exceed 5 %. On this basis, consolidation behaviors of soft soils with partially penetrating PVDs under different conditions were analyzed by extensive calculations. Finally, the proposed analytical solution for the large strain consolidation model is applied to the settlement calculation of the Bachiem Highway Project, which further demonstrates the applicability of the consolidation model.