Nonlinear Consolidation Research Articles

An Analytical Solution for Nonlinear Consolidation of Composite Foundations Improved by Impermeable Columns and Vertical Drains with Time-Dependent Well Resistance

An Analytical Solution for Nonlinear Consolidation of Composite Foundations Improved by Impermeable Columns and Vertical Drains with Time-Dependent Well Resistance

Semi‐Analytical Solution for One‐Dimensional Nonlinear Consolidation of Multilayered Soil Considering Self‐Weight and Boundary Time Effect

ABSTRACTThe self‐weight stress in multilayered soil varies with depth, and traditional consolidation research seldom takes into account the actual distribution of self‐weight stress, resulting in inaccurate calculations of soil consolidation and settlement. This paper presents a semi‐analytical solution for the one‐dimensional nonlinear consolidation of multilayered soil, considering self‐weight, time‐dependent loading, and boundary time effect. The validity of the proposed solution is confirmed through comparison with existing analytical solutions and finite difference solution. Based on the proposed semi‐analytical solution, this study investigates the influence of self‐weight, interface parameter, soil properties, and nonlinear parameters on the consolidation characteristics of multilayered soil. The results indicate that factoring in the true distribution of self‐weight leads to a faster dissipation rate of excess pore water pressure and larger settlement and settlement rate, compared to not considering self‐weight. Both boundary drainage performance and soil nonlinearity have an impact on consolidation. If the boundary drainage capacity is inadequate, the influence of soil nonlinearity on consolidation diminishes.

Effect of cross-correlated hydraulic conductivity and compression index on nonlinear consolidation in randomly heterogeneous highly compressible aquitards

The problem of land subsidence due to groundwater pumping in highly compressible, randomly heterogenous aquitards with stress-dependent parameters is analyzed through one-dimensional Monte Carlo numerical simulations of nonlinear groundwater flow and consolidation. The natural logarithm of hydraulic conductivity (Y) and compression index (Cc) are considered spatially cross-correlated random variables. A stochastic simulation method based on a bivariate normal copula was applied to generate positive, negative, and uncorrelated realizations of the two random variables. The results show that when Y and Cc are correlated random parameters, the ensemble average total settlement is consistently larger (between 13% and 40% for the synthetic cases tested) than the total settlement obtained when the parameters are deterministic (perfectly known). In addition, the results of negative and no correlation between Y and Cc are similar in terms of the ensemble average and variance of total settlement, while positive correlation leads to larger values of total settlement and its variance. The stochastic approach employed here allows incorporating the uncertainty in the parameters in the simulation of the subsidence process, which is relevant for geotechnical engineering, design of structures and groundwater management.

One‐dimensional consolidation analysis of layered soil with exponential flow under continuous drainage boundary

AbstractTo comprehensively consider the influence of boundary conditions, non‐Darcy flow, load forms, and soil stratification on soil consolidation, a one‐dimensional soil consolidation equation is established. By subdividing the soil layer and employing time discretization, the nonlinear consolidation equation is linearized, resulting in an analytical solution for layered soil foundation at any given time. Subsequently, an iterative approach for time solution is employed to obtain a semi‐analytical solution. The correctness of the solution is verified by comparison with solutions based on Darcy's flow and the semi‐analytical method under traditional drainage boundary conditions. Subsequently, the influence of interface parameters, loading conditions, flow index, and other factors on consolidation characteristics is analyzed. The results indicate that higher interface parameter values for continuous drainage boundaries correspond to faster average consolidation rates for stratified soil foundations, while these parameters have little effect on the time required for complete consolidation of the soil layers. Improved boundary drainage performance amplifies the influence of exponential flow on pore water pressure and average consolidation degree. Conversely, poor boundary drainage performance diminishes the impact of exponential flow on soil consolidation, rendering it negligible. Moreover, faster loading rates accentuate the influence of the flow index on the average consolidation degree defined by pore pressure.

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.

Coupled model for electro‐osmosis consolidation and ion transport considering chemical osmosis in saturated clay soils

AbstractThe electro‐osmosis approach efficiently facilitates the rapid dewatering of soil with high water content and contributes to reducing contaminant levels within the clay soil. However, the changes of chemical field caused by ion transport in the clay soil during electro‐osmosis process will also influence the clay soil consolidation effect. Existing theories predominantly tend to disregard this crucial physical process and its resultant effects, thereby restraining a comprehensive analysis of electro‐osmosis consolidation (EOC) behavior under intricate chemical conditions. This study introduces a concise model of EOC and ion transport considering chemical osmosis. The model considers the nonlinear variation of clay soil parameters such as compressibility, permeability, and effective diffusion coefficients, along with the interaction between EOC and ion transport. Meanwhile, the correctness of the model is verified from different aspects such as theoretical derivation and model comparison. Based on the proposed model, the impacts of the variation in electrical field intensity and chemical concentration on the coupled behaviors between EOC and ion transport are systematically investigated, with and without incorporating nonlinear consolidation characteristics. The results show that diffusion and electro‐migration exhibit a more pronounced effect on ion transport during EOC. Simultaneously, with the increase of ion concentration in clay soil pore solution, the effects of chemical osmosis become increasingly apparent, thereby enhancing clay soil settlement.

Analytical Solution for Nonlinear Consolidation Considering Time-Dependent Well Resistance and Lateral Deformation under Vacuum Preloading

Analytical Solution for Nonlinear Consolidation Considering Time-Dependent Well Resistance and Lateral Deformation under Vacuum Preloading

Nonlinear consolidation finite element analysis of a layered soft soil foundation under multistage loading based on the continuous drainage boundary

To comprehensively consider the impacts of stratification, residual pore water pressure, soil nonlinearity, and boundary permeability on consolidation settlement of soft soil foundations for accurate prediction, a continuous drainage boundary condition is proposed in this study that reflects the residual pore pressure under multistage loading, and a nonlinear elastic constitutive model based on the double logarithmic model is adopted to account for the nonlinear consolidation behaviour of soils. A UMAT subroutine is developed based on the proposed boundary condition and nonlinear elastic constitutive model. Subsequently, the developed subroutine is compared with the built-in linear elastic soil constitutive model in ABAQUS and engineering examples. The application of continuous drainage boundaries in stratified foundations is analysed, as well as the influence of factors such as the loading rate and soil nonlinearity on consolidation settlement. The results indicate that, compared to the built-in model, the subroutine developed in this study can be employed to more accurately calculate the nonlinear consolidation of multilayered foundations under multistage loading. By adjusting the loading rate parameter αk, consolidation under different loading conditions can be predicted. Additionally, the proposed boundary condition simplifies the calculations for soft soil foundations with sand layers, providing a novel computational approach for the design of construction loading schemes and long-term settlement predictions in soft soil foundations.

Analysis on Large-Strain Nonlinear Consolidation of PVD-Improved Soft Soils with Non-Darcian Flow Considering Variable Well Resistance and Vacuum Pressure

Analysis on Large-Strain Nonlinear Consolidation of PVD-Improved Soft Soils with Non-Darcian Flow Considering Variable Well Resistance and Vacuum Pressure

Variation of negative vacuum pressure in vertical drains with time and depth under variable well resistance

AbstractMost solutions for the large strain nonlinear consolidation of soils with vertical drains are based on the assumption that the negative vacuum pressure only depends on the depth. In response to the shortcomings of this assumption, a large strain nonlinear consolidation model of soils with vertical drains under vacuum preloading is developed by considering the time‐and depth‐dependent well resistance. By fitting the data under different well resistances, the influence of well resistance parameters on the negative vacuum pressure variation in vertical drains is investigated, and the relevant empirical formulas describing the negative vacuum pressure variation in vertical drains are provided. The results obtained from the empirical formulas are in good agreement with the theoretical results as well as the experimental data, by which the reliability of the proposed empirical formulas is verified. The advantages of proposed empirical model can be identified by comparing it with the conventional model in which negative vacuum pressure is only linearly distributed with depth.

Simplified solution for large-strain consolidation considering the time-dependent well resistance

In this study, a simplified solution of the large-strain consolidation theory, which considers the time-dependent well resistance, has been presented. This solution is suitable for consolidation issues involving the influence of either the smear zone or the soil column. To confirm the proposed solution's accuracy, it was compared to fully nonlinear consolidation results calculated using the finite element method. Parametric analysis was conducted to examine the impact of the time-dependent well resistance in combination with the soil thickness, the ratio of the compression index to the radial and vertical permeability indices, and the initial void ratio at the soil surface. Finally, the proposed solution’s applicability was confirmed through a comparison of calculated results based on two case studies with both field measurements and numerical simulations.

Air-boosted vacuum preloading method for land reclamation with vertical drains: Numerical and analytical solutions

As an emerging ground treatment technique, the air-boosted vacuum preloading method accelerates the consolidation process of soils with vertical drains and enhances the bearing capacity and stability of grounds. This improvement is achieved by augmenting the horizontal pressure differential between the drainage body and the surrounding soils. In the realm of existing theories, consolidation models are primarily established under the assumption of linear characteristics of soils. Nonetheless, for marine sedimentary soft soils characterized by high compressibility, the application of nonlinear consolidation theory becomes more appropriate. The well resistance effect of the drainage body over time is also considered in this study, and a comprehensive consolidation model tailored to soft soils with air-booster pipes and vertical drains is proposed. Subsequently, the analytical and numerical solutions for this consolidation model are derived, respectively. Comparisons are made with existing conventional linear consolidation models to substantiate the validity of the proposed consolidation model. This investigation delves into the influence of nonlinear compressibility and permeability of soils, variable well resistance, and drain spacing ratio, on consolidation behaviors. Particular emphasis is placed on the determination of the startup time for the air-boosted system. Finally, the proposed consolidation model is applied to the actual field prediction, affirming the accuracy and applicability of the developed consolidation model in practical soft soil treatments.

Nonlinear consolidation of arbitrary layered soil with continuous drainage boundary: An approximate closed-form solution

Based on the double nonlinear consolidation constitutive associated with the compression and permeability coefficients, presented by Mesri and Rokhsar (1974), this paper derives an approximate closed-form solution for the one-dimensional nonlinear consolidation of the arbitrary layered soils incorporating the continuous drainage boundary condition. The approximate closed-form solution is obtained by the homogenization of the boundary conditions and eigenfunction method. A model test is conducted to justify the rationality of the approximation and the continuous drainage condition utilized in this study. The calculated results are also compared with those acquired from the simplified analytical solution and the finite difference method. A parametric study is conducted to investigate the influence of various parameters on the consolidation process. The most significant finding is that the influence of Nq appears to be completely different for the cases when Cc/Ck>1 and Cc/Ck<1. When Cc/Ck>1, the increase of Nq shows an adverse influence on the consolidation, whereas the influence becomes positive when Cc/Ck<1. The approximate solution derived herein offers a rigorous analytical approach for the double nonlinear consolidation problems of arbitrary layered soils, providing an effective benchmark for comparison and verification of future sophisticated numerical approaches.

Coupled creep and nonlinear consolidation of soft soils in disturbed state concept framework

A simplified solution for coupled creep and nonlinear consolidation of soils has been presented based on the disturbed state concept (DSC). The nonlinearity of the problem due to the change of the material properties and thicknesses of the soil layer, and creep was considered in the proposed solution. The state of the soil before primary consolidation was considered as initially relatively intact, and after primary consolidation during the pure creep phase was considered as finally fully adjusted state. The state of the soil during the coupled creep and consolidation process was related to its relatively intact and fully adjusted states using two consolidation and creep state functions that have been derived based on the numerical solution of the problem. Using the consolidation state function, the solutions of Terzaghi’s theory of consolidation in two initial and end of the primary consolidation states were interpolated to achieve the solution of the nonlinear primary consolidation phase. The creep state function was used to implement the effect of the creep deformation during and after the primary consolidation in the settlement calculations. The result of the proposed method was verified by the results of the numerical and approximate methods along with laboratory data in the literature.

Large-Strain Nonlinear Consolidation of Sand-Drained Foundations Considering Vacuum Preloading and the Variation in Radial Permeability Coefficient

The vacuum preloading method effectively strengthens soft soil foundations with vertical drainage, which produces a smear effect when laying sand drains. Meanwhile, the seepage of pore water and soil deformation during consolidation exhibit nonlinear characteristics. Therefore, based on Gibson’s 1D large-strain consolidation theory, this paper developed a more generalized large-strain radical consolidation model of sand-drained soft foundations under free-strain assumptions. In this system, the double logarithmic compression permeability relationships for soft soils with large-strain properties, the variation in the radical permeability coefficient in the smear zone, and the effect of the non-Darcy flow were all included. Then, the partial differential control equations were numerically solved by the finite difference method and validated with existing radical consolidation test results and derived analytical solutions. Finally, the influences of relevant model parameters on consolidation are discussed. The analysis shows that the greater the maximum dimensionless vacuum negative pressure P0, the faster the consolidation rate of sand-drained foundations. Meanwhile, the decrease in the negative pressure transfer coefficient k1 will result in a decreasing final settlement amount. Moreover, the consolidation rate of sand-drained foundations is slower considering the non-Darcy flow, but the final settlement is unaffected.

A One-Dimensional Nonlinear Consolidation Analysis of Double-Layered Soil with Continuous Drainage Boundary

Based on the soil nonlinearity assumptions proposed by Mesri, the one-dimensional nonlinear consolidation of double-layered soil is investigated. To better align with engineering reality, a continuous drainage boundary is introduced, bolstering the reliability of the derived solution through comparison against existing findings. Subsequently, the consolidation behavior of double-layered soil is analyzed for the soil permeability, compressibility, nonlinear parameters, and interface parameters. The outcomes elicit a positive correlation between the consolidation rate of the double-layered soil and both the ratio of permeability coefficient from the lower to upper soil layers and the value of the interface parameter. Furthermore, it is observed that a lower compressibility coefficient ratio between the lower and upper soil layers, along with a reduced ratio of compression index to penetration index, both contribute to an increased consolidation rate within the context of double-layered soil. The one-dimensional nonlinear consolidation of double-layered soil is intricate, intertwined with the relative permeability and compressibility of soil layers, and the influence of nonlinear parameters and drainage boundary configuration. Integrating these factors is crucial for analyzing the consolidation traits of double-layered soil, leading to a more precise portrayal of the consolidation behavior of coastal soft soils.

Nonlinear analysis for consolidation of soft soils improved by composite piles with stiff core and gravel shell

The implementation of composite piles has emerged as an appealing technology for reinforcing soft ground through fulfilling the requisite bearing capacity and facilitating consolidation. Nonetheless, previous investigations into the consolidation behavior of composite pile-improved ground have neglected the nonlinearity of soil compression and permeability. In this context, the logarithm models of e-lgσ and e-lgk are introduced to establish an analytical model for the nonlinear consolidation of composite ground with composite piles. Based on equal strain assumption and annular equivalent method, detailed solutions under four special loading schemes are then obtained. Additionally, a comprehensive analysis is conducted to assess the influence of various parameters on the nonlinear consolidation behavior of composite ground, and the feasibility of current model is verified by degenerations. The results show that ignoring the nonlinearity will lead to an overestimation of consolidation rate when the soil’s compression indices exceed the permeability indices. Moreover, the consolidation rate of composite ground is inversely proportional to σ¯u/σ¯s0′ and Cc/Ckh(v), while demonstrating a direct proportionality to Ksp, Ksg, and kg/kv0. However, σ¯u/σ¯s0′ mainly influences excess pore water pressure at the upper layer, and the influence of Cc/Ckv on the consolidation rate is limited and can even be ignored in comparison to Cc/Ckh. Finally, the proposed model is successfully applied to an engineering project in situ, where the obtained results exhibit a noteworthy agreement with the measured data.

Benchmark for Nonlinear Consolidation of a Soil Deposit by Considering Depth-Dependent Initial Effective Pressure

Analytical solutions for 1D nonlinear consolidation of soils are widely applied to calculate consolidation settlement for their simplicity and convenience. Furthermore, analytical solutions can provide valid benchmark for numerical solutions of nonlinear consolidation. However, the existing analytical solutions for 1D nonlinear consolidation assume the initial effective stress to remain constant in the whole deposit. In practice, the initial effective stress increases with depth in a soil deposit. The existing analytical solutions for 1D nonlinear consolidation are lack of consideration about the variation of initial effective stress along with depth, so there is no benchmark for evaluating the corresponding numerical calculation. In this study, an analytical solution for nonlinear consolidation is developed under a special case, considering the linear increase of initial effective stress with the depth, which provides a benchmark for the corresponding numerical calculation of nonlinear consolidation. To facilitate the verification of the reliability of the numerical calculations of nonlinear consolidation, the pore pressure dissipation curves and settlement curves with time for conditions of PTIB (the case for a permeable top surface and an impermeable bottom surface is referred to as PTIB) and PTPB (the case for a permeable top surface and a permeable bottom surface is named as PTPB) are provided in this paper, thus providing some validation data for future calculations of nonlinear consolidation considering a linear increase in the initial effective stress with depth.

One-dimensional thermal consolidation analysis of saturated clay with variable compressibility and permeability considering partial drainage boundaries

The nonlinear consolidation characteristics of saturated clay will be markedly impacted by temperature. However, despite the ample progress of calculation methods for the one-dimensional consolidation of soft ground, theoretical investigations into thermal consolidation have not been thoroughly explored. Moreover, partially drained boundary is more consistent with the engineering practice, which is imperative to be involved to mitigate computational error when determining the consolidation behavior. In this context, a mathematical model is established to incorporate the temperature-dependent nonlinear characteristics of compressibility and permeability. Subsequently, the resulting governing equations and numerical solutions for the one-dimensional nonlinear thermal consolidation of saturated clay are obtained under partial drainage boundaries. Then the accuracy and reliability of the proposed model are validated by degradation analysis and simulation analysis with good agreements. Furthermore, the computed results of current study are adopted to conduct an in-depth assessment of the influence of several crucial parameters on the nonlinear consolidation behavior. The results demonstrate that increasing the temperature can remarkably accelerate the dissipation rate of excess pore water pressure, thereby promoting the consolidation process of saturated clay. The inclusion of partial drainage boundaries also has a significant influence on the consolidation performance, with a maximum difference in the dissipation rate of excess pore water pressure reaching up to 40 % when transforming a completely drained boundary into a completely undrained boundary. Additionally, the increment of pre-consolidation pressure will induce a gradual acceleration of consolidation rate.

Nonlinear consolidation analysis of saturated multi‐layered soil with continuous drainage boundary

AbstractContinuous drainage boundary is widely accepted to overcome the shortcoming of the traditional assumption of fully permeable or impermeable drainage boundary in consolidation theories. This study presents an analytical solution for one‐dimensional small‐strain nonlinear consolidation of saturated multi‐layered soil with constant consolidation coefficients under continuous drainage boundary condition. The proposed solution is validated by comparison with the existing solutions in literature, which shows that the existing solutions are special cases of this solution. A parametric study performed on saturated four‐layered soil with continuous drainage boundary indicates that the interface parameter and the loading stress ratio have great influences on the nonlinear consolidation of saturated multi‐layered soil. The present solution can be effectively applied to provide more reasonable design for soil foundation.