One-dimensional Nonlinear Consolidation Research Articles

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.

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.

Analytical Solutions for One-Dimensional Large-Strain Nonlinear Consolidation of Soft Soils by Considering a Time-Dependent Drainage Boundary

Over the past decades, many advances have occurred for theories on large-strain nonlinear consolidation of soft soils with regard to traditional drainage boundaries, which are completely permeable and impermeable cases and which may not truly reflect the whole process of drainage boundary. Thus, some further considerations related to a time-dependent drainage boundary are adopted in the analysis of soft soil consolidation by incorporating biologarithmic compressibility and permeability models. Also, the analytical solutions are obtained by means of variable substitution and Laplace transform. Additionally, the proposed solution is degenerated and compared with the existing solution and the laboratory tests to validate its correctness and feasibility. Finally, the soil consolidation behavior is analyzed under different values of the interface parameter, nonlinear compressibility and permeability, and external loading. The results indicate that the drainage boundary permeability is largely determined by the interface parameter; the larger the interface parameter, the better the boundary permeability. Besides, the consolidation rate decreases with the increasing value of Ic(α − 2) when the external loading remains constant. While the parameter Ic(α − 2) is a constant value, the consolidation rate varies with the external loading. Therefore, appropriate parameter values are more conducive to the full consolidation of soft soil foundations.

One-Dimensional Nonlinear Consolidation for Soft Clays with Continuous Drainage Boundary Considering Non-Darcy Flow

Adopting the non-Darcy flow presented by Hansbo and considering the nonlinear compression and permeability characteristics of soils, the one-dimensional nonlinear consolidation problem of soft clays is investigated by means of a continuous drainage boundary. The numerical solutions of average consolidation degrees defined by settlement and excess pore water pressure are derived by using the finite difference method, and the correctness of these solutions is verified by comparing them with existing analytical and numerical solutions. Based on the proposed solutions, a parametric study is conducted to study the influence of interface parameter, non-Darcy flow parameter and soil nonlinearity on the consolidation behavior of soft clays. The results show that the solutions based on the continuous drainage boundary can be degenerated into the solutions based on the Terzaghi drainage boundary if the interface parameter is taken as a reasonable value. The soil consolidation behavior considering both non-Darcy seepage and nonlinear characteristics of soil is very complex.

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.

Analytical solution for one-dimensional nonlinear consolidation of layered soils with continuous drainage boundary

Analytical solution for one-dimensional nonlinear consolidation of layered soils with continuous drainage boundary

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

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

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

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

General Approximate Analytical Solutions for One-Dimensional Nonlinear Consolidation of Soft Soils under Time-Dependent Loading

A surcharge preloading method with time-dependent loading is widely used for accelerating the consolidation process of soft soils, and different loading patterns have a great effect on the consolidation characteristics. For one-dimensional nonlinear consolidation of soft soils considering the variable compressibility and permeability, the general approximate analytical solutions for one-dimensional nonlinear consolidation under time-dependent loading are derived. Moreover, two forms of boundary conditions are considered according to engineering practice. With reference to the general analytical solutions presented, the expressions for the solutions under several common loading patterns, such as the multistage instantaneous loading pattern, multistage linear loading pattern, and cyclic loading pattern, are given. The accuracy and correctness of the approximate analytical solutions are proven by comparing the approximate analytical solutions with the finite-difference solutions and two experimental results with different boundary conditions. Based on the approximate analytical solutions proposed, the consolidation behaviors of soft soils under different loading patterns are analyzed. In conclusion, the proposed approximate analytical solutions have a simple and clear form, which is convenient for calculations in engineering applications.

One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary

Analytical Solution for One-Dimensional Nonlinear Consolidation of Saturated Double-Layered Soil Subjected to Cyclic Loadings

Cyclic loading-induced consolidation behavior of soft soil is of great interest for the analysis of offshore and onshore structures. In this study, an analytical solution for one-dimensional (1D) nonlinear consolidation of saturated double-layered soil under various types of cyclic loadings such as trapezoidal cyclic loading, rectangular cyclic loading, and triangular cyclic loading was derived. The proposed solution was subsequently degenerated into solutions for special cases and compared to the existing solutions. The degenerate solutions show good agreement with the existing results, which proves that the proposed solutions are more general ones for 1D nonlinear consolidation of saturated soils under time-dependent loading. Finally, a comprehensive parametric study was conducted to investigate the influences of different layer parameters, drainage conditions, and loading parameters on nonlinear consolidation of saturated double-layered soil under cyclic loadings.

Analysis of one-dimensional nonlinear consolidation of a saturated lumpy porous clay layer

In reclamation projects, excavated clay is dumped without any compaction to form a landfill with a heterogeneous pore structure. In this clay,interlump fissures isseveral orders of magnitude larger thanintralump pores, forming lumpy porous clay with double porosity. In this study, a nonlinear consolidation model is proposed for lumpy porous clay based ondouble porosity concept and mixture theory. The analysis follows these steps: in step 1, a representative saturated lumpy porous clay is considered as a 3-part composition, i.e., solid, fissure fluid and pore fluid, and the volume fractions are defined; in step 2, the decomposition equation is given for each part’s strain, and the homogenization relation of mixture theory is used to provide the stress relation inside the saturated lumpy porous clay; in step 3, the energy balance equation is derived in terms of the energy conjugation; in step 4, according to the energy conjugation pairs, new nonlinear constitutive equations are proposed for saturated lumpy porous clay; and in step 5, using Darcy's law, the consolidation control equations are given. The model calculations are compared with experimental data, indicating that the proposed model can effectively simulate the consolidation curves of the clay observed in the laboratory.

Experimental study on the one-dimensional nonlinear consolidation and seepage of saturated clay considering stress history under ramp loading

Experimental study on the one-dimensional nonlinear consolidation and seepage of saturated clay considering stress history under ramp loading

Analytical solution for one-dimensional nonlinear consolidation of double-layered soil with improved continuous drainage boundary

Following the assumptions proposed by Davis and Raymond, an analytical solution for one-dimensional nonlinear consolidation of double-layered soil under constant loading is derived by introducing an improved continuous drainage boundary condition. The effectiveness of the present solution is assessed by comparing against other existing analytical solutions and laboratory consolidation test results. A parametric study is then conducted to investigate the consolidation behaviour of double-layered soil for different interface parameters or stress ratios (i.e. final effective pressure over initial effective pressure, Nσ ). The results show that, the average consolidation degree defined by soil settlement U s increases with the increase of N σ, and the average consolidation degree defined by excess pore water pressure U p decreases with the increase of Nσ . The magnitude of U s is always larger than U p, and the difference between U s and U p increases with the increase of Nσ . Compared with the Xie's solution, the stress ratio Nσ has little effect on U p in the solution with continuous drainage boundary condition.

Nonlinear Consolidation Analysis of a Saturated Clay Layer with Variable Compressibility and Permeability under Various Cyclic Loadings

This paper presents an analytical solution for one-dimensional nonlinear consolidation of a saturated clay layer with variable compressibility and permeability under various cyclic loadings. Based on the assumption that the initial effective stress was constant with depth and the nonlinear variations of compressibility and permeability were expressed by the logarithm relations (e − log σ′ and e − log kv), two new variables were introduced to the 1D nonlinear consolidation equation. The analytical solutions were derived for trapezoidal, rectangular, and triangular cyclic loadings. The presented solution could degenerate into all of the existing solutions for nonlinear consolidation, which showed the analytical solution proposed in this paper was the most general one for nonlinear consolidation. The validity of the proposed solutions was verified against the numerical results from the finite difference method (FDM). The effects of different parameters on nonlinear consolidation behavior of the saturated clay layer subjected to various cyclic loadings were investigated using the solutions developed. The proposed solutions could be effectively utilized in the analysis of nonlinear consolidation of a saturated clay layer under various cyclic loadings.

Analytical solution for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading

This paper presents analytical solutions for one-dimensional nonlinear consolidation of saturated multi-layered soil under time-dependent loading. Analytical solutions are derived for one-dimensional nonlinear consolidation of multi-layered soil subjected to constant loading and ramp loading. The proposed solutions are verified through the comparison with the existing solutions for double-layered soil and single-layered soil, which shows the proposed solutions are more general ones for one-dimensional nonlinear consolidation of saturated soils subjected to time-dependent loading. Based on the proposed solutions, nonlinear consolidation behavior of saturated multi-layered soil under time-dependent loading is investigated.

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

Initial stress and additional effective stress distributions in soil greatly influence the degree of ground consolidation when calculating one-dimensional soft clay ground consolidation in deep soil. The one-dimensional nonlinear consolidation governing equations of soft ground under uniform loads are derived and solved with the finite difference method. This method is based on the assumptions that the initial stress in soil varies with the ground depth and the additional effective stress caused by external loads changes with both the ground depth and consolidation time, and the hyperbolic model of the soil stress-strain relationship. Formulas for the degree of consolidation and the settlement of the ground are presented. A case study shows that the degree of consolidation of the ground calculated with the finite difference method agrees with the traditional analytical solution, and the computational efficiency of the finite difference method can be effectively improved when the segmental calculation method is used throughout the consolidation process. The results of another example show that the settlement of the ground calculated with the finite difference method agrees with the in situ data. The suggested method can greatly simplify the consolidation calculation and has a high application value in engineering.

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.

Nonlinear consolidation of multilayer soil under cyclic loadings

This paper proposes a uniform approach for modelling one-dimensional nonlinear consolidation of multilayer soil under various cyclic loadings based on the differential quadrature method. Various cyclic loading forms and boundary conditions are readily treated. The current differential quadrature formulation using harmonic function coefficients (HDQM) is proven more efficient in solving the consolidation problem of multilayer soil under cyclic loadings than conventional differential quadrature formulation using Lagrangian interpolation polynomial. The computation indicates that the pore pressure and average consolidation degree of a multilayer soil are highly dependent on the loading form and the length of the loading period in each loading–unloading cycle. The influence of the various boundary conditions on the distribution of the pore pressure in soil layers and consolidation rate is also discussed. An analysis on field measurements in Ningbo subway line 1 is presented to demonstrate the application of the proposed method. Analysis reveals that at the initial stage of the subway services, the main settlement is contributed by the consolidation settlement, which is quite considerable, about 0.5 mm per month. When the Up reach 50%, the consolidation settlement tends to stable state, then, the accumulative settlement becomes noticeable.

One-dimensional nonlinear consolidation behavior of structured soft clay under time-dependent loading

This research investigated the nonlinear compressibility, permeability, the yielding due to structural degradation and their effects on consolidation behavior of structured soft soils. Based on oedometer and hydraulic conductivity test results of natural and reconstituted soft clays, linear log (1+e) ~ log sigma\'v and log (1+e) ~ log kv relationships were developed to capture the variations in compressibility and permeability, and the yield stress ratio (YSR) was introduced to characterize the soil structure of natural soft clay. Semi-analytical solutions for one-dimensional consolidation of soft clay under time-dependent loading incorporating the effects of soil nonlinearity and soil structure were proposed. The semi-analytical solutions were verified against field measurements of a well-documented test embankment and they can give better accuracy in prediction of excess pore pressure compared to the predictions using the existing analytical solutions. Additionally, parametric studies were conducted to analyze the effects of YSR, compression index (lambda_r and lambda_c), and permeability index (eta_k) on the consolidation behavior of structured soft clays. The magnitude of the difference between degree of consolidation based on excess pore pressure (Up) and that based on strain (Us) depends on YSR. The parameter lamda_c/eta_k plays a significant role in predicting consolidation behavior.