Analytical solution to 1D coupled water infiltration and deformation in two‐layer unsaturated soils

An analytical solution to 1D coupled water infiltration and deformation in layered soils is derived using a Laplace transformation. Coupling between seepage and deformation, and initial conditions defined by arbitrary continuous pore‐water pressure distributions are considered. The analytical solutions describe the transient pore‐water pressure distributions during 1D, vertical infiltration toward the water table through two‐layer unsaturated soils. The nonlinear coupled formulations are first linearized and transformed into a form that is solvable using a Laplace transformation. The solutions provide a reliable means of comparing the accuracy of various numerical methods. Parameters considered in the coupled analysis include the saturated permeability (k_s), desaturation coefficient (α), and saturated volumetric water content (θ_s) of each soil layer, and antecedent and subsequent rainfall infiltration rates. The analytical solution demonstrates that the coupling of seepage and deformation plays an important role in water infiltration in layered unsaturated soils. A smaller value of α or a smaller absolute value of the elastic modulus of the soil with respect to a change in soil suction (H) for layered unsaturated soils means more marked coupling effect. A smaller absolute value of H of the upper layer soil also tends to cause more marked coupling effect. A large difference between the saturated coefficients of permeability for the top and bottom soil layers leads to reduced rainfall infiltration into the deep soil layer. The initial conditions also play a significant role in the pore‐water pressure redistribution and coupling effect. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical analysis of seepage–deformation in unsaturated soils

A coupled elastic–plastic finite element analysis based on simplified consolidation theory for unsaturated soils is used to investigate the coupling processes of water infiltration and deformation. By introducing a reduced suction and an elastic–plastic constitutive equation for the soil skeleton, the simplified consolidation theory for unsaturated soils is incorporated into an in-house finite element code. Using the proposed numerical method, the generation of pore water pressure and development of deformation can be simulated under evaporation or rainfall infiltration conditions. Through a parametric study and comparison with the test results, the proposed method is found to describe well the characteristics during water evaporation/infiltration into unsaturated soils. Finally, an unsaturated soil slope with water infiltration is analyzed in detail to investigate the development of the displacement and generation of pore water pressure.     

A simple analytical solution to one‐dimensional consolidation for unsaturated soils

This paper presents a simple analytical solution to Fredlund and Hasan's one‐dimensional (1‐D) consolidation theory for unsaturated soils. The coefficients of permeability and volume change for unsaturated soils are assumed to remain constant throughout the consolidation process. The mathematical expression of the present solution is much simpler compared with the previous available solutions in the literature. Two new variables are introduced to transform the two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved with standard mathematical formulas. It is shown that the present analytical solution can be degenerated into that of Terzaghi consolidation for fully saturated condition. The analytical solutions to 1‐D consolidation of an unsaturated soil subjected to instantaneous loading, ramp loading, and exponential loading, for different drainage conditions and initial pore pressure conditions, are summarized in tables for ease of use by practical engineers. In the case studies, the analytical results show good agreement with the available analytical solution in the literature. The consolidation behaviors of unsaturated soils are investigated. The average degree of consolidation at different loading patterns and drainage conditions is presented. The pore‐water pressure isochrones for two different drainage conditions and three initial pore pressure distributions are presented and discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

成层非饱和土渗流的耦合解析解

成层土在工程中很常见,研究降雨过程中成层非饱和土的渗流-变形耦合对非饱和土土力学的发展具有重要的意义。由流体质量守恒,Darcy定律和Lloret等的非饱和土本构模型可得成层非饱和土渗流-变形耦合的控制方程。采用Gardner的非饱和土的渗透系数公式以及Boltzman模型,基于Laplace变换得到耦合方程的解析解。解析及其参数分析表明,渗流和变形耦合是具有时间效应的。与吸力变化相关的土的模量F,对成层土的孔隙水压力分布有明显影响。两层土的F差异越大,孔隙水压力消散得越慢,耦合效应越不显著。增大表层土的F值有利于降低耦合效应。成层土饱和体积含水率变化对吸力变化产生有限的影响     

Experimental study of steady seepage in unsaturated loess soil

The complexity of unsaturated soil means that its permeability coefficient and seepage law are important topics in soil mechanics and geotechnical engineering. In this study, a new type of equipment for measuring the seepage of unsaturated soil was used to study the steady seepage of unsaturated loess soil collected from northern Shaanxi province in China. The entire process of the steady seepage of unsaturated soil under different seepage hydraulic gradients was obtained, and the permeability coefficient in the steady seepage state was measured. When the soil water content was low, the soil moisture remained only in small pores or at the junction of soil particles, the effective seepage area of the sample was reduced, and the seepage path was extended. Therefore, the lower the water content, the smaller the permeability coefficient of unsaturated soil and the longer the time required for the seepage to reach a steady state. The matric suction of the unsaturated loess soil was measured under different water contents. With decreasing water content, water remained only in the smaller pores, which provided shrink films with a smaller radius of curvature. This allowed the shrink films to withstand a larger pore air pressure and transmit a smaller pore water pressure, so that the matric suction of the loess soil increased with decreasing soil water content. The Gardner model provided an accurate fit of how the matric suction varied with the volumetric water content of the unsaturated soil. The seepage velocity and seepage hydraulic gradient were correlated well with a linear relationship, indicating that the seepage law of unsaturated loess soil accords with Darcy’s law. The experimental results show that the new unsaturated soil permeameter has good performance and controllability, thereby providing support for studying the steady seepage of unsaturated soil.

     

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory,implementation, and application

Although numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F²Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical analysis of a one‐dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method

A multiphase coupled elasto‐viscoplastic finite element analysis formulation, based on the theory of porous media, is used to describe the rainfall infiltration process into a one‐dimensional soil column. Using this framework, we have numerically analyzed the generation of pore water pressure and deformations when rainfall is applied to the soil. A parametric study, including rainfall intensity, soil–water characteristic curves, and permeability, is carried out to observe their influence on the changes in pore water pressure and volumetric strain. From the numerical results, it is shown that the generation of pore water pressure and volumetric strain is mainly controlled by material parameters α and n′ that describe the soil–water characteristic curve. A comparison with the laboratory results shows that the proposed method can describe very well the characteristics observed during the experiments of one‐dimensional water infiltration into a layered unsaturated soil column. Copyright © 2010 John Wiley & Sons, Ltd.     

膨胀土边坡非饱和渗流及渐进性破坏耦合分析

膨胀土边坡受降雨影响产生膨胀变形,是典型的非饱和土多场耦合问题。为探究降雨入渗对其渐进性破坏的失稳过程,基于饱和-非饱和渗流理论、膨胀土弹塑性本构关系和应变软化理论,利用应变软化模型、FLAC3D二次开发平台和内置FISH语言,提出了一种综合考虑非饱和渗流、膨胀变形和应变软化的多场耦合数值分析法。结合工程实例,通过该方法探讨了降雨入渗条件下膨胀土边坡非饱和渗流、位移响应及渐进性破坏的变化规律。结果表明：膨胀变形和应变软化受控于非饱和渗流的时空分布,对边坡位移响应过程影响显著,也易导致饱和-非饱和分界带形成剪应力集中区。膨胀土边坡渐进性破坏由局部破坏转变为整体性失稳,其塑性破坏区首先随悬挂型暂态饱和区的变化向坡内扩展,雨后逐渐形成第二条由坡脚向坡顶扩展的滑动带,呈现出多重滑动性和后退牵引式的破坏特征。     

Implementation of a hydromechanical elastoplastic constitutive model for fully coupled dynamic analysis of unsaturated soils and its validation using centrifuge test results

Prediction of unsaturated soil behavior during earthquake loading has received increasing attention in geotechnical engineering research and practice in recent years. Development of a fully coupled analysis procedure incorporating a coupled hydromechanical elastoplastic constitutive model for dynamic analysis of unsaturated soils has, however, been limited. This paper presents the implementation of a coupled hydromechanical elastoplastic constitutive model into a fully coupled dynamic analysis procedure and its validation using a centrifuge test. First, the fully coupled finite element equations governing the dynamic behavior of unsaturated soils with the solid skeleton displacement, pore water pressure, and pore air pressure as nodal unknowns are briefly presented. The closest point projection method is then utilized to implement the coupled hydromechanical elastoplastic constitutive model into the finite element equations. The constitutive model includes hysteresis in soil–water characteristic curves, cyclic elastoplasticity of the solid skeleton, and the coupling mechanisms between the SWCCs and the solid skeleton. Finally, the analysis procedure is validated using the results from a dynamic centrifuge test on an embankment constructed of compacted unsaturated silt subjected to base shaking. Reasonable comparisons between the predicted and measured accelerations, settlements, and deformed shapes are obtained.

     

非饱和土入渗的数值模拟

入渗引起土中孔隙水压力的变化,是影响非饱和土性状的最重要的原因之一。因此,正确地分析和模拟非饱和土入渗过程具有重要意义。通过对一维和二维降雨入渗问题的研究,展示了湿润锋面、地下水位面及孔隙水压力分布随时间的变化,使得对入渗问题的认识更加直观和清楚。     

An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis

Surficial slope failures in residual soils are common in tropical and subtropical regions as a result of rainfall infiltration. This study develops an analytical solution for simulating rainfall infiltration into an infinite unsaturated soil slope. The analytical solution is based on the general partial differential equation for water flow through unsaturated soils. It can accept soil–water characteristic curve and unsaturated permeability function of the exponential form into account. Numerical simulations are conducted to verify the assumptions of the analytical solution and demonstrate that the proposed analytical solution is acceptable for the coarse soils with low air entry values. The pore‐water pressure (pwp) distributions obtained from the analytical solution can be incorporated into a limit equilibrium method to do infinite slope stability analysis for a rain‐induced shallow slip. The analysis method takes into account the influence of the water content change on unit weight and hence on factor of safety. A series of analytical parametric analyses have been performed using the developed model. The analyses indicate that when the residual soil slope, consisting of a completely decomposed granite layer underlain by a less permeable layer, is subjected to a continuous heavy rainfall, the loss of negative pwp and the reduction in factor of safety were found to be most significant for the shallow soil layer and during the first 12 h. The antecedent and subsequent rainfall intensity, depth of a less permeable layer and slope angle all have a significant influence on the pwp response and hence the slope stability. Copyright © 2012 John Wiley & Sons, Ltd.     

Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Limitations of suction‐controlled triaxial tests in the characterization of unsaturated soils

Behavior of unsaturated soils is influenced by many factors, and the influences of these factors are usually coupled together. Suction‐controlled triaxial (SCTX) tests are considered to allow researchers to investigate influences of individual variables on unsaturated soils under specified stress path with controls of stresses, pore water, and air pressures. In the past 50 years, SCTX testing method has been established as a standard approach to characterize constitutive behavior of unsaturated soils. Most important concepts for modern unsaturated soil mechanics were developed upon results from the SCTX tests. Among these, one of the most important contributions in the constitutive modeling of elasto‐plastic behavior for unsaturated soils is the Barcelona basic model (BBM) proposed by Alonso et al. in 1990. The BBM successfully explained many features of unsaturated soils and received extensive acceptance. However, the SCTX tests are designed based upon the divide‐and‐conquer approach in which an implicit assumption is used: soil behavior is stress‐path independent. However, it is well‐established that unsaturated soil behavior is elasto‐plastic and stress‐path dependent. It is found that the SCTX tests in fact cannot control the stress path of an unsaturated soil during loading. This incapability, in combination with complicated loading/collapse behavior of unsaturated soils, makes the SCTX tests for characterizing unsaturated soil questionable. This paper discusses the limitations of the SCTX tests in the characterization of unsaturated soils. A possible solution to the problem was proposed based on a newly developed modified state surface approach. The discussions are limited for isotropic conditions. Copyright © 2015 John Wiley & Sons, Ltd.     

A bounding surface model for unsaturated soils considering the microscopic pore structure and interparticle bonding effect due to water menisci

The interparticle bonding effect due to water menisci plays an important role in the hydromechanical coupling properties of unsaturated soils. This paper presents an unsaturated hydromechanical coupling model that considers the influence of matric suction, degree of saturation, and microscopic pore structure on the interparticle bonding effect. The enhanced effective stress and bonding variable are selected as constitutive variables. The bonding variable is correlated with the ratio between unsaturated void ratio and saturated void ratio. The deformation characteristics of unsaturated soils are described based on the bounding surface plasticity theory. A soil–water characteristic model that considers deformation and hydraulic hysteresis is integrated into the constitutive model to achieve hydromechanical coupling. The proposed model can effectively describe the hydromechanical coupling characteristics and the meniscus bonding force of unsaturated bimodal structure soils; the model parameters can be easily obtained through routine experiments. The experimental results of unsaturated isotropic compression, the wetting/drying cycle, and unsaturated triaxial shear tests are used to validate the capability of the proposed model.

     

非稳定渗流条件下非饱和土质边坡稳定性的矢量和分析法研究

研究可以同时考虑渗流、变形与稳定的非饱和土质边坡稳定性分析方法具有重要的理论意义及工程实用价值。基于Fredlund双应力变量理论进行非饱和非稳定渗流-应力耦合分析,同时与传统非耦合渗流方法确定的孔压场进行对比发现,两种方法确定的浸润线变化过程相近,堤底处孔压的最大相对误差为8.8%,验证了耦合分析结果的可靠性。将基质吸力对强度的贡献纳入黏聚力中得到坡体强度参数的空间分布规律,又基于滑面强度参数时空分布规律借助Matlab平台开发了非稳定渗流条件下非饱和土质边坡稳定性的矢量和法分析程序。以库水位下降条件下堤坡的稳定性分析为例,将不同方法的计算结果进行对比,发现文中方法搜索得到的滑面位置相对于传统方法要深缓,但总体位置相差不大,不同方法对应的安全系数相差不足0.096,验证了所提方法的合理性。     

Incorporating hydro-mechanical coupling in an analysis of the effects of rainfall patterns on unsaturated soil slope stability

Rainfall-induced landslides can cause loss of life and damage to property, infrastructure, and the environment. Rainfall patterns affect the pore-water pressure of unsaturated soil slopes, and are related to the slopes’ stability. Four rainfall patterns were chosen to represent natural rainfall patterns for an examination of rainfall infiltration into soil slopes using numerical models incorporating coupled water infiltration and deformation in unsaturated soils. Our analysis showed that rainfall patterns play a significant role in the distribution of the pore-water pressure in soil slopes, and influence the slope stability. The pore-water pressure profile of soil slopes and the factor of safety are affected by the ratio of rainfall intensity and the coefficient of permeability. The depth and shape of the shallow sliding plane of the landslide is closely related to the rainfall pattern; moreover, the results showed a correlation between the factor of safety of the slope and the rainfall intensity. This relationship can be described by a dimensionless rainfall intensity. The nonlinear relationship can be used to estimate the slope stability resulting from rainfall infiltration when the hydro-mechanical coupling in unsaturated soil slopes is considered.     

Numerical analysis on seepage failures of dike due to water level-up and rainfall using a water–soil-coupled smoothed particle hydrodynamics model

For seepage failures of dike due to water level-up and rainfall, surface infiltration and strength change induced by suction reduction are important factors; thus, numerical analysis should consider the coupling of water and soil, as well as the effect of saturation to obtain more precise failure mechanism. Based on the advanced smoothed particle hydrodynamics (SPH) method, this work proposed a two-phase-coupled SPH model in coordination with a novel constitutive model for unsaturated soils. Then, a triaxial compression test is simulated to check the applicability of the SPH method on the soil phase. After that, the failure test of a dike due to water level-up is discretized and simulated, from which the seepage process, the distribution of maximum shear strain, the slip surface, and pore water pressure are obtained. The two-phase-coupled SPH model is also applied to a slope failure test of heavy rainfall, and the results are compared to the model test. Finally, a dike failure test due to rainfall is analyzed using the proposed SPH model to reproduce the surface infiltration and suction reduction. The proposed SPH model provides several insights of seepage failures and can be a helpful tool for the analysis of dike failures induced by water level-up and rainfall.     

Time‐scale analysis in unsaturated porous media under external wave loads

Extreme waves caused by tsunamis and storm surges can lead to soil failures in the near‐shore region, which may have severe impact on coastal environments and communities. Multiphase flows in deformable porous media involve several coupled processes and multiple time scales, which are challenging for numerical simulations. The objective of this study is to investigate the roles of the various processes and their interactions in multiphase flows in unsaturated soils under external wave loading, via theoretical time‐scale analysis and numerical simulations. A coupled geomechanics–multiphase flow model based on conservation laws is used. Theoretical analysis based on coupled and decoupled models demonstrates that transient and steady‐state responses are governed by pore pressure diffusion and saturation front propagation, respectively, and that the two processes are essentially decoupled. Numerical simulations suggest that the compressibility of the pore fluids and the deformation of the soil skeleton are important when the transient responses of the media are of concern, while the steady‐state responses are not sensitive to these factors. The responses obtained from the fully coupled numerical simulations are explained by a simplified time‐scale analysis based on coupled and decoupled models. Copyright © 2010 John Wiley & Sons, Ltd.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled transient saturated–unsaturated seepage and limit equilibrium analysis for slopes: influence of rapid water level changes

This study investigates the influence of the water level fluctuation on the stability of soil slopes using coupled seepage and slope stability analysis. A simulation framework was proposed and implemented seamlessly using Python code to seek insights into three factors that have not been thoroughly studied for this issue: soil unit weight variation in the unsaturated zone, unsaturated shear strength models, and velocity of water drawdown. For this purpose, the seepage analysis was carried out by discretizing a numerical seepage analysis model using a finite element analysis platform, FEniCS. The output of the seepage analysis, i.e., pore water pressure distribution, was used as input for the slope stability analysis. Limit equilibrium methods including the Bishop Simplified method and the Ordinary Method of Slices were modified to take into consideration the unsaturated shear strength, unit weight variation in the unsaturated zone, and hydrostatic pressure changes in response to the water level fluctuation of a reservoir. Both seepage and slope analysis modules were validated against commercial programs. Analysis results obtained with the validated framework clearly revealed the distinct influences of the three factors in representative silty and sandy slopes.