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.     

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

An analytical solution to 1D coupled water infiltration and deformation is derived using a Fourier integral transform. Exponential functional forms are used to represent the hydraulic conductivity–pore‐water pressure relationship and the soil‐water characteristic curve. Fredlund's incremental‐linear constitutive model for unsaturated soils is adopted. The analytical solution considers arbitrary initial pore‐water pressure distributions and flux and pressure boundary conditions. The corresponding analytical solutions to coupled steady‐state problems are also obtained. The analytical solutions demonstrate that the coupling of seepage and deformation plays an important role in water infiltration in unsaturated soils. In the early stages of infiltration, the difference between uncoupled and coupled conditions becomes marked over time, and in late stages, the difference caused by the coupling effects diminishes toward the steady state. The difference between the uncoupled and coupled conditions increases with decreasing desaturation coefficient (α). Pore‐water pressure or deformation changes caused by the coupling effects are mainly controlled by the degree of soil volume change due to a change in soil suction (H). The smaller the absolute value of H, the greater the effect of coupling on the infiltration and deformation. The ratio of rainfall intensity to saturated permeability (q/k_s) also has a strong influence on the coupled seepage and deformation. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of undrained cavity expansion in elasto‐plastic soils with non‐linear elasticity

A large strain analysis of undrained expansion of a spherical/cylindrical cavity in a soil modelled as non‐linear elastic modified Cam clay material is presented. The stress–strain response of the soil is assumed to obey non‐linear elasticity until yielding. A power‐law characteristic or a hyperbolic stress–strain curve is used to describe the gradual reduction of soil stiffness with shear strain. It is assumed that, after yielding, the elasto‐plastic behaviour of the soil can be described by the modified Cam clay model. Based on a closed‐form stress–strain response in undrained condition, a numerical solution is obtained with the aid of simple numerical integration technique. The results show that the stresses and the pore pressure in the soil around an expanded cavity are significantly affected by the non‐linear elasticity, especially if the soil is overconsolidated. The difference between large strain and small strain solutions in the elastic zone is not significant. The stresses and the pore pressure at the cavity wall can be expressed as an approximate closed‐form solution. Copyright © 2001 John Wiley & Sons, Ltd.     

降雨对滑坡稳定性影响过程分析

通过对滑坡土条的受力分析进行改进,建立起能考虑滑带内存在任意孔隙水压分布情况下的稳定性计算公式。结合Lumb入渗理论和太沙基一维固结理论得到了滑坡在降雨期间的极限稳定性计算方法,该方法能够同时考虑降雨入渗导致土体重度和滑带内孔隙水压力变化。利用上述结果,提出了某些深层滑坡触发的一种机理,并可根据常用的土质参数比较容易得到滑坡在降雨期间稳定性演化过程。通过对某滑坡分析得到,降雨导致滑体重量增加而降低滑坡稳定性小于孔隙水压增加对稳定性的影响;超孔隙水压力的存在大幅提高了剩余下滑力值。     

Stress–strain behaviour of a loosely compacted volcanic-derived soil and its significance to rainfall-induced fill slope failures

The stress–strain behaviour of a soil is crucial to the recognition of the mechanism of slope failure. Triaxial tests, composed of isotropically consolidated drained (ICD) and undrained compression (ICU) tests and anisotropically consolidated constant deviatoric stress path (CQD) tests, were carried out with the aim of investigating the stress–strain behaviour of loosely compacted volcanic-derived soils. The fact that the critical states are the same for ICU, ICD and CQD tests may show that the critical state is independent of the above three stress paths. The critical state line, as defined in critical state soil mechanics, is obtained from the e–log p′ and q–p′ plots based on the results of the above tests. The initial state of the consolidated specimens at initiation of failure may be classified as dilative or contractive in the light of the locations of the soil state relative to the critical state line. For contractional soils, the increased pore water pressure generated by rainfall infiltration leads to a contractive failure in a drained manner, giving rise to high excess pore water pressure. The excess pore water pressure caused by contraction cannot be dissipated instantly, resulting in a decrease in the shear resistance of the soil. The failure process is rapid. The failed soil mass is prone to flow after failure under the action of gravity due to its high moisture content and inflow of surface runoff and rainwater. For dilational soils, the increased pore water pressure resulting from infiltration leads to dilation, which reduces pore water pressure and thus increases the shear resistance of the soil. However, continued rainfall infiltration may be able to equilibrate the reduction in pore water pressure caused by dilation and, therefore, the dilation or displacement can continue. In Hong Kong, volcanic-derived soil is characterized by high permeability. Both the high permeability of volcanic-derived soil and a shallow failure surface make it possible for the reduction in pore pressure to equilibrate relatively quickly. Therefore, the failure is also rapid, at least for poorly compacted fill slopes.     

降雨形式对毛细阻滞覆盖层防渗性能的影响研究

毛细阻滞覆盖层的防渗性能对于控制渗滤液和减轻垃圾填埋场周边环境的污染具有重要意义,因此得到广泛研究。前人在研究中多采用恒定降雨强度来模拟降雨气象条件,而对降雨形式对毛细阻滞覆盖层防渗性能的影响关注较少。因此,采用自主研发的土柱降雨入渗试验系统,分别对短时强降雨和长时弱降雨两种降雨情况下,降雨形式对毛细阻滞覆盖层防渗性能的影响开展了研究,并揭示了最不利降雨形式。同时,采用SEEP/W软件对各试验工况进行数值模拟,以使模拟结果与试验结果能够相互印证。研究结果表明：试验结果与模拟结果基本一致,最大误差不大于3%;在短时强降雨情况下,降雨形式仅对覆盖层上部的体积含水率和孔隙水压力有较大影响;而在长时弱降雨条件下,降雨形式对整个覆盖层的体积含水率和孔隙水压力均有显著影响;降雨形式对覆盖层突破时间及渗漏量均有影响,前锋型降雨的突破时间最短,产生的渗漏量最大,后锋型降雨的突破时间最长,产生的渗漏量最小;前锋型降雨更易造成覆盖层突破失效而产生较大的渗漏量,为最不利降雨形式。该研究结果可为毛细阻滞覆盖层设计提供参考依据。     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

降雨诱发堆积体滑坡水土响应与稳定性时空演化试验研究

降雨在松散堆积土中入渗引起内部水土力学的变化是影响稳定性的关键。目前研究多侧重考虑颗粒粒径、含量等因素对斜坡破坏的影响,但是针对斜坡体内部水土响应及稳定性时空演化方面的研究存在不足。基于野外滑坡案例,通过室内降雨滑坡模型试验、土力学试验和理论分析手段,研究了降雨触发松散堆积体斜坡变形破坏过程及模式,采用Van Genuchten模型（VG模型）重构了土体的土-水特征曲线,重点探究了斜坡内部水土力学变化以及稳定性时空演化规律。结果表明：（1）堆积体斜坡破坏经历了微裂隙发育-局部破坏-整体破坏3个阶段,呈现出“初期拉裂-坡面坍塌-塑性滑动”的破坏模式;（2）入渗过程斜坡体积含水率以及孔隙水压力急速增加,而土颗粒之间基质吸力下降甚至消散,促进了斜坡破坏发展;（3）土体力学强度随体积含水率升高呈指数下降,体积含水率为36.3%时,有效黏聚力和有效内摩擦角仅为0.27 kPa、3.39°;（4）基于极限平衡理论和斜坡土水特征监测数据,构建了斜坡稳定性时空演化图谱,与模型试验破坏特征有较好的一致性。研究结果对降雨作用下的堆积层斜坡监测预警与防灾减灾提供理论支撑。     

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.     

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.     

Analysis of soil consolidation by vertical drains with double porosity model

The soil around a drain well is traditionally divided into smeared zone and undisturbed zone with constant hydraulic conductivity. In reality, hydraulic conductivity of the soil changes continuously and it may not be always appropriate to approximate its distribution with two zones. In this study, the horizontal hydraulic conductivity of the soil is described by an arbitrary function of radial distance. The horizontal flow under equal strain condition is analysed for a soil–drain system with a circular or regular polygonal boundary. It is found that the horizontal flow can be generally characterized with a linear equation in which the flow rate of water through soil–drain interface is proportional to the difference between the average excess pore pressure in the soil and the excess pore pressure in the drain well. The water exchange between the drain and the soil is analogous to that between fractures and matrix in a double porosity system, a popular conceptual model of fracture rocks. On the basis of this characterization, a simplified approach to analyse soil–drain systems is developed with one‐dimensional double porosity model (DPM). Analytical solutions for both fully and partially penetrating drains are derived. The solution for partially penetrating drains is compared with both numerical and approximate analytical results in literature. Copyright © 2004 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.     

Hybrid time integration and coupled solution methods for nonlinear finite element analysis of partially saturated deformable porous media at small strain

The goal of the paper is to determine the most efficient, yet accurate and stable, finite element nonlinear solution method for analysis of partially saturated deformable porous media at small strain. This involves a comparison between fully implicit, semi‐implicit, and explicit time integration schemes, with monolithically coupled and staggered‐coupled nonlinear solution methods and the hybrid combination thereof. The pore air pressure p_a is assumed atmospheric, that is, p_a=0 at reference pressure. The solid skeleton is assumed to be pressure‐sensitive nonlinear isotropic elastic. Coupled partially saturated ‘consolidation’ in the presence of surface infiltration and traction is simulated for a simple one‐dimensional uniaxial strain example and a more complicated plane strain slope example with gravity loading. Three mixed plane strain quadrilateral elements are considered: (i) Q4P4; (ii) stabilized Q4P4S; and (iii) Q9P4; “Q” refers to the number of solid skeleton displacement nodes, and “P” refers to the number of pore fluid pressure nodes. The verification of the implementation against an analytical solution for partially saturated pore water flow (no solid skeleton deformation) and comparison between the three time integration schemes (fully implicit, semi‐implicit, and explicit) are presented. It is observed that one of the staggered‐coupled semi‐implicit schemes (SIS(b)), combined with the fully implicit monolithically coupled scheme to resolve sharp transients, is the most efficient computationally. Copyright © 2015 John Wiley & Sons, Ltd.     

A new approximation for pore pressure accumulation in marine sediment due to water waves

The residual mechanism of wave‐induced pore water pressure accumulation in marine sediments is re‐examined. An analytical approximation is derived using a linear relation for pore pressure generation in cyclic loading, and mistakes in previous solutions (Int. J. Numer. Anal. Methods Geomech. 2001; 25 :885–907; J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11) are corrected. A numerical scheme is then employed to solve the case with a non‐linear relation for pore pressure generation. Both analytical and numerical solutions are verified with experimental data (Laboratory and field investigation of wave– sediment interaction. Joseph H. Defrees Hydraulics Laboratory, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, 1983), and provide a better prediction of pore pressure accumulation than the previous solution (J. Offshore Mech. Arctic Eng. (ASME) 1989; 111 (1):1–11). The parametric study concludes that the pore pressure accumulation and use of full non‐linear relation of pore pressure become more important under the following conditions: (1) large wave amplitude, (2) longer wave period, (3) shallow water, (4) shallow soil and (5) softer soils with a low consolidation coefficient. Copyright © 2006 John Wiley & Sons, Ltd.     

Effect of wave non‐linearity on the standing‐wave‐induced seabed response

A standing wave in front of a seawall may reach a height more than twice of its incident component. When excess pore pressure occurs, it may even induce seabed instability, hence endangering the structure. This issue was studied previously using only linear wave theory. In this paper, standing‐wave theory to a second‐order approximation is applied, in order to demonstrate the differences between these two solutions. The spatial and temporal variations in the instantaneous pore pressure are first calculated, in addition to their vertical distributions. The effects of wave height, water depth and the degree of soil saturation on pore pressure distributions are then discussed, followed by the net pore pressure averaged over one wave cycle. The results suggest the existence of a residual pore pressure in the seabed and its net pore pressure can be used to estimate the wave‐induced liquefaction potential in a soil column. It also indicates that, in deep water, the second‐order solution predicts that a negative pore pressure at an antinode which may be greater than a positive pressure. Overall, the second‐order solution is found to agree better with the experimental results of the pore pressures available, compared to the linear solution. Copyright © 2000 John Wiley & Sons, Ltd.     

考虑气相影响的降雨入渗过程分析研究

降雨入渗过程是水在下渗的过程中驱替空气的水-气二相流过程,对这一过程的精确模拟一直是渗流计算的难点,目前的处理方法通常是忽略孔隙气压力变化的影响。根据多相流理论,结合质量守恒定律和达西定律,建立了水-气二相流模型,模型的求解采用积分有限差分法和Newton-Raphson迭代方法,通过变换主要变量来表达相态的变化,实现了水相、气相边界条件及降雨入渗边界的精确模拟。利用上述模型对一土柱试验进行模拟,从而验证了模型的正确性,研究了一均质土层的降雨入渗过程,得到了孔隙水压力、孔隙气压力和毛细压力及含水率的变化过程。根据入渗率与地表孔隙气压力的变化关系,验证了孔隙气压力的增大对入渗水流产生阻滞作用。在求解非稳定渗流问题中,考虑空气压力变化的影响是值得研究的。     

Monitored and simulated variations in matric suction during rainfall in a residual soil slope

This research combines field, laboratory and numerical investigations to estimate the development of a wetting front within a 1.2 m residual soil mantle on a steep forested slope during rainfall events. The field-monitored variations in matric suction due to rain-water infiltration during various events revealed that the maximum infiltration rate was much higher when the wetting front resided in the upper 20 cm of soil compared to the case when the wetting front advanced to depths > 20 cm. Laboratory investigations on soil hydraulic properties (i.e., soil water characteristic curve, and hydraulic conductivity) were useful to establish the parameters of a multilayer finite-element model for one-dimensional vertical infiltration. These parameters were subsequently calibrated by matching the predicted and field measured transient pore water pressure responses during actual rainstorms with irregular rainfall patterns. The calibrated simulation model was used to assess the migration of the wetting front under uniform rainfall with different intensities. Based on the numerical results, a hyperbolic equation was developed to predict the duration of uniform rainfall required for the propagation of wetting front to a certain depth for a given rainfall intensity. The proposed equation was subsequently tested against field-monitored advancements of the wetting front during real rainstorms with variable rainfall intensity.     

Response of a loess landslide to rainfall: observations from a field artificial rainfall experiment in Bailong River Basin,China

Rainfall-induced landslides are a significant hazard in many areas of loess-covered terrain in Northwest China. To investigate the response of a loess landslide to rainfall, a series of artificial rainfall experiments were conducted on a natural loess slope, located in the Bailong River Basin, in southern Gansu Province. The slope was instrumented to measure surface runoff, pore water pressure, soil water content, earth pressure, displacement, and rainfall. The hydrological response was also characterized by time-lapse electrical resistivity tomography. The results show that most of the rainfall infiltrated into the loess landslide, and that the pore water pressure and water content responded rapidly to simulated rainfall events. This indicates that rainfall infiltration on the loess landslide was significantly affected by preferential flow through fissures and macropores. Different patterns of pore water pressure and water content variations were determined by the antecedent soil moisture conditions, and by the balance between water recharge and drainage in the corresponding sections. We observed three stages of changing pore water pressure and displacement within the loess landslide during the artificial rainfall events: Increases in pore water pressure initiated movement on the slope, acceleration in movement resulting in a rapid decrease in pore water pressure, and attainment of a steady state. We infer that a negative pore water pressure feedback process may have occurred in response to shear-induced dilation of material as the slope movement accelerated. The process of shear dilatant strengthening may explain the phenomenon of semi-continuous movement of the loess landslide. Shear dilatant strengthening, caused by intermittent or continuous rainfall over long periods, can occur without triggering rapid slope failure.     

Correlation of unsaturated soil and dielectric property for monitoring of subsurface characteristics: development of unsaturated dielectric mixing models and its application

The behavior due to rainfall infiltrating the ground plays a role in landslides, groundwater recharge and various other ground responses. Most of these geotechnical behaviors have a correlation between soil pore space and soil volumetric water content in the unsaturated and saturated soil porous media. Therefore, the soil porosity associated with soil pores and the distribution of volumetric water content are significantly important hydrological characteristics. In the case of shallow slope failure such as landslide, the infiltration activity due to the connectivity of soil pore spaces in a porous media is induced. Slope failure may be attributed to the effect of a wetting front with the slope due to liquid infiltration, which changes the volumetric water content, soil matric suction and shear strength of the slope. This study was performed with an unsaturated injection test using a frequency domain reflectometry (FDR) dielectric device which measures the dielectric constant of unsaturated soil and the study then proposed the unsaturated dielectric mixing models to calculate soil porosity and effective porosity of unsaturated soils. From the experimental results the ratio of effective porosity to porosity of soils are measured in a range of 70–85%. These experimental results show a decrease of about 5–10% for unsaturated soil compared to the ratio of effective porosity to porosity of saturated soil. The infiltration passages of tracer material are restricted within the pore connectivity in the unsaturated soil which is caused by dead-pores in the soil. Using the FDR device and the unsaturated dielectric mixing models, we can consider the acquisition of physical properties to detect the infiltration activity, the response of the dielectric constant along with the injected tracer and hydrological parameters for the unsaturated soil porous media.