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.     

Revisiting the thermodynamics of hardening plasticity for unsaturated soils

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.     

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.     

Finite element modelling of transport of organic chemicals through soils

Aquifer contamination by organic chemicals in subsurface flow through soils due to leaking underground storage tanks filled with organic fluids is an important groundwater pollution problem. The problem involves transport of a chemical pollutant through soils via flow of three immiscible fluid phases: namely air, water and an organic fluid. In this paper, assuming the air phase is under constant atmospheric pressure, the flow field is described by two coupled equations for the water and the organic fluid flow taking interphase mass transfer into account. The transport equations for the contaminant in all the three phases are derived and assuming partition equilibrium coefficients, a single convective – dispersive mass transport equation is obtained. A finite element formulation corresponding to the coupled differential equations governing flow and mass transport in the three fluid phase porous medium system with constant air phase pressure is presented. Relevant constitutive relationships for fluid conductivities and saturations as function of fluid pressures lead to non-linear material coefficients in the formulation. A general time-integration scheme and iteration by a modified Picard method to handle the non-linear properties are used to solve the resulting finite element equations. Laboratory tests were conducted on a soil column initially saturated with water and displaced by p-cymene (a benzene-derivative hydrocarbon) under constant pressure. The same experimental procedure is simulated by the finite element programme to observe the numerical model behaviour and compare the results with those obtained in the tests. The numerical data agreed well with the observed outflow data, and thus validating the formulation. A hypothetical field case involving leakage of organic fluid in a buried underground storage tank and the subsequent transport of an organic compound (benzene) is analysed and the nature of the plume spread is discussed.     

Assesing the effect of an olive mill wastewater evaporation pond in Sousse, Tunisia

Olive oil is a typical and valuable agro-industrial product in Mediterranean countries. In Tunisia, olive mill wastewaters (OMW) reach an amount of about 1,000,000 t year⁻¹ and constitute a serious organic pollution risk because of the high chemical oxygen demand values and the presence of phytotoxic and antibacterial polyphenols. OMW have been generally stored in pond sites to be eliminated by natural evaporation or valorised by spreading on cultivated soils or by composting. Many researches on the interactions of OMW with soils at laboratory scale (columns) have been reported, but less attention have been paid to the effect of OMW on soils at field scale. The aim of this work is to investigate an area used for >15 years as an uncontrolled OMW pond site. The transformations of soil properties and groundwater occurring during OMW storage were characterised by the pH, phenolic contents, electrical conductivity (EC), moisture content and organic contents. The soil samples were taken from two borings and compared to those of a control one located near the pond site. Groundwater samples were taken on the accessible and nearest water wells to the evaporation ponds. The permeable silty and sandy layers in the site support the infiltration of OMW near the evaporation ponds. This infiltration has reached a depth of 6 m at a distance of almost 50 m laterally. The results show that the OMW infiltration in the subsoil has affected the pH, EC, organic content, phenolic compounds and the moisture.     

Slope stability analysis on a regional scale using GIS: a case study from Dhading,Nepal

A spatially distributed physically based slope stability model combined with a hydrological model is presented and applied to a 350-km² area located in Dhading district, Nepal. Land slide safety factor maps are generated for five cases, including three steady state conditions assuming either completely dry soils, half saturated soils, or fully saturated soils, and two quasi-dynamic conditions, i.e. soil wetness resulting from storm events with, respectively a 2 or 25-year return period. For the quasi-dynamic cases, two methods are used, one based on accumulation of groundwater flow from upstream areas, and the other on accumulation of soil water from direct infiltration. The methodology delineates areas most prone to shallow land sliding in function of readily available data as topography, land-use and soil types. For the study area only 29% of the soils are unconditionally stable, while 25% of the soils are found to be unstable under fully saturated conditions. The comparison between the methods based on contributing area or on infiltration for quasi-dynamic conditions show that the approach based on infiltration is more reliable for the study area. The proposed methodology for predicting landslide susceptibility on a regional scale, based on basic data in GIS form, may be useful for other remote regions where detailed information is not available.     

Unsaturated structured soils: constitutive modelling and stability analyses

The paper presents a new single-surface elasto-plastic model for unsaturated cemented soils, formulated within the critical state soil mechanics framework, which should be considered as an extension to unsaturated conditions of a recently proposed constitutive law for saturated structured soils. The model has been developed with the main purpose of inspecting the mechanical instabilities induced in natural soils by bond degradation resulting from the accumulation of plastic strains and/or the changes in pore saturation. At this scope, the constitutive equations are used to simulate typical geotechnical testing conditions, whose results are then analysed in light of the controllability theory. The results of triaxial tests on an ideal fully saturated cemented soil and on the corresponding unsaturated uncemented one are first discussed, aiming at detecting the evidence of potentially unstable conditions throughout the numerical simulations. This is followed by similar analyses considering the combined effects of both the above features. For each analysed case, a simple analytical stability criterion is proposed and validated against the numerical results, generalizing the results, and highlighting the crucial role of state variables and model parameters on the possible occurrence of failure conditions.

     

Dynamics of unsaturated soils using various finite element formulations

Unsaturated soils are three‐phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress–strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydro‐mechanical response of collapsible soils under different infiltration events

The behavior of a partially saturated soil during surface‐water infiltration is analyzed by means of an elasto‐plastic constitutive model formulated in terms of effective stress and extended to unsaturated conditions. The model is calibrated considering laboratory‐scale experimental results under suction‐controlled conditions. The wetting process in two collapsing soils, initially loaded at in situ stresses, is simulated by imposing two different boundary conditions: surface ponding and water flow. The stress paths resulting from the imbibition process are analyzed at different points inside the layer. Copyright © 2015 John Wiley & Sons, Ltd.     

Geotechnical Facets of Active Sediments and its Bearing on Natural Hazards and Mitigation Measures: An Approach on Sediments of the Nubra Valley (Ladakh), Trans-Himalaya,India

Slope stability has been identified as a major obstacle to construction in the rapidly developing countries of Indonesia and Malaysia. In these countries, slope failure has been identified as one of the most commonly occurring natural disasters, leading to financial losses and deaths. Slope failure is often related to prolonged rainfall events where rainfall infiltration increases pore water pressure, reducing soil strength. This failure mechanism will accelerate with the existence of cracks, which are usually caused by differential settling, drying and shrinking of soil, and associated construction activities, among other causes. The existence of cracks on slopes usually provides an easy pathway for rainfall infiltration into soil, allowing rain to infiltrate to deeper layers than in the absence of cracks. The moisture content in deep layers is therefore higher in cracked slopes than in slopes without cracks. To address this issue, we investigated the effects of cracks on slope stability when subjected to rainfall. The influence of crack location, depth, size, and direction on pore water pressure distribution and slope stability was studied by imposing different rainfall intensities. Analysis of seepage and stability were conducted using the GEO STUDIO 2007 softwares SEEP/W and SLOPE/W. Results suggested that pore water pressure and slope stability were influenced by the existence of cracks. Analysis showed that slope factors of safety decreased sharply when cracks were located adjacent to the slope crest, as compared to when cracks were located in the middle of the slope. Furthermore, slope factors of safety decreased with increasing crack depth. Pore water pressure and slope factors of safety decreased further when slopes were subjected to small rainfall intensities for long periods, as compared to when slopes were subjected to high rainfall intensities for short periods. The present study shows that study of cracks should be an integral part of the slope stability analysis.     

Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns

Rainfall infiltration poses a disastrous threat to the slope stability in many regions around the world. This paper proposes an extreme gradient boosting (XGBoost)-based stochastic analysis framework to estimate the rainfall-induced slope failure probability. An unsaturated slope under rainfall infiltration in spatially varying soils is selected in this study to investigate the influences of the spatial variability of soil properties (including effective cohesion c′, effective friction angle φ′ and saturated hydraulic conductivity k_s), as well as rainfall intensity and rainfall pattern on the slope failure probability. Results show that the proposed framework in this study is capable of computing the failure probability with accuracy and high efficiency. The spatial variability of k_s cannot be overlooked in the reliability analysis. Otherwise, the rainfall-induced slope failure probability will be underestimated. It is found that the rainfall intensity and rainfall pattern have significant effect on the probability of failure. Moreover, the failure probabilities under various rainfall intensities and patterns can be easily obtained with the aid of the proposed framework, which can provide timely guidance for the landslide emergency management departments.     

Modelling landslides in unsaturated slopes subjected to rainfall infiltration using material point method

This paper presents a dynamic fully coupled formulation for saturated and unsaturated soils that undergo large deformations based on material point method. Governing equations are applied to porous material while considering it as a continuum in which the pores of the solid skeleton are filled with water and air. The accuracy of the developed method is tested with available experimental and numerical results. The developed method has been applied to investigate the failure and post‐failure behaviour of rapid landslides in unsaturated slopes subjected to rainfall infiltration using two different bedrock geometries that lie below the top soil. The models show different failure and post‐failure mechanisms depending on the bedrock geometry and highlight the negative effects of continuous rain infiltrations. Copyright © 2016 John Wiley & Sons, Ltd.     

Explicit meshfree solution for large deformation dynamic problems in saturated porous media

In this paper a new methodology to simulate saturated soils subjected to dynamic loadings under large deformation regime (locally up to 40% in equivalent plastic strain) is presented. The coupling between solid and fluid phases is solved through the complete formulation of the Biot’s equations. The additional novelty lies in the employment of an explicit time integration scheme of the \(u-w\) (solid displacement–relative fluid displacement) formulation which enables us to take advantage of such explicit schemes. Shape functions based on the principle of maximum entropy implemented in the framework of Optimal Transportation Meshfree schemes are utilized to solve both elastic and plastic problems.     

Numerical investigation of rainfall-induced fines migration and its influences on slope stability

Rainfall-infiltration-induced fines migration within soil slopes may alter the local porosity and hydraulic properties of soils, and is known to be a possible cause of the failure of slopes. To investigate the intrinsic mechanisms, a mathematical formulation capable of capturing the main features of the coupled unsaturated seepage and fines migration process has been presented. Within the formulation, an unsaturated erodible soil is treated as a three-phase multi-species porous medium based on mixture theory; mass conservation equations with mass exchange terms together with the rate equations controlling fines erosion and deposition processes are formulated as the governing equations and are solved by the FEM method. The influences of both the fines detachment and deposition on the stability of slopes under rainfall infiltration have been investigated numerically. The results show that depending on whether the fines move out or get captured at pore constrictions, both desired and undesired consequences may arise out of the fines migration phenomenon. It is suggested that more attention should be paid to those slopes susceptible to internal erosion whose safety analysis cannot be predicted by traditional methods.     

An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure

The method of smoothed particle hydrodynamics (SPH) has recently been applied to computational geomechanics and has been shown to be a powerful alternative to the standard numerical method, that is, the finite element method, for handling large deformation and post‐failure of geomaterials. However, very few studies apply the SPH method to model saturated or submerged soil problems. Our recent studies of this matter revealed that significant errors may be made if the gradient of the pore‐water pressure is handled using the standard SPH formulation. To overcome this problem and to enhance the SPH applications to computational geomechanics, this article proposes a general SPH formulation, which can be applied straightforwardly to dry and saturated soils. For simplicity, the current work assumes hydrostatic pore‐water pressure. It is shown that the proposed formulation can remove the numerical error mentioned earlier. Moreover, this formulation automatically satisfies the dynamic boundary conditions at a submerged ground surface, thereby saving computational cost. Discussions on the applications of the standard and new SPH formulations are also given through some numerical tests. Furthermore, techniques to obtain the correct SPH solution are also proposed and discussed throughout. As an application of the proposed method, the effect of the dilatancy angle on the failure mechanism of a two‐sided embankment subjected to a high groundwater table is presented and compared with that of other solutions. Finally, the proposed formulation can be considered a basic formulation for further developments of SPH for saturated soils. Copyright © 2011 John Wiley & Sons, Ltd.     

裂隙性膨胀土饱和-非饱和渗流分析

降雨入渗条件下的裂隙性膨胀土边坡稳定性与其渗流场分布密切相关,对渗流分析中的积水深度进行了数值模拟,结果显示,不同的积水深度对渗流场的影响很小,因此,在进行裂隙性膨胀土渗流分析时,积水深度为0的假定是可以接受的。基于膨胀土开裂裂隙的规模及渗透性的不同,提出了考虑裂隙系统的膨胀土边坡渗流分析方法,计算结果表明,土体开裂显著改变了膨胀土内部的渗流场分布。该方法可以更好地模拟坡渗流场随时间的变化规律,以及更合理地解释了降雨入渗引起的膨胀土边坡浅层滑动机制。     

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.     

基于非饱和渗流的水库库岸滑坡稳定性计算

三峡水库蓄水后,库水位涨落和降雨入渗是导致滑坡的主要因素。本文以秭归县下土地岭滑坡为例,在一个水文年内根据库区水位调控方案并考虑库区降雨情况,运用非饱和土力学的渗流和抗剪强度理论,对滑坡稳定性进行了分析,得出在库水位涨落和降雨条件下滑坡渗流和稳定性的变化规律,对库区滑坡稳定性评价和治理有一定的指导作用。     

Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments

Spatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required. Copyright © 2011 John Wiley & Sons, Ltd.     

Water characteristic curve of soil with bimodal grain-size distribution

Soil–water characteristic curve (SWCC) is the most fundamental and important soil property in unsaturated soil mechanics. It has been used for analyzing slope stability due to the infiltration of rainfall into slopes and water flow in unsaturated embankments. Generally, SWCC is obtained by laboratory tests. However high cost, long duration and difficulty of the tests impede the application of unsaturated soil mechanics to practical design or analysis. Therefore, several equations have been developed to predict the SWCC using grain-size distribution (GSD) curve. However, most of the equations were limited to soils with unimodal characteristics and the parameters of the equations are not related to the physical properties of the soil. In this paper, an equation to predict SWCC for soils with bimodal characteristics is proposed. The parameters of the proposed equation are related to the physical properties of soil and the variables of SWCC closely. The proposed equation is evaluated with data from the literature and laboratory tests carried out in this study. In addition, the computer codes for the computation of the predicted bimodal SWCC are presented.