Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

A Simple Triaxial System for Evaluating the Performance of Unsaturated Soils Under Repeated Loading

Unsaturated soils constitute a large proportion of the foundation materials supporting infrastructure throughout the world and they are subject to various loading conditions. This paper describes the development of a simple system for testing unsaturated soils under repeated loading. The equipment was comprised of a modified triaxial cell with hydraulic loading system, hall-effect transducers for on-sample strain measurements, and thermocouple psychrometer for suction measurements. A number of undrained monotonic and repeated loading triaxial tests were performed on compacted samples of kaolin clay in order to attest the newly developed system. The results yielded some useful information on the resilient modulus and permanent deformation of a soil when subjected to repeated loading. There is some difference between the failure deviator stress of samples subjected to repeated and monotonic loading, though repeated loading continued to result in a significant permanent deformation. This paper is aimed at demonstrating the key features of the equipment using preliminary data generated as part of the on-going research.

The influence of high air entry filter on the testing of unsaturated soils using the axis translation technique

Suction is an important stress variable that is required for reliable predictions of the likely performance of unsaturated soils. The axis translation technique is the best established method of measuring or controlling suction; however, the success of this application is heavily dependent on the rating of the high air entry filter (HAF) and how it is incorporated into the testing system. This paper reports some basic experiments in which samples of unsaturated kaolin were brought to saturation in stages using 5 bar and 15 bar HAFs. The results have shown that the water equilibrium in unsaturated soils is greatly affected by the rating of filters. The findings also suggest that the flow through unsaturated soils is not necessarily governed by the one-dimensional consolidation theory that was developed for saturated soils, and this may be attributed to the bimodal pore size distribution of unsaturated soils.

Laboratory measurement of hydraulic conductivity functions of two unsaturated sandy soils during drying and wetting processes

The importance of applying unsaturated soil mechanics to geotechnical engineering design has been well understood. However, the consumption of time and the necessity for a specific laboratory testing apparatus when measuring unsaturated soil properties have limited the application of unsaturated soil mechanics theories in practice. Although methods for predicting unsaturated soil properties have been developed, the verification of these methods for a wide range of soil types is required in order to increase the confidence of practicing engineers in using these methods. In this study, a new permeameter was developed to measure the hydraulic conductivity of unsaturated soils using the steady-state method and directly measured suction (negative pore-water pressure) values. The apparatus is instrumented with two tensiometers for the direct measurement of suction during the tests. The apparatus can be used to obtain the hydraulic conductivity function of sandy soil over a low suction range (0-10 kPa). Firstly, the repeatability of the unsaturated hydraulic conductivity measurement, using the new permeameter, was verified by conducting tests on two identical sandy soil specimens and obtaining similar results. The hydraulic conductivity functions of the two sandy soils were then measured during the drying and wetting processes of the soils. A significant hysteresis was observed when the hydraulic conductivity was plotted against the suction. However, the hysteresis effects were not apparent when the conductivity was plotted against the volumetric water content. Furthermore, the measured unsaturated hydraulic conductivity functions were compared with predictions using three different predictive methods that are widely incorporated into numerical software. The results suggest that these predictive methods are capable of capturing the measured behavior with reasonable agreement.

Direct shear testing on unsaturated silty soils to investigate the effects of drying and wetting on shear strength parameters at low suction

A modified conventional direct shear device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying and wetting paths of soil water characteristic curves (SWCCs). The results revealed that the internal friction angle of the soils was not significantly affected by either the suction or the drying wetting SWCCs. The apparent cohesion of soil increased with a decreasing rate as suction increased. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as suction increased. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behavior than that of soil in drying at the same net normal stress and suction.

Unconfined shear strength of compacted unsaturated plastic soils

A central goal in unsaturated soil mechanics research is to create a smooth transition between traditional soil mechanics approaches and an approach that is applicable to unsaturated soils. Undrained shear strength and the liquidity index of reconstituted or remoulded saturated soils are consistently correlated, which has been demonstrated by many studies. In the liquidity index range from 1 (at w(l)) to 0 (at w(p)), the shear strength ranges from approximately 2 kPa to 200 kPa. Similarly, for compacted soil, the shear strength at the plastic limit ranges from 150 kPa to 250 kPa. When compacted at their optimum water content, most soils have a suction that ranges from 20 kPa to 500 kPa; however, in the field, compacted materials are subjected to drying and wetting, which affect their initial suction and as a consequence their shear strength. Unconfined shear tests were performed on five compacted tropical soils and kaolin. Specimens were tested in the as-compacted condition, and also after undergoing drying or wetting. The test results and data from prior literature were examined, taking into account the roles of void ratio, suction, and relative water content. An interpretation of the phenomena that are involved in the development of the undrained shear strength of unsaturated soils in the contexts of soil water retention and Atterberg limits is presented, providing a practical view of the behaviour of compacted soil based on the concept of unsaturated soil. Finally, an empirical correlation is presented that relates the unsaturated state of compacted soils to the unconfined shear strength.

Application of electrical resistivity method to detect deep cracks in unsaturated residual soil slope

Crack is a significant influential factor in soil slope that could leads to rainfall-induced slope instability. Existence of cracks at soil surface will decrease the shear strength and increase the hydraulic conductivity of soil slope. Although previous research has shown the effect of surface-cracks in soil stability, the influence of deep-cracks on soil stability is still unknown. The limited availability of deep crack data due to the difficulty of effective investigate methods could be one of the obstacles. Current technology in electrical resistivity can be used to detect deep-cracks in soil. This paper discusses deep cracks in unsaturated residual soil slopes in Indonesia using electrical resistivity method. The field investigation such as bore hole and SPT tests was carried out at multiple locations in the area where the electrical resistivity testing have been conducted. Subsequently, the results from bore-hole and SPT test were used to verify the results of the electrical resistivity test. This study demonstrates the benefits and limitations of the electrical resistivity in detecting deep-cracks in a residual soil slopes.

Experimental study on shrinkage behaviour and prediction of shrinkage magnitudes of residual soils

The present study examines the shrinkage behaviour of residually derived black cotton (BC) soil and red soil compacted specimens that were subjected to air-drying from the swollen state. The soil specimens were compacted at varying dry density and moisture contents to simulate varied field conditions. The void ratio and moisture content of the swollen specimens were monitored during the drying process and relationship between them is analyzed. Shrinkage is represented as reduction in void ratio with decrease in water content of soil specimens. It is found to occur in three distinct stages. Total shrinkage magnitude depends on the type of clay mineral present. Variation in compaction conditions effect marginally total shrinkage magnitudes of BC soil specimens but have relatively more effect on red soil specimens. A linear relation is obtained between total shrinkage magnitude and volumetric water content of soil specimens in swollen state and can be used to predict the shrinkage magnitude of soils.

Mechanical behaviour of unsaturated kaolin (with isotropic and anisotropic stress history). Part 1: wetting and compression behaviour

Over the last 40 years considerable progress has been made in understanding the complex behaviour of unsaturated soils. Research using constitutive modelling has extended the critical state framework and the concept of yielding in saturated soils to encompass unsaturated soils experiencing suction. However, validation testing of the framework for unsaturated soils has shown disagreement with the basic propositions. The main reason for this disparity is the anisotropic properties of the soil specimens tested as a result of preparation using one-dimensional compaction. The paper describes the detailed testing carried out to justify this statement. As part of the work presented, samples of unsaturated kaolin were prepared using isotropic compression. The suctions in these samples were reduced to predefined values by wetting under low isotropic loading. The pore size distributions, the pressure–volume relationships and yielding under subsequent isotropic loading are compared with tests on samples prepared by statically compressing kaolin into a one-dimensional compaction mould. The anisotropically compressed samples had initial water contents and specific volumes similar to those of the isotropically prepared samples and were also tested under reducing suctions; they exhibited distinctly different behaviour when tested under similar conditions. The results obtained from the isotropically prepared and tested samples have shown, probably for the first time, the existence of a unique normal compression surface that is not dependent on the initial conditions of the samples. The shape of the loading–collapse (LC) yield locus is shown to be different from the generally accepted form.

Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay, Part 1: Wetting and Isotropic Compression

The influence of compaction pressure, compaction water content and type of compaction (static or dynamic) on subsequent soil behaviour during wetting and isotropic loading has been investigated by conducting controlled-suction tests on samples of unsaturated compacted speswhite kaolin. The results are interpreted within the context of an elastoplastic framework for unsaturated soils, to examine which compaction-induced effects can be explained simply by variation in the initial state of the soil and which require that soils produced by different compaction procedures are modelled as fundamentally different materials. The compaction pressure influences initial state, by affecting the initial position of the yield surface, but it also influences, to a limited degree, the positions of the normal compression lines for different values of suction. The compaction water content influences the initial suction, but also has a significant influence (greater than does compaction pressure) on the positions of the normal compression lines. A change from static to dynamic compaction has no significant effect on subsequent behaviour