Keywords

1 Introduction

Soil, in general, is considered to be comprised of soil solids and pore spaces (filled with air and water). Yet, the analysis of geotechnical problems in day-to-day world is often based on a two-phase saturated soil model which assumes the soil to consist of soil solids and a water-filled pore space (saturated condition). In practice though, soil is seldom fully saturated. Seasonal saturation and desiccation, a commonly observed phenomena in soils all over the world, often results in soils that are in a state of varying degrees of saturation. The term ‘unsaturated’ has been adopted to distinguish soils whose behaviour is influenced by this variable degree of saturation. Since no completely dry or completely saturated soil exist permanently, soils which are partially saturated can be called as ‘unsaturated soils’ [3, 16, 21, 26].

Expansive soils, remoulded soils, compacted soils, collapsible soils, residual soils—all fall under the purview of unsaturated soils. Unsaturated soil behaviour is prominently seen in dry and arid climates around the world. The influence of highly unpredictable environmental factors has been one of the earliest deterrents to the lack of development of unsaturated soil mechanics on par with that of saturated soil mechanics.

The top-most part of the ground surface is often subject to changing environmental and climatic flux, as seen in Fig. 1. Since it is the region which has direct interaction with the surrounding environment, the soil pores are largely filled with air, leading to a discontinuous water phase. But with increasing depth below the ground, as the groundwater table is approached, the water phase tends to be continuous. The soil pores still consist of some air since the soil is above the groundwater table. In the vicinity of the groundwater table, the pores in the soil are filled with water due to capillary action while the pore air is discontinuous. All of these constitute an unsaturated soil, with varying degrees of saturation.

Fig. 1
figure 1

Soil profile exhibiting varying degree of saturation [10]

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For a realistic description of the observed geotechnical phenomena and to obtain a result that is as close a solution to the problem at hand, it is important to take into account all the soil components. A thorough understanding of the behaviour of unsaturated soils would be highly beneficial in such a study.

2 Historical Developments in Unsaturated Soil Mechanics

Historical records of research on unsaturated soils obtained as conference proceedings and publications show the gradual emergence of the need to focus exclusively on unsaturated soils. The use of capillary theory in the 1950s to account for the behaviour of movement of water from the groundwater table towards the surface, although not successful, can be considered to be one of the earliest attempts made in the field of unsaturated soil research.

The applicability of independent state variables to describe the physical behaviour of any material has been relevant in soil mechanics right from its earliest conception stage. In the beginning, several effective stress equations were proposed for unsaturated soils (similar to that of saturated soils). However, researchers since then have come to the conclusion that the effective stress (\(\sigma \, {-} \, u_{\text{w}}\)) alone is not sufficient to holistically describe the processes associated with unsaturated soil mechanics. Gens et al. [16] note that attempts to justify the observed phenomena in unsaturated soils by applying the concept of effective stress, as known in saturated soil study, were not entirely successful.

According to Fredlund [9], the acceptance of the presence of pore air in the voids and the recognition of the pressure this pore air exerts challenge the very concepts of soil mechanics that is often in practice. By the 1960s, the matric suction (\(u_{\text{a}} {-} \, u_{\text{w}}\)) was recognized as an important independent stress state variable that has to be considered to portray the behaviour of an unsaturated soil.

As a modification of Terzaghi’s effective stress equation, Bishop [2] proposed the following equation for the effective stress of unsaturated soils, by introducing a parameter χ (related to the degree of saturation):

$$\sigma{'} = \left( {\sigma {-} u_{\text{a}} } \right) + \chi \left( {u_{\text{a}} {-} u_{\text{w}} } \right)$$
(1)

in which \(\sigma {'}\) is the effective stress for unsaturated soils, \(u_{\text{a}}\) is the pore air pressure, \(u_{\text{w}}\) is the pore water pressure and χ is a function of the degree of saturation (S), with values ranging from 0 (when soil is dry) to 1 (when soil is saturated). However, it has been noted by researchers that the form of the function \(\chi (S)\) has been difficult to determine, and Eq. (1) has often been questioned ever since [21].

The 1970s saw further development of the theoretical foundation for the establishment of stress state variables. The 1980s concentrated on solving problems in unsaturated soils by assuming suitable boundary values. The increasing advancements in the computational sciences in the form of computers with superior computational prowess during this period also smoothened the way for the transition of unsaturated soil mechanics from theoretical concepts to problem-solving methods. However, this did not translate into a practicing science, that is, application of unsaturated soil mechanics into practice did not pick up at a pace as expected by the pace of advancements in unsaturated soil science [10].

The 1990s saw the focus shift towards implementation into practice. The major obstructions here were the excessive time and cost involved in experimental determination of the unsaturated soil properties. The move to concentrate the research focus on unsaturated soils from the erstwhile broad spectrum of expansive soils began from 1992 onwards. Till then, soils with a negative pore water pressure (like residual soils and expansive soils) were grouped under expansive soils. Fredlund [9, 10] notes that this shift towards unsaturated soils has paved the way forward for a better understanding and theoretical conception to experimentation and subsequent push towards a practical implementation.

3 Soil–Water Characteristic Curve (SWCC)

Soil–water characteristic curve (SWCC) or soil–water retention curve (SWRC) is the plot of the volumetric water content or gravimetric water content against the matric suction. The SWCC exhibits hysteresis and has drying, wetting and scanning branches. A typical soil–water characteristic curve is presented in Fig. 2. The desorption curve is also known as the drying curve, and the adsorption curve is also known as the wetting curve. The hysteresis results in the adsorption and desorption curves not being a single, unique curve. The air entry value (AEV) of the soil is the matric suction at which air starts to enter the largest pores in the soil. The residual water content is that value of water content for the soil at which a large suction is needed to remove further water from the soil [11]. It mainly describes the interaction of soil air and soil water. SWCCs are useful in the study and analysis of the behaviour of an unsaturated soil. Properties such as shear strength, volume change and permeability are dependent on SWCC.

Fig. 2
figure 2

Typical soil–water characteristic curve

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Rao and Singh [24] and Rostami et al. [25] based on their study concluded that SWCC can be used to determine hydraulic conductivity, shear strength, chemical diffusivity, chemical adsorption, volumetric water content, specific heat, thermal conductivity and volume change of soils. Fredlund [10] opines that it will not be wrong to conclude that the determination of the SWCC is the first and foremost requirement for a study on an unsaturated soil. SWCC is considered one the most important aspect of an unsaturated soil, which, when obtained, can further lead to the determination of many other unsaturated soil parameters.

To plot a SWCC, suction measurement is important. Filter paper, axis translation technique, vapor equilibrium method, osmotic method, pressure plate apparatus, tempe cell, tensiometer, pressure membrane extractor, dew-point potentiometer and so on are used to measure suction. The measurement techniques and procedures have their own limitations. The filter paper method is simple and affordable with its validity over a large suction range. However, its implementation needs extreme caution. The axis translation technique (ATT) also has some disadvantages—equilibration time required for soil with porous plate is lengthy, contact of soil with the plate has to be continuously ensured and the presence of occluded bubbles should be taken into consideration [4]. The insertion tensiometers, geotechnical centrifuges and pressure membrane extractors are valid for suctions between 80 and 1500 kPa while the dew-point potentiometer (WP4) is valid for suctions ranging from 1500 to 80000 kPa. Type of soil, size of soil specimen, applied air pressure and so on also influence the measurement time, as noted by Yang et al. [30]. Malaya and Sreedeep [20] reported that soil aging induces hydration which may in turn affect the SWCC through different suction measurement techniques and internal pore water redistributions over time.

The determination of SWCC by direct measurements is a time-intensive process and considering the economics involved, the search for alternative methods of obtaining an accurate and reliable SWCC in a cost and time-effective manner has been the focal point of many studies. The measurement of the complete SWCC is a difficult process with only a few data points actually measured on the desorption curve. The rest of the data points are plotted by using suitable curve-fitting equations to get the SWCC over the entire soil range. This has often led researchers to find alternative ways of obtaining or estimating the SWCC such as correlating the fitting parameters of SWCC with the plasticity as well as with the grain-size distribution curve. Since the shape of the SWCC resembles the grain-size distribution curve, many researchers have focused on establishing a relationship between these two so as to use the grain-size distribution curve parameters to estimate SWCC [9].

Table 1 gives a few well-known curve-fitting equations for SWCC (\(\theta_{\text{w}}\)—volumetric water content, \(\theta_{\text{s}}\)—saturated volumetric water content, \(\theta_{\text{r}}\)—residual volumetric water content, \(a,b,c\)—parameters of the curve-fitting functions). Fredlund and Houston [13] have noted that the Fredlund and Xing [11] and van Genutchen [27] equations yield an accurate SWCC and hence are considered a best fit up to residual soil suction.

Table 1 Soil–water characteristic curve functions
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Although the various methods of indirect measurement of SWCC give an estimation, they can never replace an SWCC obtained by actual measurements. The prediction/estimation of soil suction directly from the SWCC is not encouraged as the hysteretic behaviour of SWCC results in a range of soil suction values rather than a single suction value. The errors involved in the measurement of SWCC may also show up as cumulative and lead to erroneous predicted suction values. Limitations such as these show that the soil suction estimation from SWCC is a potential area for future research.

4 Utility of Unsaturated Soil Mechanics in Prediction–Protection–Prevention of Landslides

The concepts of unsaturated soils can be effectively implemented in addressing a large variety of soil-related problems, especially in a country like India, which has a predominant tropical climate. With a booming population, the strain on our resources is at an all-time high. In such scenarios, the pressure or burden on soils is also heavy. Some of the areas where unsaturated soil mechanics can be successfully applied are in slope stability cases (subject to rainfall), landfill liner systems (mining, natural resources and waste management), nuclear waste disposal through clay barriers, water recharge through deep wells and bore holes, foundations, pavements, retaining walls, buried structures and so on. Issues related to expansive soils such as damage to foundations of buildings, infrastructure like roads and bridges can also be addressed by employing the concept of unsaturated soil mechanics [19].

Slope stability has been a significant issue in the field of soil engineering. From an economic point of view, the losses incurred as a result of slope failures in a variety of domains from road and railway embankments to natural slopes are huge. Hence, the study of stability of slopes is of great economic importance.

It is well known that the stability of a slope is largely due to the shear strength of the soil comprising it, which in turn is dependent on numerous factors. The angle of inclination of the slope, the soil density, surcharge acting on the slope are also influential in the stability. Some of the factors affecting shear strength of unsaturated soils are rate of strain, matric suction, initial water content and so on [28]. The extended Mohr–Coulomb failure envelope, as shown in Fig. 3 (which is a modification of the Mohr-Coulomb failure envelope for saturated soils), is considered for unsaturated soils. The additional cohesion provided by the matric suction contributes to the shear strength of an unsaturated soil. Hence, when the matric suction decreases, the associated cohesion also decreases and the shear strength reduces.

Fig. 3
figure 3

Mohr–Coulomb failure envelope for an unsaturated soil [12]

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The shear strength of a saturated soil is given by the equation proposed by Terzaghi:

$$\tau = c^{\prime} + \left( {\sigma - u_{\text{w}} } \right)\tan \phi^{\prime}$$
(2)

where

\(\tau\):

shear stress at failure

\(c^{\prime}\):

intercept on the shear stress axis for a zero effective normal stress

\(\left( {\sigma - u_{\text{w}} } \right)\):

effective normal stress at failure

\(\phi^{\prime}\):

effective angle of internal friction.

To account for the pore air pressure and its effects in an unsaturated soil, the above shear strength equation has been modified as [12]:

$$\tau = c^{\prime} + \left( {\sigma - u_{\text{a}} } \right)\tan \phi^{\prime} + \left( {u_{\text{a}} - u_{\text{w}} } \right)\tan \phi^{b}$$
(3)

where

\(c^{\prime}\):

intercept on the shear stress axis of the extended Mohr–Coulomb failure envelope when the net normal stress and the matric suction are equal to zero

\(\left( {\sigma - u_{\text{a}} } \right)\):

net normal stress at failure

\(\phi^{\prime}\):

angle of internal friction identified with net normal stress state

\(\left( {u_{\text{a}} - u_{\text{w}} } \right)\):

matric suction at failure

\(\phi^{b}\):

angle signifying the rate of increase in shear strength relative to the matric suction.

Similar to the determination of SWCC, the experimental procedures to determine unsaturated shear strength are most often slow and expensive. Alternative procedures for estimating the unsaturated shear strength using various tools like the soil–water characteristic curve, relationship between the air entry value and confining pressure have been reported. The lack of a universal, unique equation that can satisfactorily predict the shear strength of all unsaturated soils has been noted by Garven and Vanapalli [15]. Most of the proposed equations deal with the drying shear strength of the unsaturated soil and do not address wetting shear strength [17]. There is a need for further research to provide more improved and reliable techniques for the estimation of shear strength of soils. More experimental studies are required to be conducted following standard testing procedures to achieve this.

Studies on stability of slopes have been the focal point of many researches worldwide, especially in the areas subjected to rainfall. A typical slope failure due to rainfall-infiltration is exhibited in Fig. 4. Many instances of slopes being stable with a factor of safety less than one (as computed by using saturated concepts) is proof enough that there is a necessity to widen our horizons and look beyond the theories of saturated soils. The inclusion of unsaturated soil properties in a slope stability analysis is important, particularly for slopes in tropical areas where the residual soils are often partially saturated and are highly susceptible to failure under rainwater infiltration [7, 12, 18].

Fig. 4
figure 4

Slope failure due to rainfall-infiltration [23]

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According to Cho [8], the infiltrating rainwater displaces the air from the pores in the soil, causing an increase in the air pressure which results in a delay in the advancement of the wetting front. As the water starts filling the soil pores, the bulk weight (γ) of the soil increases, altering the shear stress distribution along the slope depth. The critical failure surface for a slope under infiltration conditions is not constant and is influenced by the interactions between the air and the infiltrating water. For an accurate slope stability analysis, the influence of hydraulic hysteresis has to be suitably considered to avoid underestimating the safety factor associated with slope stability. Air entrapment is an important factor that has a considerable influence on the suction stress profile and correspondingly on the factor of safety. Thus, the concept of unsaturated soils can also be effectively applied as a slope protection measure [6, 29].

Landslides in tropical regions are often caused due to water seeping into the soil. The introduction of any form of drainage system to expel the excess pore water pressure makes the negative pore water pressure a permanent fixture, which has to suitably accounted during the modelling and analysis of stability of a slope [1]. Providing surface and sub-surface drainage is important as a preventive action to increase the stability of the landslide-prone slope. Use of unsaturated concepts has also been proven beneficial in cover systems designed to protect slopes. These act as a retaining wall and help to maintain suction values, thereby preserving the shear strength of the slopes [22].

5 Summary and Conclusion

A developing country like India, pushing for a massive overhaul in the infrastructure sector, necessitates the focus to be on the development and maintenance of these infrastructures on a low cost-maximum benefit basis. With natural disasters such as floods and droughts ravaging large parts of the country, a transition towards reliable, robust technologies and monitoring systems for the maintenance of these infrastructures is the need of the hour.

The need for considering multi-phase aspect of soil behaviour for a better engineering judgment is significant for any type of geotechnical problem encountered in the field. These issues can be realistically described by considering soil as a multi-phase material where the presence of pore air influences the behaviour of the soil. A deviation from the two-phase saturated soil behaviour increases the complexity of soil mechanics with the introduction of the suction component. With more and more ‘problematic soils’ being encountered in the field, the need to understand unsaturated soils has never been as acute and important as in the present.

As interest in unsaturated soil mechanics is gaining momentum and with people realizing that the adoption of unsaturated soil concepts can, in fact, produce better results which are closer to reality, implementation is gaining traction, albeit at a slow pace. It is often opined that a major hindrance to the successful implementation of the principles of unsaturated soil mechanics in routine geotechnical applications is a lack of sufficient technical knowledge in engineers together with the high cost expected in the measurement of unsaturated soil properties such as SWCC.

The estimation and indirect determination methods and techniques become significant as laboratory determination of parameters of unsaturated soils is still considered complex and is not as popular as its saturated counterparts. The search for cost-effective alternatives for the expensive testing procedures is a prime area for research. The theoretical knowledge on unsaturated soils has been developed over the decades into a robust science and the versatility of the applications of unsaturated soil mechanics has opened up a wide range of possibilities for future research.

The ultimate goal of any theoretical formulation or research is a sound practical implementation. The technological advancements in the form of superior instrumentation and computational tools has resulted in further enrichment of our knowledge and comprehension of the behaviour of unsaturated soils. It is high time we apply this theoretical knowledge to solve and optimize the solutions to a variety of situations often faced in civil engineering practice.