LIQUEFACTION IN NON-SATURATED SANDY SOILS

Unlike saturated soils (Sr=1) which are composed by two phases: soil skeleton and water, the soils with Sr<1 consists of three phases: soil skeleton, water and air. The distinction between unsaturated and saturated conditions was illustrated by Fredlund and Rahardjo (1993) and can be shown in Figure 2.49 (Tsukamoto et al., 2014), where the distinctions between “unsaturated”, “partially saturated” and “fully-saturated” conditions is shown.

Tsukamoto et al. (2014) reported the distributions of pore air and pore water pressure, ua

and uw, respectively, with depth. The difference between pore air pressure and pore water pressure is called matric suction (s) and it depends on the surface tension and the radius of curvature of the meniscus. When the degree of saturation decreases, the matric suction increases because the meniscus retracts into small pore spaces where the radius of curvature of the meniscus is reduced. In Figure 2.49 the matric suction is also plotted with the degree of saturation (Sr); this chart is called soil water retention curve (SWRC). At a soil layer located well above a ground water table large matric suction comes into effect due to the surface tension developed at the pore air and pore water interfaces within soil structures. In this layer, the air phase is continuous. When the depth increases, the confining stress (σ0) increases as well, together with pore air and pore water pressures.

The rate of such increases is defined by the pore pressure coefficients: Ba=dua/dσ0 (for air) and Bw=duw/dσ0 (for water). They are lower than 1 because of surface tension. The pore water tends to increase faster than pore air pressure in response to the confining stress increase, so that the matric suction decreases gradually. With depth, the occluded

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bubble becomes predominant, even though they do not interact with soil structure, they affect the compressibility of pore fluids. Bw is still lower than 1and it reaches a value equal to 1 only when the degree of saturation is equal to 1 (fully saturated soils).

Moreover, Mihalanche and Buscarnera (2016) showed a useful and schematic representation of the phases in soils, when the degree of saturation increases (Fig. 2.50).

In saturated soils, only two phases (soil and water) co-exist, while for high Sr, but lower than 1 (partially saturated soils), water has a continuous phase, while air presents occluded bubbles, trapped within the continuous water phase. Finally, for low Sr (unsaturated soils), air phase is prevalent than that of water.

In this thesis, the soils with a Sr<1 will be called generally, non-saturated soils. The terms unsaturated and partially saturated soils will be identified individually when necessary.

Moreover, the attention in this research will be focused on IPS technique that, as mentioned above, consists of introducing bubbles of gas into the void of the soil. In other words, this technology aims to achieve partially saturated soils (bubble occluded) to increase the resistance to liquefaction. Nevertheless, tests on unsaturated sandy soils have been performed as well because they were extremely useful to introduce a new interpretation of liquefaction for non-saturated sandy soils.

Figure 2.49. Schematic interpretation of fully, partially and unsaturated soil deposit (Tsukamoto et al., 2014).

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Figure 2.50. Schematic interpretation of fully, partially and unsaturated soils (Mihalache and Buscarnera, 2016).

As well-known in saturated soils the mechanical behaviour is regulated by Terzaghi’s principle (Terzaghi, 1943) by means of effective stresses (σ’). In non-saturated soils it is still possible to define effective stress. The way to define such a stress depends on the degree of saturation, or better on the continuity of the air phase: for partially saturated soils, Terzaghi’s definition could be used, whereas for unsaturated soils, the effect of matric suction has to be taken into account.

Among the different proposals, the one most used with this aim is probably that proposed by Bishop and Blight many years ago (Bishop and Blight, 1963):

𝜎′_𝑢𝑛 = (𝜎 − 𝑢_𝑎) + 𝜒 ∙ (𝑢_𝑎− 𝑢_𝑤) (2.46)

where σ is the total stress; ua, uw and χ are, respectively, the pore air pressure, the pore water pressure and the material parameter accounting for the effect of the degree of saturation (Bishop’s parameter). The term (σ-ua) is called ‘net stress’, while (ua-uw) is the matric suction or more simply ‘suction’ (s). Several definitions of the parameter χ have been proposed by several researchers (e.g. Bishop and Blight, 1963; Vanapalli et al., 1996; Gallipoli et al., 2002); in this thesis, it will be assumed that χ = Sr (Gallipoli et al., 2003; Wheeler et al., 2003).

As indicated by Unno et al. (2008), even under non-saturated condition, soil can reach the liquefaction state. Based on the eq. (2.46), the complete liquefaction state can be achieved when both the pore air and water pressure are the same as the initial total confining pressure. The suction reaches zero when the specimens become liquefied and so the effective stress approach to zero, regardless of the parameter χ.

Because of the difficulties to evaluate effective stresses in non-saturated conditions (σ’un) and the need to compare the results of tests carried out on saturated and non-saturated soils, the triggering criterion traditionally used to evaluate the attainment of liquefaction is the strain one. As for saturated soils, it can be assumed that liquefaction occurs when the strain in double amplitude is 5% in cyclic triaxial tests. Nevertheless, it is possible to define excess pore pressure ratio for non-saturated soils. In this case, ru can be defined as the ratio between Δu and the initial confining stress (σ’0), where Δu is the excess pore air

Unsaturated Partially saturated Saturated

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pressure for specimens with positive suction measurements, otherwise it is the excess pore water pressure (Wang et al., 2016).

Unlike saturated soils, in non-saturated soils subject to cyclic tests in undrained conditions, the volumetric strains are not equal to 0 and it depends on the compressibility of their fluid phase.

In the saturated soil specimens, the voids are filled with water and during cyclic loading, if the soil tends to contract, particle grains tend to re-arrange more closely together, but in undrained condition, water cannot be released and consequently pore pressure increases. In unsaturated soil, the voids are occupied by water and air that has the smallest compressibility. If the soil exhibits contractive behaviour, the application of cyclic loading also triggered an increase in pore water pressure, but it directly replaced the air void in order to dissipate an excessive energy. The phenomenon of increasing pore water pressure in unsaturated and saturated soil is clearly described in detail in Figure 2.51. It means that during undrained cyclic triaxial tests performed on partially saturated soils, the positive volumetric strains that rises, generate an increase of Sr. In other words, Sr

changes during the tests.

Figure 2.51. Particle configurations before and after testing in saturated (a) and unsaturated contractive soils (b) (modified from Kusumawardani et al., 2016).

From a qualitative point of view, also the presence of occluded bubbles can increase the compressibility of the fluid mixture (βf), as shown by Mihalache and Buscarnera (2016):

𝛽_𝑓 = 1 − 𝑆_𝑟

𝑢 + 𝑝_𝑎+ 𝛽_𝑤𝑆_𝑟 (2.47)

where pa is the atmospheric pressure, βw is the compressibility of water (4·10^-7 kPa^-1), while u=ua=uw, assuming that the pressure inside the gas bubbles and the surrounding liquid are identical.

Δu increase

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Ultimately, during undrained cyclic loading, if the soil tends to contract, the volume of the gas phase decreases and consequently the pore pressure build-up is reduced. This is one of the reasons why a non-saturated sandy soil has a higher resistance to liquefaction than the saturated one. According to Okamura and Soga (2006), the presence of air in the voids increases the resistance against liquefaction in two ways: the first mechanism is connected to the very low volumetric stiffness of gases, because of which during undrained loading there is a volumetric reduction of the gas phase and therefore reduced excess pore pressures. This mechanism is the ruling one for high degrees of saturation (i.e. dispersed air bubbles). The second mechanism is due to the matric suction of unsaturated soils, which increases the stiffness and strength of soils (Bishop and Blight, 1963). This latter mechanism becomes relevant when the degree of saturation is low enough to have a continuous air phase.

Although it is well-known that non-saturated soils have a higher resistance to liquefaction than the saturated ones, the parameters governing the liquefaction resistance of non-saturated soils are not so clear. Yoshimi et al. (1989) proposed the degree of saturation (Sr) simply. In Figure 2.52, Okamura and Soga (2006) reported some literature results in form of relationship between Sr and the resistance of partially saturated soils (CRR15, evaluated for Nliq=15) normalized with that of fully saturated soils or Liquefaction Resistance Ratio (LRR). As expected, liquefaction resistance increases when Sr

decreases; however, the liquefaction resistance ratios were different for different sands tested at different conditions. It seems that Sr is not the predominant factor in liquefaction resistance of partially saturated soils. Yang et al. (2004) indicated the B-value as the key parameter in determining the increase of liquefaction resistance, B-value can be defined as:

𝐵 = 1

1 + 𝑛 ∙𝐾_𝑏

𝐾_𝑤+ 𝑛 ∙𝐾_𝑏

𝑝_𝑎 ∙ (1 − 𝑆_𝑟)

(2.48)

where n is the porosity; pa is the absolute fluid pressure; Kb is the bulk modulus of soil skeleton and Kw is the bulk modulus of pore water.

Figure 2.52. Effect of Sr on liquefaction resistance (Okamura and Soga, 2006).

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Yang et al. (2004) also proposed the elastic wave velocity, and finally Okamura and Soga (2006) the potential volumetric strain (εv*).

It can be determined easily from Boyle and Mariotte law, under the hypothesis of pore air as ideal gas and isothermal condition:

𝑢_𝑎,0∙ 𝑉_𝑎,0 = 𝑢_{𝑎,𝑙𝑖𝑞}∙ 𝑉_{𝑎,𝑙𝑖𝑞} = 𝑐𝑜𝑛𝑠𝑡 (2.49)

where ua,0 and ua,liq are absolute pore air pressure at the beginning of the cyclic phase and at liquefaction, respectively, while Va,0 and Va,liq are the initial volume of air and at liquefaction, respectively.

Known that Va,0 can be written as:

𝑉_𝑎,0 = 𝑉_𝑡𝑜𝑡∙ [(1 − 𝑆_𝑟0) ∙ 𝑛] (2.50)

where Vtot is the total volume of the specimen, while Sr0 is the initial degree of saturation and n is the porosity of the specimen, substituting eq. (2.50) in (2.49) gives:

𝑢_𝑎,0∙ 𝑉_𝑡𝑜𝑡∙ [(1 − 𝑆_𝑟0) ∙ 𝑛] = 𝑢_{𝑎,𝑙𝑖𝑞}∙ (𝑉_𝑎,0− Δ𝑉) (2.51)

where ΔV is the variation of volume induced by the compressibility of the fluid, assuming soil grains to be incompressible. Substituting again eq. (2.50) in (2.51) gives:

𝑢_𝑎,0∙ 𝑉_𝑡𝑜𝑡∙ [(1 − 𝑆_𝑟0) ∙ 𝑛] = 𝑢_{𝑎,𝑙𝑖𝑞}∙ (𝑉_𝑡𝑜𝑡∙ [(1 − 𝑆_𝑟0) ∙ 𝑛] − Δ𝑉) (2.52)

Dividing both parts of the equation for Vtot and considering that liquefaction occurs according to its traditional definition: ua,liq=uw,liq=σ, where σ is the total stress, eq. (2.52) becomes:

𝑢_𝑎,0∙ [(1 − 𝑆_𝑟0) ∙ 𝑛] = 𝜎 ∙ [(1 − 𝑆_𝑟0) ∙ 𝑛 − 𝜀_𝑣] (2.53)

where the definition of volumetric strain (εv) has been introduced (εv=ΔV/V). Then, volumetric strain can be found:

𝜀_𝑣 = 𝑒₀

1 + 𝑒₀∙ (1 − 𝑆_𝑟0) ∙ (1 −𝑢_𝑎,0

𝜎 ) (2.54)

where the porosity (n) has been replaced by its definition in terms of void ratio (e) as e/(1+e).

The same formula was achieved by Okamura and Soga (2006) by introducing the definitions of bulk moduli of air and water.

εv of eq. (2.54) is defined potential volumetric strain (εv*) by Okamura and Soga (2006) and it is worth noting that even though it was obtained for ua,liq=uw,liq=σ, this formula can be also used to evaluate the volumetric strain expected at a fixed pore air pressure (ua), replacing its value to σ. Moreover, one of the most findings is that the value of εv does not depend on the kind of soil.

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Okamura and Soga (2006) plotted experimental results of already published papers in terms of potential volumetric strain versus liquefaction resistance ratio, showing a logarithmic fitting curve. Nevertheless, later, Wang et al. (2016) showed that this correlation was not in agreement with their experimental results for extremely loose specimens.

In this thesis a new innovative and promising state parameter (Ev,liq: specific volumetric energy to liquefaction) will be introduced in Chapter 8 as a key in interpreting the behaviour of non-saturated sandy soils and besides, it will be used in the proposed design tools for desaturation interventions against liquefaction.

The effectiveness of desaturation as a countermeasure against liquefaction is now known, but the problem is how to introduce bubbles into sand, or how to “desaturate” the soil.

Several solutions have been proposed. These include: air injection (Okamura et al., 2010);

water electrolysis (Yegian et al., 2006); sand compaction pile (Okamura et al., 2006) and the use of sodium perborate (Eseller-Bayat, 2009). In recent years, attempts have also been made to apply microbiology to geotechnical engineering.

Recently, some in-situ trial applications of this technology have been carried out to decrease the susceptibility of liquefiable soil deposits (e.g. Okamura et al., 2010; Nagao et al., 2015; Flora et al., 2019), confirming the beneficial effect of desaturation as countermeasure against liquefaction also a large scale.