A laboratory study of liquefaction of partially saturated sand

This experimental study was designed to assess the effects of soil water saturation on the liquefaction of Hostun RF sand. Cyclic undrained triaxial tests were conducted at different soil saturation levels, as given by Skempton’s coefficient, and liquefaction potential curves constructed for each value of this coefficient. Our findings indicate that a lower soil saturation level results in the increased resistance of the sand to liquefaction, in agreement with the tendency observed in other sands. In addition, the variation in sand resistance to liquefaction produced with Skempton’s coefficient was found to be consistent with the semi-empirical relation proposed by Yang et al. (2004).


Introduction
The phenomenon of soil liquefaction has been observed in response to moderate and large earthquakes, for example those of Loma (1989), Luzon (1990), Manjil (1990), Kobe (1995), Manzanillo (1995), Chi-Chi (1999), Kocaeli (1999), andBhuj (2001) (Bird et al., 2004).Understanding the mechanism of liquefaction in watersaturated soils and developing methods to evaluate their liquefaction potential have been the subjects of intense research (Seed and Idriss, 1971;Seed, 1979).However, in geotechnical engineering partially saturated soils are frequently encountered, especially above the water table.Further, due to the presence of small air bubbles, soils below the water table could also be partially saturated and this issue has been explored in both experimental and analytical analyses.Thus, Mulilis et al. (1978) reported that a change in Skempton's coefficient (B) from 0.91 to 0.97 moderately affected the liquefaction of Monterrey sand.Chaney (1978) specified that coefficient B has to be higher than 0.96 so that the soil is well saturated and Sherif et al. (1977) showed that a fine or clayey sand could be considered saturated if the value of B exceeded 0.8.More recently, laboratory test results have indicated that the liquefaction resistance of sands increases with a decreasing degree of saturation (Ishihara et al., 2001;2004;Yang, 2002;Yang et al., 2004;Atigh and Byrne, 2004;Bouferra et al., 2007).As an in situ measure of the level of water saturation of a soil, Berryman et al. (1988) and Santos et al. (1990) reported the use of compression wave speed.Recently, a constitutive relation based on the multiphase approach was used to address the liquefaction of partially saturated sand (Bian and Shahrour, 2009).
In triaxial tests, the extent of saturation (S r ) is generally controlled by means of Skempton's coefficient (B) according to the following equation: where, K s and K w are the bulk modulus of the solid skeleton and water, respectively; n is the porosity of the soil and u a is the water pore pressure.
The aim of the present laboratory study was to determine the influence of soil saturation level on the liquefaction of Hostun RF sand across a wide range of Skempton coefficient B values (between 0.25 and 0.90).After describing the experimental procedure, we analyse the experimental results obtained by constructing liquefaction potential curves for several values of the Skempton coefficient B. These results are then compared to those reported in the literature for other sands and fitted to the equation proposed by Yang et al. (2004) to describe how sand resistance to liquefaction varies according to Skempton's coefficient.

Experimental procedure
Laboratory tests were conducted on samples of medium grained Hostun RF sand.This sand is composed of angular particles of mean grain size D 50 =0.47mm (Fig. 1); its properties are summarized in Table 1.This sand is widely used in France to investigate sand behaviour under complex loading paths and conditions.It arose from a thick series of Eocene sand layers that fill karst pockets on the western side of Vercors at Hostun (Drôme, France).Experimental results for this sand obtained at low confining pressures may be found in Lancelot et al. (2004Lancelot et al. ( , 2006)).
Alternating undrained cyclic triaxial tests were performed on soil samples at an initial relative density I D =0.65 across a wide range (0.25 to 0.9) of the Skempton coefficient (B).Table 2 shows the values of B used in this study with their corresponding saturation values calculated using Equation 1.
For each value of B, tests were conducted at several loading levels (CSR) to construct liquefaction potential curves (Table 3).The loading level (CSR) was defined as: was lower than that observed for B = 0.9.Liquefaction occurred after 21 cycles.
For B = 0.53, a regular increase in water pore-pressure was also detected but at a rate lower than that observed for B = 0.67.Liquefaction took place after 27 cycles; initial effective pressure was cancelled at an axial strain of 4%.
For B = 0.25, we noted a slight increase in water porepressure and stabilization of the amplitude of axial strain at 0.4%.Liquefaction was only observed for higher loading levels.Thus, an increase in the cyclic loading level to CSR = 0.4 led to liquefaction after 52 cycles (Fig. 6).When the loading level was substantially increased (CSR = 0.5), liquefaction was observed after 12 cycles (Fig. 7).
Further tests were conducted for each value of B to obtain data for the liquefaction potential curves (Table 2).Figure 8 shows the results obtained for the different values of B. For each level of loading (CSR), the curves give the number of cycles needed for liquefaction.Analysis of these results revealed a general tendency for an increase in the number of loading cycles necessary for liquefaction (N liq ) as Skempton coefficient B decreased.To better illustrate this tendency, Figure 9 shows how N liq varies with coefficient B for each value of the loading level.
where q m and c σ ′ are the cyclic loading amplitude and initial mean effective stress, respectively.
Experiments were conducted in two stages.In the first stage, we prepared the partially saturated sand samples, and in the second stage, conventional undrained cyclic triaxial tests were performed using a Bishop cell.To ensure good control of the degree of saturation, the carbon dioxide procedure was used (Skempton, 1954).In the first stage, the soil sample is purged with carbon dioxide for 20 minutes and then percolated with deaired water until a volume of water greater than one and a half times the sample volume has been collected.Samples of different saturation level were obtained by varying the time of carbon dioxide passage and percolation with deaired water.

Results and discussion
Figures 2 to 5 provide the results obtained in tests performed for 4 values of the Skempton coefficient (B = 0.90, 0.67, 0.53, and 0.25) at the cyclic loading level CSR = 0.35.The figures illustrate that for the quasi-saturated sample (B = 0.9), water pore-pressure increased regularly and reached the value of the initial effective confining pressure (100 kPa) after 7 cycles at an axial deformation of 2%.This state corresponds to liquefaction of the sand through cancellation of the effective confining pressure.For the soil sample whose B = 0.67, we observed a similar trend in water pore-pressure but the rate of increase   Hence, for the low cyclic loading levels (CSR = 0.25 and 0.3), significant variation in N liq with coefficient B was observed.Specifically for CSR = 0.25, N liq increased from 12 to 200 cycles as B diminished from 0.9 to 0.73.Conversely, for the higher of loading levels (CSR= 0.4 and 0.5), scarce variation in N liq was produced according to coefficient B such that for CSR = 0.50, N liq increased from 9 to 12 cycles as B fell from 0.73 to 0.25.
Figure 10 shows the influence of Skempton's coefficient (B) on the sand resistance to liquefaction (CR), which is defined as the cyclic loading level required to cause initial liquefaction within 15 cycles.Thus, the Skempton's coefficient has an important impact on this resistance (CR), which increases from 0.25 to 0.40 when  To quantify the saturation effect on sand resistance to liquefaction, Yang (2002) used normalized cyclic resistance (RLn), which is the ratio between resistance to liquefaction of a partially saturated sand (CR) to that of a saturated sand.In Figure 11 we compare the results obtained here with those reported for other soils.These data indicate good agreement between our experimental results for Hostun sand and results for the other sands, especially Ottawa sand (Sherif et al., 1997) and Tongjiazhi sand (Xia and Hu, 1991).Yang et al. (2004) proposed the following equation to describe the variation in normalized cyclic resistance to ( 3) Parameter α indicates the slope of the linear regression in the (( Log(RLn), B) plane.Figure 12 shows how this equation can be applied to the data obtained in the tests conducted on the Hostun RF sand.The linear approximation in the ( Log(RLn), B) plane gives α= 1.03 with a cor- relation coefficient Cc = 0.99.

Conclusions
This paper describes a laboratory study designed to assess the liquefaction of partially saturated sand using Skempton's coefficient (B) as a measure of soil saturation.Tests were conducted at several levels of cyclic loading (CSR) to construct liquefaction potential curves for 7 values of coefficient B ranging between 0.25 and 0.90.Our experimental results clearly show that a decrease in the Skempton coefficient leads to a large increase in the number of cycles necessary for sand liquefaction, in particular, for low cyclic loading levels (CSR < 0.3).Thus, liquefaction resistance, defined here as the level of cyclic loading (CSR) that leads to liquefaction in 15 cycles, appreciably decreases with coefficient B. In addition, our data showed good fit to the equation proposed by Yang et al. for the variation in normalized resistance to liquefaction RLn (ratio of the liquefaction resistance of a partially saturated to a saturated soil) produced with coefficient B: ( RLn = e α(1−B ) ) where α = 1.03.

Aknowledgements
The Editorial Office of Journal of Iberian Geology aknowledges the reviews by two anonymous referees and the English editing by A. Burton.

Fig. 11 .
Fig. 11.-Comparing the experimental results of this study to those conducted on a further four sands.Fig. 11.-Comparación de los resultados experimentales de este estudio con otros cuatro de otros estudios.