Development of Wetting-Drying Curves from Elastic Wave Velocities Using a Novel Triaxial Test Apparatus

In this study, Edosaki sand sourced from a natural slope in Ibaraki, Japan, was utilized. For all the experiments, the gravimetric water content percentage was set at 10%. The sand has specific gravity Gs = 2.71, maximum dry density, g_dmax = 1.762 g/ml, minimum void ratio, e_min = 0.647, and maximum void ratio, e_max = 1.16. The initial height of the specimen was 40 mm, whereas the diameter was 74 mm. Three specimens having relative density (Dr) of 85%, 56%, and 39% were prepared and tested.

In the experiment, there were a variety of procedures involved. The procedures involve saturating the ceramic disk, sample preparation, and acquiring SWCC for drying and wetting with elastic wave measurements. The first step of the test was to saturate the ceramic disk. For this purpose, it was dipped inside a water container. The negative pressure ceramic disk was subjected to was −101.78 kPa. It was immersed inside the tank for 24 h. After that, it was taken out and fitted in the triaxial apparatus. To negate the risk of desaturation, a water bottle was attached to it. As the next step for setting up of split mold, a 0.3-mm-thick rubber membrane was added on the circumference of the base pedestal. Computation of the weight of the overdried Edosaki sand in question was done for achieving the required density. Edosaki sand sourced from a natural slope in Ibaraki, Japan, was utilized. For all the experiments, the gravimetric water content percentage was set at 10%. Water was added to the soil sample and mixed thoroughly to achieve this target. As the ceramic disk was saturated, any connection of water to the disk was stopped right there and the surface was dried with the help of tissue paper. For preparation of the sample, a wet tamping technique was used. In this technique, the wet soil was tamped into four identical layers. The sample preparation was done on top of the ceramic disk. Saturation of the sample was achieved by water flow through the ceramic disk. However, the water head was kept quite minimal (1–2 kPa) to negate any chances of piping occurring inside the sample. Together, all the apparatus (the base pedestal and the mold, excluding the water bottle) alongside the soil sample was weighed at specified intervals. Attainment of constant weight indicated saturation of the sample. It took 3–4 days to achieve the saturation point. Figure 2 shows all the steps involved in the preparation and saturation of the specimen.

Figure 2:

Once the soil specimen was prepared, it was subjected to matric suction of various distinctive magnitudes. The changes in moisture of the sample were recorded and used for the determination of wetting and drying SWCC. After the setup was achieved, the center of the specimen was marked and the water in the bottle was brought to exactly that point. Pore air pressure present inside the specimen was reduced to zero, that is, u_a = 0 (Figure 3). This was an indication of zero matric suction (u_a – u_w = 0). This condition was sustained until the achievement of a constant water bottle weight. After this, the drying path started. During the drying process, the matric suction was incrementally increased to 0.5, 1.0, 2.0, 4.0, 7.0, 10.0, 15.0, 30.0, and 50.0 kPa, respectively. Lower values of matric suction, that is, between 0 and 4 kPa, were achieved by lowering the water level in the bottle. During this, the pore air pressure was kept at 0. Numerically, for the application of 4 kPa suction pressure, a 40-cm lowering of the water level was done. Beyond 4 kPa, the water level was returned to the original position and was not disturbed. Using the top cap, the pore air pressure was enhanced for suction greater than 4 kPa. During the experiment, the applied pore air pressure was equal to the magnitude of the applied suction. To maintain a constant axial stress throughout the experiment, a counterweight equivalent to the magnitude of the applied pore air pressure was placed on the top cap.

Figure 3:

Every increment in the matric suction resulted in water flowing outside the specimen. This kept on going until an equilibrium position was attained. The time taken to reach the equilibrium condition was around 24–48 h. It was indicated when the weight of the water bottle became constant. Shear and compression wave velocities were determined after the attainment of equilibrium. The water bottle and the soil specimen were linked by a non-spill coupling valve that was disconnected for measurement of water drained out of the specimen. The water bottle was weighed for this purpose after disconnection. The other bottle in the apparatus for measuring water losses due to evaporation was also weighed to apply the required corrections. The entry value of the air into the ceramic disk is the limiting factor for the maximum suction pressure. For this apparatus, the maximum pressure that can be applied was 100 kPa. However, in the present study, the application of suction beyond 50 kPa was practically impossible because, beyond this limit, the airtightness of the system was remarkably difficult to maintain. For simulation of the wetting path, the value of pore air pressure was lowered from this value, that is, from 50 kPa. This was done alongside maintaining the water level at the required position, that is, at the center of the sample. As soon as the pore air pressure decreased, water started flowing into the specimen. This flow occurred through the ceramic disk. This kept on going until equilibrium was established. Again, the water bottle was disconnected from the apparatus. The weight of the bottle was determined to figure out the amount of water that flowed inside the specimen. For matric suction values higher than 4 kPa, the procedure remained the same. However, below 4 kPa values, the procedure used was different. The values were applied by venting the pore air pressure to the atmosphere, and then lowering of the water level was done below the center point position.

The shear and compression wave velocities were determined after the attainment of equilibrium using disk-type piezoelectric transducers [39, 40]. The apparatus used in this study has components of wave-measuring setup. The equipment used in the experiment included a Tektronix AFG3022B function generator (marked as ⑪), an NF Corp. HSA4012 power amplifier (marked as ⑫), and a HIOKI 8860 digital oscilloscope with a HIOKI 8957 high-resolution input module (marked as ⑬). A schematic diagram of the apparatus is shown in Figure 4 for a better understanding.

Figure 4:

3.4.1

Determination of Elastic Wave Velocities

The calculation of wave velocities can be based on the basic formula for velocity, which relates the distance traveled to the time elapsed. By using specific formulas, it was possible to determine the compression wave (Vp) and shear wave (Vs) velocities in this study. (1) Vp=H/t {{\rm{V}}_{\rm{p}}} = {\rm{H}}/{\rm{t}} (2) Vs=H/t {{\rm{V}}_{\rm{s}}} = {\rm{H}}/{\rm{t}} The distance traveled by a wave (H) can be determined based on the time it takes for the wave to travel that distance. In this study, the time of flight for compression and shear waves was used to calculate the corresponding travel distances.

The travel time, denoted as t, of each wave was determined by examining the response of both the transmitted and received signals. In the case of compression waves, the initial deflection in the receiver signal was identified as the arrival time of the compression wave. This interpretation of the first arrival time is appropriate because compression waves propagate the fastest and therefore arrive at the receiver before any other wave. Thus, the time between the first deflection of the input and output signals was used to calculate the flight time of the compression waves, as depicted in Figure 5.

Figure 5:

Determining the travel time of shear waves is more complex than that of compression waves. This is because the initial deflection in the shear wave signal may not correspond to the arrival of the S-wave itself, but instead to the arrival of the “near-field” component, which propagates at the velocity of P-waves [41]. To calculate the travel time of the shear wave while ignoring the initial disturbance caused by the P-wave and the near-field effect, the “first-zero cross over” method was utilized [29]. Specifically, the travel time of the shear wave was estimated as the difference between the start of the transmitted signal and the start of the first significant positive polarity increase, as depicted in Figure 6.

Figure 6:

To measure the velocity of elastic waves, an excitation voltage was generated by a function generator and amplified by a power amplifier. This voltage was then applied to the transmitter disk transducer. The wave propagated through the soil specimen and was received by the receiver disk transducer located at the top cap. The received signal was then transferred to a digital oscilloscope for display. The input signal from the power amplifier was also sent to the oscilloscope via a monitoring channel, allowing for simultaneous recording of both the input and output signals. The process of determining elastic wave velocities (Vs and Vp) was conducted in a similar manner to that of the drying path, which involved equalizing matric suction at each level. The whole assembly was disconnected when zero matric suction was achieved during the wetting process. After that, the specimen was oven-dried and moisture content was determined through it. This moisture content and water bottle readings determined at different suction levels were used to calculate the corresponding moisture content of the specimen. This moisture content was obtained at various suction levels.

A series of tests have been conducted on the Edosaki sand with 85% relative density under the effect of net normal stress (σ-u_a) 10 kPa. Contrary to a typical SWCC test, a small net stress was required in this case to establish sound contact between the disk transducer and soil. Without the establishment of this contact, the transmission of elastic waves from the sensor to the soil was not possible. SWCC of the studied soil is presented in Figure 7, and the correlation of SWCC is carried out with the established [42] model. Fitting data confirm that the results of SWCC are reliable and consistent with the results of [23].

Figure 7:

A test series (Series-01) was performed on the specimen prepared at 85% relative density and under the effect of net normal stress (σ-u_a) 10 kPa. Figure 8a, b shows that the shear and compression wave velocities increase with the matric suction. The graph shows that the indicated behavior is bilinear with a depiction of clear hysteresis that is between the wetting and the drying curves. An increase in matric suction is accompanied by a decrease in water content of the soil. Dry soils are relatively stiff and may have contributed to the increase in wave velocities. The graphs show that both shear and compression wave velocities increase with matric suction. Effective stress between soil particles is enhanced by suction, thereby facilitating the propagation of waves through the soil skeleton. A direct relationship is, therefore, observed between matric suction and wave velocities. This is further substantiated by the fact that an increase in suction is accompanied by a decrease in the water content of the soil (as shown in Figure 7). Dry soils are relatively stiff and possess high modulus, that is, high wave speed [43]. The reliability and accuracy of the measurements was verified by performing another test series (Series-02) at 85% relative density and effect of net normal stress (σ-u_a) 10 kPa. The test results of the second series performed to determine the reliability and accuracy are shown in Figure 8 (a, b). A comparison of graphs demonstrates the direct dependence of wave velocities on the matric suction of soil. Wave velocities increase/decrease nonlinearly with an increase/decrease in matric suction. It can be noted that the results of tests performed in Series-01 and Series-02 as shown in the figure are comparable. This justifies the reliability and repeatability of experimental work.

Figure 8:

Figure 9 shows the effect of variation of relative densities on matric suction, compression, and shear wave velocities with volumetric water content. For each specimen variation, matric suction, compression wave velocity, and shear wave velocity have been drawn, which show a bilinear behavior that depicts a clear hysteresis between the drying and wetting curves. Various researchers [12, 13, 29, 44] have shown the dependency of wave velocities on soil moisture. The general trend observed in the figure is similar as wave velocities increase with decreasing soil moisture and vice versa. Owing to the similarity in shape of wave velocity response to SWCC, the curve is being termed as WVCC. Identical to SWCC, WVCC of each specimen shows three distinct zones: saturation zone, transition zone, and residual zone. In the saturation zone, during the drying path, water is pushed out of the soil. At the start of the experiment, upon an increase in matric suction, air starts entering the soil skeleton, but is yet to break the surface tension of water. Before reaching AEV, water does not get pushed out of the soil skeleton, but effective stress increases due to an increase in matric suction. Thus, an increase in matric suction in this saturation zone leads to an increase in effective stress between soil particles. An increase in particle-to-particle contact stress causes an increase in wave velocities. In the transition zone, water is ejected from the soil rapidly without any significant change in matric suction. An increase in wave velocity follows a similar trend to matric suction (i.e., no rapid rise). In the residual zone (drying), wave velocities increase rapidly since effective stress increases due to matric suction. An increase in wave velocity is further substantiated by the ejection of water from the specimen, that is, the drier the specimen, the higher will be its modulus/wave velocity. In the residual zone (wetting), a decrease in matric suction causes a loss of effective stress. As the particle-to-particle contact force diminishes, wave velocities start decreasing. The pattern of compression wave velocities in unsaturated specimens exhibits similarities with that of shear wave velocities, but with a magnitude nearly twice as large. It is interesting to note that the wave velocities for the same matric suction during the wetting and drying parts is different, thereby causing a hysteresis identical to SWCC. A possible explanation for this phenomenon can be attributed to the stress history of soil. When a virgin soil sample is dried by an increase of matric suction, the soil “remembers” the stress history and even upon release of applied matric suction, the effective stress between soil particles is not completely lost. A stronger particle-to-particle contact during the wetting phase, therefore, causes higher wave velocities. This phenomenon may, however, be related to the stress path the sample has been subjected to during these tests, that is, drying of an initially wet sample and subsequent wetting. A comparison of graphs also demonstrates direct dependence of wave velocities on the matric suction of soil. Wave velocities increase/decrease nonlinearly with an increase/decrease in applied matric suction.

Figure 9:

Poisson’s ratio, which is defined as the ratio of the lateral strain to the longitudinal strain under uniaxial loading, is an elastic property of soil. Instead of directly measuring lateral and longitudinal strains, the authors inferred Poisson’s ratio indirectly through the measurements of shear and compression wave velocities in the soil specimens. Figure 10 depicts the experimental determination of Poisson’s ratio based on the measurements of shear and compression wave velocities [33, 45]. The figure includes a PRCC [38], which, similar to SWCC and WVCC, relates the Poisson’s ratio to the degree of saturation and matric suction. PRCC follows three distinct water retention regimes and exhibits variations between the dry and saturated states. At the dry state (I), the Poisson’s ratio is minimal due to the high compressibility of the soil. Conversely, at the saturated state (III), the soil becomes almost incompressible, resulting in a maximum Poisson’s ratio. Hence, there exists an inverse relationship between Poisson’s ratio and soil compressibility. As the soil undergoes a transition from saturated to unsaturated state, both the degree of saturation and Poisson’s ratio decrease at varying rates, depending on the dominant water retention state. Laboratory measurements reveal that the rate of change in the Poisson’s ratio is higher when the water content decreases, resulting in increased soil compressibility [38, 39]. In the saturated state (capillary state), the Poisson’s ratio undergoes minimal changes. This is because the compressibility of water is negligible compared to that of the soil matrix. Therefore, in the near-saturated condition, the pore water dominates over the soil skeleton, leading to a high and relatively constant Poisson’s ratio. The Poisson’s ratio value in the saturated state represents stage III in PRCC. Due to the stress history of soil, the drying and wetting curves show some difference in Poisson’s ratio values. However, for different relative densities, there is very little difference in final values.

Figure 10:

Elastic moduli such as Young’s modulus and shear modulus are measures of the stiffness of materials that respond to recoverable deformations. For materials that are elastic, isotropic, and homogeneous, the elastic constants are given by the following equations [46]. (3) G=ρVs2 G = \rho V_s^2 (4) M=ρVp2 M = \rho V_p^2 The elastic constants of shear and constrained, denoted as G and M respectively, are important parameters for evaluating the immediate settlement and dynamic response of geotechnical structures in engineering practice. These constants can be determined based on shear and compressive wave velocities, denoted as Vs and Vp, respectively, for materials that are elastic, isotropic, and homogeneous. Figure 11 illustrates the variations in G and M for different relative densities under different degrees of saturation. It can be observed that the elastic constants of shear and constrained tend to increase as the degree of saturation decreases due to drying. The moduli exhibit gradual increases during the early stages of drying, with more significant changes observed as the drying progresses. The observation in this point is, however, interesting from a practical viewpoint, wherein the modulus of soils in the vadose zone can be expected to show similar hysteresis, for example, a soil layer having seasonal fluctuations of water (i.e., lowering followed by an increase in water level) is expected to demonstrate a higher modulus (i.e., lower settlement potential) the following year. The graphs show a clear hysteresis for both wetting and drying curves and a difference in both curves due to the possible stress history of the soil. The values for the elastic constant of constrained are approximately four times the values of the elastic constant of shear. The specimens with higher relative density showed more values of both elastic constants.

Figure 11: