Water Resources Research

Effects of soil skeleton deformations on hysteretic soil water characteristic curves: Experiments and simulations

Authors


Abstract

[1] Soil water characteristic curves (SWCCs) represent the relationship between suction and water content in unsaturated soils. The SWCCs exhibit hysteresis during wetting-drying cycles; however, the empirical expressions used to describe SWCCs have typically ignored the hysteresis. Additionally, the shape of the SWCC will vary depending on the void ratio of the soil and changes resulting from soil skeleton deformations, which may also show hysteretic behavior under various loading conditions. Therefore, it is important to investigate, both experimentally and theoretically, the relationship between soil skeleton deformations and the SWCC for different soils. There is limited information in the literature that examines, both experimentally and theoretically, the complex coupling between the soil skeleton deformation and SWCC behavior, and generally, this behavior is not well understood. This paper presents laboratory test results of SWCCs determined under different confining stresses on similarly prepared samples of a silty soil; drying, wetting, second drying, and scanning curves were obtained. The influence of soil skeleton deformations on SWCCs is inferred from the curves measured in an oedometer under different stress conditions. An elastoplastic phenomenological constitutive model based on the bounding surface plasticity theory was utilized to simulate the coupled mechanical-hydraulic behavior of measured results. This research demonstrates that the model is capable of predicting hysteresis in SWCCs and soil skeleton deformation and the coupling between the hydraulic and mechanical behavior of unsaturated soils.

1. Introduction and Background

[2] In recent years, the important role of the soil water characteristic curve (SWCC) in unsaturated soil mechanics has come to the forefront of geotechnical engineering research. Unfortunately, the SWCC exhibits hysteresis; or in other words, the relationship between the amount of water and matric suction (pore air pressure minus pore water pressure) in soil is not unique. This adds considerable challenges to inclusion of the SWCC in constitutive models, analysis of boundary value problems, and design of unsaturated soil structures. Graphically, the position of a point on the SWCC relative to the water content and the matric suction axes depends on whether the soil was wetted or dried, the previous wetting and drying history, and the stress history of the soil. Since matric suction and the amount of water in the soil directly impact the soil skeletal stress, it stands to reason that the mechanical behavior of unsaturated soil is strongly dependent on the soil state relative to the SWCC. Consequently, early constitutive models for unsaturated soil [e.g., Alonso et al., 1990], while providing an important conceptual foundation on which to build, were unable to capture certain aspects of real soil behavior because they did not incorporate the hysteretic and stress dependent nature of the SWCC. More recently, hysteresis and stress dependency of the SWCC have been incorporated in constitutive models [e.g., Wheeler et al., 2003; Gallipoli et al., 2003; Li, 2004; Wei and Dewoolkar, 2006; Li, 2007a, 2007b; Sun et al., 2007].

[3] While major progress has been made, it is apparent that additional research is needed to improve and validate existing models and develop new models. This realization is based partly on the following observations: first, there is a wide variety of opinions regarding the proper selection of stress state variables for unsaturated soil [e.g., Fredlund and Morgenstern, 1977; Wheeler and Sivakumar, 1995; Gallipoli et al., 2003; Khalili et al., 2004; Lu and Likos, 2004; Zhang and Lytton, 2006]. Second, as noted above, there are relatively few models incorporating hysteresis in existence and none are widely accepted, partly because they are relatively recent. Finally, there are limited experimental data available that reveal detailed hysteretic behavior between suction and water content (i.e., SWCC) under different levels of externally applied stress (or at different void ratios). Regarding the latter, some valuable data do exist [e.g., Romero et al., 1999; Ng and Pang, 2000; Karube and Kawai, 2001; Tarantino and Tombolato, 2005; Ho et al., 2006]; however, the data typically includes primary drainage and primary wetting, but not secondary drainage or scanning curves. Furthermore, much of the available data that reveals relationships between the SWCC and initial void ratio comes from tests where samples were prepared at different initial void ratios and thus differences in behavior may originate from variations in fabric/structure caused during sample preparation and not variations in void ratio caused by externally applied stress. The lack of SWCC results beyond primary drying and wetting curves is largely due to the enormous time requirements for unsaturated soil testing.

[4] The research presented in this paper is intended to contribute to the forward progression of constitutive modeling by presenting a novel approach for modeling the hysteretic behavior of the SWCC coupled to the mechanical behavior of unsaturated soil. This is accomplished using the bounding surface plasticity theory to model the coupled mechanical-hydraulic behavior, including the hysteresis in SWCCs. In addition, a very important set of experimental results are presented; resulting SWCCs include primary drainage and wetting, secondary drainage and scanning curves for two different normal stress states. Scanning curves in this paper are defined as drainage and wetting curves that initiate inside the secondary drainage and primary wetting curves. It was possible to obtain these experimental results in a reasonable amount of time by using manufactured soil that provided levels of matric suction consistent with a silty soil, but with considerably greater hydraulic conductivity than most natural soils with similar suction ranges. Historically, excessively long periods have been necessary to produce experimental data for unsaturated soils, particularly if wetting and drying cycles were involved. This has been an obstacle to timely and proper validation of constitutive models. Thus, for this study an artificial soil was used to allow more rapid testing and better control over soil properties.

2. Experimental Program: Determination of Soil Water Characteristic Curves and Mechanical Behavior Under One-Dimensional Loading

2.1. Test Procedure

[5] Soil Water Characteristic Curves were experimentally determined using a relatively simple device built at the University of Oklahoma. A test cell was fabricated to fit into a one dimensional consolidation apparatus so that incremental vertical loading could be externally applied while independently controlling the pore air and pore water pressure in the soil sample. As shown schematically in Figure 1, the pore water pressure was digitally controlled using a commercially available high-precision motorized piston pump and transmitted to the soil via a high air entry porous disc. A similar pump having a larger piston volume was used to control the air pressure in the cell. These pumps can resolve pressure and volume changes on the order of 1 kPa and 1 mm3, respectively. Vertical normal stress was applied to the sample through a stainless steel piston acting against the rigid top platen above the sample using the incremental loading features of the oedometer. Vertical deformation of the sample was measured via a linear variable differential transformer (LVDT). The experimental apparatus allowed for independent control/measurement of the pore air pressure, pore water pressure, vertical normal stress and measurement of vertical deformation throughout testing so that a variety of loading sequences with respect to net normal stress and matric suction could be investigated.

Figure 1.

(a) Schematic of test cell cross section and measurement control system. (b) Photographs of modified oedometer setup.

[6] As mentioned previously, it was desired to obtain a significant amount of data in a relatively short period. Timely acquisition of experimental data was achieved in three ways: (1) a porous disc with a relatively low air entry value was used (three bar) to gain maximum efficiency with respect to water transmission into and out of the soil. The air entry value is the theoretical maximum pressure difference between the air pressure and water pressure that can be maintained across the porous disc without air fully penetrating and flowing through the pore channels in the disc. (2) A mixture of two commercially available manufactured soils, Sil-Co-Sil 250 manufactured by U.S. Silica Company and Glass Beads, Size BT-9, manufactured by Zero Products was used as the test soil. The mixture of 75% ground silica and 25% glass beads has a relatively higher hydraulic conductivity, compared with natural soils with similar suction range. The grain size distribution of the mixed test soil is given in Table 1. As shown, the test soil has a grain size distribution similar to that of fine sandy silt having about 48% fine sand (0.075–0.25 mm), 46% silt (0.002–0.075 mm), and 6% clay size material (≤0.002 mm). (3) The height of the soil sample, and hence volume of soil and water required to saturate the soil, was minimized to shorten equilibrium time [Khoury and Miller, 2008]. A series of tests was conducted to determine the minimum height of soil sample that could be used while practically achieving results similar to samples with heights more typical of one dimensional testing. The samples used had a height of 6.4 mm and a diameter of 63.5 mm. Note, the time required to complete testing was reduced by about 50% when the sample height was reduced from 25.4 to 6.35 mm. Using the system developed, the total time for testing, including primary drainage, primary wetting, secondary drainage, and a scanning curve loop was about 48 days.

Table 1. Grain Size Distribution for Test Soil
 D (mm)Percent Passing
Sieve number 600.250100.0
Sieve number 700.21297.4
Sieve number 1000.15087.1
Sieve number 1400.10664.5
Sieve number 2000.07552.1
Hydrometer0.033632.7
0.024229.0
0.016523.1
0.012520.1
0.009316.4
0.006811.9
0.00498.9
0.00407.4
0.00175.9

[7] Prior to conducting the research experiments presented in this paper, numerous tests were conducted to calibrate and evaluate the performance of the testing device with respect to experimental error and repeatability. Results of testing on four different samples are presented in this paper, including data from one retest conducted to investigate repeatability. Each sample was prepared in an identical fashion to achieve nominally the same initial void ratio (0.69) and gravimetric moisture content (17.2%) in the test specimens. Samples were prepared by moist tamping (i.e., volume-based compaction) the soil directly into the test cell on top of the preconditioned high air entry porous disc. The test cell was then placed in the oedometer frame and a seating load (5 kPa) was applied to assure a good contact between the top cap and the soil. The cell was then flooded with water and water was forced under low pressure through the sample by increasing the air pressure above the water in the cell. This process continued until a minimum of three pore volumes of water had flowed through the sample to remove entrapped air. Following saturation, samples were loaded incrementally to the desired vertical normal stress, after which the drying (drainage) and wetting cycles were initiated.

[8] Suction was controlled during testing by using the axis translation method whereby the air pressure was increased while maintaining a constant water pressure of 0 kPa using the precision pumps. To maintain constant net normal stress during an increase in air pressure the axial normal force exerted by the oedometer was adjusted slightly to compensate for the air pressure acting on the portion of the axial load piston inside the air chamber. Axis translation allows one to increase suction without using water pressure below zero gage pressure, thereby avoiding cavitation.

[9] Two samples were tested at vertical net normal stresses of 10 and 200 kPa. For each net normal stress the samples were subjected to wetting and drying cycles to obtain the primary drainage, primary wetting, secondary drainage and one or more scanning curves. In addition, a repeat test was conducted at 200 kPa net normal stress to investigate repeatability and one test was conducted at 0 kPa net normal stress but in a separate cell not equipped for measurement of vertical deformation. For the 0 kPa test, only primary drainage and wetting curves were obtained.

2.2. Test Results

[10] Soil water characteristic curves for tests conducted under net normal stress of 10 and 200 kPa are presented in Figures 2 and 3, where pa and pw are pore air and pore water pressures, respectively, and nw is the volumetric water content (volume of water/total volume). The data points in Figures 2 and 3 represent the increments of suction and corresponding measurements of water volume change at equilibrium. Equilibrium was assumed to occur when negligible water volume and total volume change occurred following application of a new suction increment. In Figure 4 an example of water volume change (w is gravimetric water content) versus time for primary drainage at 200 kPa net normal stress is shown; water volume changed fairly rapidly following application of an increment of suction followed by a more gradual change until equilibrium was observed. On the basis of Figure 4 the time to complete primary drainage was about 18 days, which demonstrates the relatively fast equilibrium times that were achieved using the artificial soil and testing system described above.

Figure 2.

Soil water characteristic curve for net normal stress of 10 kPa.

Figure 3.

Soil water characteristic curve for net normal stress of 200 kPa.

Figure 4.

Water content versus time for primary drainage during testing for 200 kPa net normal stress.

[11] In Figure 5, a comparison of the secondary drainage and primary wetting curves for each test is shown. These portions of the SWCC were chosen for comparison since they represent the bounding curves employed in the bounding surface elastoplastic model presented in the next section. Note that for 0 kPa net normal stress, only the primary drainage and a portion of the primary wetting curve were obtained because the test had to be terminated prematurely; these are shown for comparison to the 10 and 200 kPa net normal stress curves.

Figure 5.

Summary of soil water characteristic curves for net normal stresses of 0, 10, and 200 kPa.

[12] In examining Figures 2, 3, and 5, some interesting observations are made.

[13] 1. For the 10 and 200 kPa net normal stresses, the scanning curves are bounded by the secondary drainage and primary wetting curve.

[14] 2. The initial volumetric water content decreases with increasing net normal stress as expected since the void ratio decreases more during application of higher net normal stress.

[15] 3. Generally, the air entry value increases with increasing normal stress, again as expected, because of the lower void ratio. However, the difference between the air entry value for 0 and 10 kPa net normal stress is negligible, probably because the change in void ratio from 0 to 10 kPa is relatively small compared to the difference between net normal stress of 10 and 200 kPa. The air entry value is the matric suction necessary for air to penetrate the void space when the soil is initially saturated.

[16] 4. Generally, the slope of the SWCC is flatter at lower net normal stress and becomes steeper with increasing net normal stress; it is especially apparent as the curves approach the lower residual saturation moisture contents. This observation is reasonable because the pore channels in soil with lower void ratio would be smaller relative to higher void ratio soil. Thus, the lower void ratio soil would generate higher capillary pressure than a higher void ratio (i.e., matric suction) at the same volumetric water content. Also, the residual moisture contents appear to increase with increasing net normal stresses.

[17] As mentioned previously, the SWCC test was repeated at 200 kPa net normal stress to investigate experimental variability. Figure 6 shows the comparison of results from the two nominally identical tests. For the repeat test, only the primary drainage and a portion of the primary wetting curve were obtained because the system developed a leak that could not be repaired during testing. Nevertheless, the comparison of the SWCC curves is favorable, as is the volume change behavior represented by specific volume (1 plus void ratio) data presented in Figure 7. While the number of repeat tests was limited, the results for duplicate tests demonstrate that the SWCC is reproducible to reasonable accuracy.

Figure 6.

Comparison of results from two nominally identical tests at 200 kPa net normal stress.

Figure 7.

Specific volume versus net normal stress during compression for three similarly prepared SWCC test specimens. Model predictions obtained during calibration shown for comparison.

[18] For the 10 and 200 kPa net normal stress SWCC tests, vertical displacements were recorded throughout testing beginning with the saturation process and continuing through the saturated compression and SWCC testing. In Figure 7, a comparison of specific volume versus net normal stress curves is presented. These curves represent compression starting from the compacted state, followed by wetting induced compression during saturation at a constant total stress, and subsequent compression under saturated conditions to reach the starting point of the SWCC tests. Although the curves exhibit some slight differences, they are generally similar and express similar soil behavior. Since samples were prepared in nearly identical fashion, similar behavior was expected. Interestingly, the samples showed considerable wetting-induced compression under a very low normal stress; the change in specific volume due to wetting represents a volumetric strain of about 1.5%. This collapse may be partly attributed to the relatively loose initial state of the sample following compaction and the significant angularity of the crushed silica particles. Both of these factors contribute to an open soil structure susceptible to collapse.

[19] During incremental loading the samples behaved similarly as evidenced by the similar slopes of each curve. Comparison of the specific volumes at 10 kPa and 200 kPa net normal stress indicates that significant compression, about 4–5% volumetric strain, occurred during incremental loading up to 200 kPa. This accounts for the differences in the initial volumetric water content for corresponding SWCCs. During the SWCC testing, the volume change as determined from LVDT measurements of vertical deformation was practically negligible with a maximum volumetric strain (due to suction change beginning from the start of the SWCC) of about 0.75%, for both the 10 and 200 kPa net normal stress specimens. While small, the volume change was included in the computation of volumetric water content.

3. Elastoplastic Constitutive Model to Simulate the Coupled Hydraulic-Mechanical Behavior

[20] The constitutive model used in this paper combines an elastoplastic description of the SWCCs with an elastoplastic description of the stress strain behavior of the solid skeleton. While the SWCCs are described using a bounding surface elastoplastic model the stress strain behavior is simulated using the classical plasticity theory. The theoretical basis and detailed description of the model can be found in work by Muraleetharan et al. [2008]. The model equations are presented here for completeness.

3.1. Stress Strain Variables

[21] The intergranular stress and solid skeleton strains are used to describe the mechanical behavior and the matric suction and volumetric water content are used to describe the hydraulic behavior. The volumetric water content is also referred to as the volume fraction of water in mixture theories. The intergranular stress tensor σ*ij in soil mechanics sign convention (i.e., compressive stresses are positive) is given by

equation image

where σij is the total stress tensor; S (= papw) is the matric suction; pa and pw are pore air and pore water pressures, respectively; nw is the volumetric water content; and δij is the Kronecker delta. By studying the plastic deformation of the solid skeleton and capillary hysteresis, Wei and Muraleetharan [2002a, 2002b] and Wei [2001] showed that the intergranular stress is conjugated to plastic solid skeleton strains and the matric suction is conjugated to the irrecoverable (plastic) changes in the volumetric water content to produce mechanical and hydraulic energy dissipations in unsaturated soils.

3.2. Description of the SWCCs

[22] Motivated by the observation that all the scanning curves are bounded by the primary wetting curve and the secondary drying curve, we chose the bounding surface plasticity theory originally proposed by Dafalias and Popov [1975, 1976] to describe the SWCCs. In order to keep the elastoplastic terminology, we define equivalent terms such as the capillary plastic modulus in the description of the SWCCs. In the description of the SWCCs, the term plastic refers to irrecoverable portion of the volumetric water content.

[23] The equation proposed by Feng and Fredlund [1999] is used to describe the bounding curves as follows:

equation image
equation image

where nsatw is the volumetric water content at zero suction; nresw is the residual volumetric water content; b1, d1, b2 and d2 are four material parameters; and b1 and b2 have the same unit as suction.

[24] Following the standard elastoplastic decomposition of the strains into elastic and plastic parts, volumetric water content is decomposed as follows:

equation image

where dnw, dnew, and dnpw are increments in total, recoverable (elastic), and irrecoverable (plastic) volumetric water contents, respectively. This decomposition leads to the definitions of the capillary elastic (Γe) and plastic moduli (Γp) given by

equation image
equation image

where dS is the increment in matric suction. In the model used, Γe is assumed a constant, but if needed it can be made as a function of S. Following Dafalias and Popov [1976], an evolution equation is proposed for Γp as follows:

equation image

where δ is the vertical distance (in suction units) between the current point and its corresponding bounding curve (either the primary wetting or the secondary drying, respectively, depending on whether the loading is either a wetting or a drying process), δin is the value of δ at the initiation of yielding for each drying/wetting process, h is a shape parameter, 〈 〉 is the Macaulay brackets, Γ0p is the value of Γp when δ = 0, i.e., the value of Γp on the bounding curves, and g is a model parameter that typically ranges from 1.0 to 2.0.

[25] For the model used in this paper the value of g was set to 1.0 and the parameter h assumed constant. Note that for δδin, Γp = ∞ (since 〈δinδ〉 = 0) and the behavior will be purely elastic. For the model used in this paper δin is set to be equal to the value of δ at the beginning of a wetting or drying cycle resulting in elastoplastic behavior from the beginning of loading, i.e., δinδ. Once the bounding curves have been defined using equations (2) and (3), the model requires only two more parameters, Γe and h. These parameters are calibrated using a single scanning curve. Once these parameters have been determined any other wetting-drying cycle can be predicted.

3.3. Coupled Hydraulic-Mechanical Behavior

[26] In order to describe the coupled hydraulic-mechanical behavior in one-dimensional problems, the SWCC model presented in section 3.2 is coupled with an isotropic stress strain model based on the classical plasticity theory in a manner similar to the one proposed by Wheeler et al. [2003]. The framework presented is, however, general enough to incorporate more sophisticated stress strain models as well as can be extended for three-dimensional stress states.

[27] The key to describing the coupled behavior comes from the hardening laws given by

equation image
equation image

[28] The hardening laws given above describe the change in bounding suction (S0) and yield mean intergranular stress (p*0) with respect to changes in plastic volumetric strain (ɛvp) and plastic volumetric water content (npw). The coefficients in equations (8) and (9) are defined as ‘plastic moduli.’ Γ0p is defined in equation (7). The other three moduli are defined as Γvp = S0ζv, K0p = p0*η0v and K1p = −p0*η1, where ζ, η0 and η1 are three material parameters and v is the specific volume.

[29] The bounding/yield surfaces are described by the following three functions:

equation image
equation image
equation image

where S0I and S0D stand for bounding suctions on the primary wetting and secondary drying curves, respectively. p* is the mean intergranular stress given by

equation image

where p is the mean total stress.

[30] Elastic response of the solid skeleton is given by

equation image

where k is a constant standing for the slope of an elastic swelling line in the v: ln p* space. In addition, the elastic changes in volumetric water content are given by equation (5).

[31] Finally the plastic strain increments are given by

equation image
equation image

Equations (15) and (16) are consistent with the flow rules dnpw/vp = 0 and vp/dnpw = 0, respectively. This implies that the yield surface given by p* = p0* and the bounding surface given by S = S0I (or S0D) are perpendicular to each other on the p* − S plane. At the intersection of the bounding surfaces and the yield surface, vp and dnpw are calculated by simultaneously solving equations (8) and (9). These solutions are given below.

equation image
equation image

[32] Four additional parameters, k, ζ, η0 and η1 are required to describe the coupled hydraulic-mechanical behavior. The parameter k can be obtained from an unloading-reloading portion of a constant suction oedometer test. With k obtained the parameter η0 can be calibrated by matching the loading curves during a constant suction oedometer test. The calibration of the parameters ζ and η1 will require coupled hydraulic-mechanical tests where the soil undergoes plastic volume and plastic water content changes. A wetting induced collapse test is one such test.

4. Calibration and Validation of the Constitutive Model

[33] For the soil used in this study, the parameters describing the SWCCs were first calibrated using the measured curves for 10 kPa net vertical stress shown in Figure 2. The calibrated parameters are as follows:

equation image

The measured and predicted SWCCs are shown in Figure 8. These values were used for all subsequent predictions unless otherwise specified.

Figure 8.

Measured and predicted SWCCs obtained during calibration of the model for a net normal stress of 10 kPa.

[34] Next, the value of k was obtained as 0.001 by using the initial portion (i.e., before flooding) of the v − log (σvpa) curve shown in Figure 7. This curve corresponds to increasing the net vertical stress from 1 kPa to 5 kPa while keeping the suction at approximately 8 kPa (suction for as-compacted samples). Note that since the tests carried out were all oedometer tests, the 1-D simulations are done with reference to vertical stresses and vertical strains. In order to initiate the calculations at 1 kPa the initial value of σv0* (initial vertical yield intergranular stress) was assumed to be 7.8 kPa. The parameters ζ and η1 were next calibrated by matching the collapse behavior shown in Figure 7. While calibrating these parameters the initial value of σv0* was also adjusted. In fact, the initial value of σv0* influences the prediction of the wetting-induced collapse the most. Therefore this step essentially involves calibrating ζ, η1, and the initial value of σv0* at 1 kPa net vertical stress. While this combination may not be unique these values give reasonable overall predictions. For the flooding the suction was reduced from 8 kPa to 0 kPa while keeping the net vertical stress at 5 kPa. The values of ζ and η1 obtained in this manner are 16.0 and 15.5, respectively. The value of the parameter η0 is calibrated as 50.0 using the loading curves for the flooded samples shown in Figure 7. Predicted v − log (σvpa) curves obtained in this way are superimposed on the experimental data shown in Figure 7. Predicted vσv* curve is shown in Figure 9. Predicted Sn curve during wetting is shown in Figure 10. Also shown in Figure 10 are the initial and final bounding curves during the wetting process.

Figure 9.

Model prediction of specific volume versus intergranular stress during compression.

Figure 10.

The wetting path and the bounding curves when suction changes from 8 to 0 kPa (only portions of the bounding curves are shown).

[35] With these calibrated model parameters, the SWCC for 200 kPa net vertical stress was predicted following a stress/suction change path that simulated the stress/suction change path for a portion of the experiment. Specifically, starting with as compacted conditions, loading and wetting paths as shown in Figure 7 were first simulated. Then the following wetting/drying cycles were simulated: start at zero suction and follow the secondary drying curve to near residual saturation at a suction of 70 kPa, wet back to a point along the primary wetting curve at a suction of 20 kPa, followed by a complete drying and wetting path (suction increase to 60 then decrease back to 20) to establish a scanning curve loop. The measured and predicted portions of the SWCCs for 200 kPa net vertical stress are shown in Figure 11. The only parameter that needed adjustment was the residual saturation. A value of nresw = 0.06 was used to predict the behavior at 200 kPa net vertical stress. The comparison in Figure 11 demonstrates that the proposed model is well suited to capture the hysteretic nature of the SWCC and a reasonable agreement with experimental results was obtained. To further appreciate the potential of the model to capture the coupled mechanical-hydraulic behavior, the predicted SWCCs for net normal stress of 10 and 200 kPa are shown together alongside a similar graph depicting the experimental data in Figure 12. In Figure 12 it is apparent that the model is capturing some of the essential features demonstrated by the experimental data. In particular, the shape and position of the model SWCCs for 10 and 200 kPa net normal stress is similar to that exhibited by the experimental curves. That is, the model SWCC for a net normal stress of 200 kPa is slightly steeper and positioned slightly above the model SWCC for a net normal stress of 10 kPa. However, the model does not show the slight difference in the air entry value observed in the experimental results.

Figure 11.

Measured and predicted SWCCs obtained during validation of the model for a net normal stress of 200 kPa.

Figure 12.

Comparison of measured and predicted SWCCs for net normal stresses of 10 and 200 kPa.

5. Summary and Conclusions

[36] Experiments were conducted in a specially fabricated one-dimensional testing cell to examine the coupled mechanical-hydraulic behavior of artificial unsaturated silt. Portions of the soil water characteristic curves, including primary drainage and wetting, secondary drainage, and scanning curves were produced for vertical net normal stresses of 0, 10 and 200 kPa. A bounding surface plasticity model was used to capture the coupled mechanical-hydraulic behavior exhibited in the experimental results. The model was calibrated using one dimensional compression data and the soil water characteristic curve (SWCC) for the 10 kPa net normal stress. The calibrated model was then used to predict the SWCC for a net normal stress of 200 kPa. While the development of this model is still in its infancy, the research described in this paper has revealed that the model has great potential for future development, which will include extending it to more general three dimensional states of stress and different soil types (i.e., clayey soils subject to greater suction-induced volume change). Furthermore, some of the experimental techniques employed proved very valuable in the timely completion of testing. Some conclusions from this study follow.

[37] 1. Use of an artificial soil composed of crushed silica and glass beads, having a grain size distribution similar to fine sandy silt, enabled a significant number of SWCC tests to be conducted in a relatively short amount of time. This included time for completing primary drainage and wetting, secondary drainage, and one scanning curve cycle in some cases. The primary advantage of this soil is that it has a relatively high hydraulic conductivity but similar suction compared to typical natural soils with similar gradations. Furthermore, there is likely better control over the uniformity of soil properties, from sample to sample, with the artificial soil.

[38] 2. Experimental time was further reduced by using relatively thin samples. While not the focus of this paper, an investigation into the influence of sample height on the time required to complete an SWCC revealed significant time gains could be achieved using relatively thin samples without sacrificing accuracy with respect to volume change measurements.

[39] 3. Experimentally determined SWCCs revealed the air entry value tended to increase as the net normal stress increased, as expected given the decreased void ratio at higher net normal stress. The residual moisture content also increased with increases in net normal stress.

[40] 4. As the net normal stress increased, the slope of experimentally determined SWCCs tended to change, particularly as the water contents approached residual saturation. Specifically, the volumetric water content corresponding to a net normal stress of 200 kPa was higher than on the corresponding curve for 10 kPa net normal stress at the same suction. The proposed constitutive model appeared to capture this behavior quite well.

[41] 5. The constitutive model was able to capture the transition from unsaturated to saturated behavior exhibited by the one-dimensional collapse that occurred during sample flooding and subsequent saturated compression prior to conducting the SWCCs.

Acknowledgments

[42] The laboratory testing equipment used for this research was developed thanks to the financial support of the National Science Foundation under grant 0079785. Special thanks to Michael F. Schmitz of the University of Oklahoma for applying his exceptional skills to the fabrication of the testing cells.

Ancillary