Reliability of HCT-based Soil Water Retention Curves

. The measurement of SWRCs using HCTs has been the subject of several recent studies. Consequently, there have been several design and experimental procedures developed. However, despite these developments, the accuracy, range and duration of HCT-based measurement is still largely characterized by uncertainties and inconsistencies, thereby, reducing the reliability of the obtained SWRCs. In this work, an experimental program is designed to address these uncertainties. SWRCs of reconstituted London clay were measured using the continuous drying method with evaporation rate control. The obtained SWRCs were analysed based on the maximum suction value recorded by HCTs ( s max ), the obtained air-entry value ( s aev ), the suction at inflection point ( s i ), the water content at inflection point ( w i ), and the slope of tangent to inflection point ( m i ). A percentage uncertainty of ±4% was obtained for the s aev and s i values. Similarly, percentage uncertainties of ±6% and ±0.5% were obtained respectively for the m i and w i values. These results were further compared with parametric analysis of the reported SWRCs of the same soil in the literature. Given the observed tolerance ranges, cautions must be taken in selecting values for these parameters e.g. as input values in mathematical curve fitting equations for prediction of the entire SWRC, or in unsaturated constitutive modelling, to enhance reliability of the outputs.


Introduction
Experimental investigation of unsaturated soils' hydromechanical behaviour and determination of unsaturated soil parameters typically involves complex, costly, and time-consuming procedures. Indirect determination of unsaturated soil parameters, such as permeability and shear strength, from the soil water retention curve (SWRC) has proven to be a pragmatic and viable alternative [1]. However, the precision and reliability of the obtained unsaturated parameters is directly influenced by the accuracy and reliability of the SWRC that is in turn dependent to the accuracy and consistency of suction measurement.
The tensiometer method is the only direct soil suction measurement method among the various techniques proposed in the literature. Since the development of high-capacity tensiometers (HCT) in early 1990s, the use of this technique in SWRC measurement has been the subject of numerous studies and resulted in development of several experimental procedures. However, despite these developments, the accuracy, range and duration of HCT-based measurement is still largely characterized by uncertainties and inconsistencies. Several factors including early cavitation of the tensiometer below its nominal capacity, lack of ultimate contact between the sensor and the soil, temperature variations during the test, non-uniform distribution of pore-water throughout the specimen, and possible ceramic filter's pore clog associated with successive use of the sensor and long-* Corresponding author: ac6031@coventry.ac.uk term contact with fine soils can influence the HCT measurements.
This paper aims at investigating the uncertainties associated with HCT-based SWRCs through statistical analysis of the derived SWRC parameters.

Test Material
The material used in this study was London clay (LC), which was collected from an engineering site in the Isle of Sheppey, UK [2]. The specimens were prepared following the procedure outlined in [3,4]. The natural samples were initially oven-dried at 105°C, then crushed into powder and sieved through a 1.18 mm sieve. The dry soil was mixed with distilled deaired water at 1.5 times the liquid limit. The obtained soil slurry was then consolidated in a 100 mm diameter consolidometer for 7 days. The consolidated sample was then extracted and cut into three equally sized subsamples of 100 mm diameter and 35 mm height. Finally, the test specimens were cored from the subsamples using a standard 75 mm diameter and 20 mm height oedometer ring. The specimens had initial void ratio of e0 = 1.0 1% and initial water content of w0 = 39.5 0.5%. It must be noted here that the presence of coarse-grained peds in the soil samples resulted in an air-entry value (AEV) of around 260 kPa that is significantly lower than that of natural LC reported in the literature [5,6]. This allowed for detection of unsaturated states on SWRC within the capacity of HCTs [7].

HCT
The HCTs used in this study were fabricated at the University of Warwick. This sensor, named Warwick tensiometer (WT) hereafter, has a nominal capacity of 1500 kPa and a measurement resolution of 0.23 kPa. It has been successfully used in several experimental studies of the unsaturated soils' behaviour for monitoring long-term soil suction evolutions [8,9]. In this work, four WTs of the same design characteristics were used for measurement of SWRCs. These sensors are denoted WT-A, WT-B, WT-C, and WT-D. Fig. 1 presents a schematic diagram of the WT. Prior to each test, the tensiometers were preconditioned following the procedure described in [10,11].

Experimental Procedure
Generally, two methods namely, static and dynamic, are available for HCT-based SWRC measurement. In the static method, the soil specimen is air-dried to known water contents and then stored in sealed containers for at least two days to attain moisture equilibrium prior to suction measurement. In the dynamic method, the soil specimen is placed on a digital balance and exposed to continuous air-drying. Changes of water content are simultaneously monitored by the electronic balance, while the evolution of suction in the continuously drying specimen is recorded by the HCT. The latter method is considered in this study.
Initially, the soil specimen, enclosed in the oedometer ring, was placed on a digital balance with a 0.01 g resolution. A porous disk was considered as the interface between the soil and the balance plate to expose the specimen's base to the atmosphere and hence facilitate the process of continuous air drying. The porous disk being dry and having a large pore size has a negligible effect on the soil specimen and only provide a passage for air circulation at the base of the specimen. Using a mini augur, four holes of 10 mm diameter and 6 mm depth were created on the specimen's surface to accommodate the WTs. The probes were then gently pushed into the holes so that their tips, covered with a thin layer of paste made of the test material, were in ultimate contact with the specimen. Installation of the probes following this procedure deemed to be effective and minimize the local consolidation of the specimen at the soil-sensor interface, non-uniform evaporation at the exposed surface, and accelerated drying in localized areas due to surface cracking [4]. Finally, a perforated chamber was placed around the specimen to control the evaporation rate, allowing more time for equilibrium establishment between the soil and the HCTs. The rate of gravimetric water content change was around 0.15%/h for all tests. The change in soil mass due to the pore water evaporation was continuously measured by the digital balance and recorded on a computer using an RS232 interface. All tests were carried out under the constant temperature and humidity conditions. Fig. 2 presents a schematic diagram of the experimental setup.

Parameter Derivation
In this study, six tests were carried out for direct measurement of the SWRCs of the reconstituted LC. In these tests, only the main drying branch of the SWRC was produced in the gravimetric water content versus suction (w -s) domain. The true air-entry values were derived based on the method suggested by [12] whereby the water retention data are plotted on both semi-log and log-log scales on the same graph and the AEV is obtained as the boundary between saturated (linear or bilinear behaviour in semi-log plot) and unsaturated (straight line in log-log plot) zones. This method was later validated by [13] using a machine learning method for estimation of the true AEV of 790 samples in the unsaturated soil hydraulic database, UNSODA [14]. Other parameters including suction at inflection point (si), the water content at inflection point (wi), and the slope of tangent to inflection point (mi) were obtained    The absolute uncertainty (measured as the range of the measurements divided by two) in smax values obtained in each test falls within a range of 98 -160 kPa. This corresponds to a range of 4.9 -13.0% relative uncertainty. Such a tolerance range necessitates the use of more than one HCT on a single specimen for measurement of SWRC, especially in fine-grained soils where the transition from saturated to unsaturated state may take place at very high suctions.   Fig. 7. It was also observed that two WTs placed on the same specimen (e.g. WT-A and WT-D in Test 1) may record varied suction at air-entry values with differences being as high as 25 kPa. As it will be explained later in this paper, such differences may result in estimation of significantly different suctions corresponding to a given water content when mathematical curve fitting methods are used for prediction of the entire SWRC beyond the HCTs' measurement capacity.

Suction at Air-entry Value
Despite every attempts made to ensure consistency in specimen preparation, HCT preconditioning, and test setup, minor differences may result in such moderately large variations in the obtained saev values from different WTs. Moreover, slight differences in the sensor manufacturing process may also cause measurement inconsistencies. For instance, the surface roughness of the inner wall of the diaphragm on the water reservoir side may be slightly different for WT-A and WT-D. This may result in more numbers of crevices and hence, higher number of entrapped gas nuclei that could potentially disrupt the suction measurements [11]. Overall, a percentage uncertainty of 4% seems reasonable for reporting the saev values. Such a small tolerance range and the relatively narrow range of mean saev values obtained are promising and confirm the reliability of the air-entry values obtained from the HCT-based SWRCs.     Fig. 8. Overall, a percentage uncertainty of 6% seems reasonable for reporting the mi values.   Fig. 9. Overall, a percentage uncertainty of 4% seems reasonable for reporting the si values.
The mi and si parameters govern the shape of the SWRC and are two input parameters in mathematical curve fitting equations [15]. Despite their relatively small percentage uncertainty, it is believed that small variation of these parameters could potentially result in significant suction changes corresponding to a given water content on the main drying branch of the SWRC.   Fig. 10. Overall, a percentage uncertainty of 0.5% seems reasonable for reporting the wi values.
In the performed tests, the water evaporation process was facilitated through both the top and bottom of the specimen. However, the distribution of pore-water at the mid-height of the specimen (approximately where suction was measured) might be different to the global change in water content measured by the digital balance. This may explain the slight differences observed in the SWRCs and the estimated wi values.

Additional Parametric Study
To further investigate the accuracy of the extracted parameters from HCT-based SWRCs and their potential impacts, a simple analysis was carried out employing the sigmoidal curve fitting equation proposed by [15]. The mi, wi and si values obtained in Test 1, along with the saturated water content wsat = 39.5% and residual soil suction sr = 7.0 MPa were used to develop a mathematical extrapolation of the variation of water content with soil suction where the data points for high suctions (>smax) were not available. Two additional analyses were carried out with si + 4% and si -4% as input values. The obtained results revealed that variation of si by 4% shifts the best-fit curves resulting in 5% change in the saev (Fig. 11) mathematical predictions up to s = 550 kPa are shown in Fig. 11.
The obtained data in this study, in terms of smax, saev, si, and wi, are in close agreement with those reported in [4] where modified performance-improved WTs were used for SWRC measurement of reconstituted Sheppey LC.

Conclusions
A statistical analysis of the data obtained from a series of SWRC measurements using HCTs was presented. Despite their occasional measurement inconsistencies, HCTs can be reliably used for development of SWRCs in laboratory. The parameters obtained from HCT-based SWRCs should be reported with an appropriate tolerance range. Analysis based on SWRCs obtained using only one HCT should consider a tolerance of 4% for the suction at air-entry value, saev , and suction at inflection point, si, a tolerance of 6% for the slope of the tangent line to the inflection point, mi, and a tolerance of 0.5% for the water content at inflection point, wi. Given the sporadic inconsistencies in HCTs' performance, it is recommended, where possible, to use two or more sensors on a specimen to record soil suction changes during SWRC measurement. Cautions must be considered in use of the extracted parameters from HCT-based SWRCs in mathematical curve fitting or numerical modelling. The recommended tolerance ranges are based on the limited data of this study. Further investigations on different soil types and using different HCT prototypes are required for validation of the obtained results. Finally, although this research is focused on the performance of a specific HCT, the procedure described could potentially be used to establish the reliability of any other commercially available or custom-made instrument used to develop water retention curves.