1 Introduction

The water content of soil is usually subjected to seasonal changes when the soil is located above the groundwater table. The water content changes of soil can cause significant variations of soil behaviours such as deformation, shear strength, creep, and stress-strain behaviour, etc. [53]. Whereas unsaturated soil testing is still a big obstacle for researchers and engineers because of the complex and expensive equipment. There are limited studies in the development of testing apparatus on unsaturated soils due to the complex structure, tedious calibration process, and high test demands [37, 38, 52, 53]. The complex structure of apparatus for unsaturated soil testing is designed to fulfil two significant requirements, including independent regulation of pressures of two pore fluids and independent measurement of total volume and water content in soil specimens [5].

In unsaturated soils, the main difficulty to fulfil the first requirement involves regulation and measurement of negative pore-water pressure that cannot be obtained by conventional apparatus without cavitation. Thus, three types of typical techniques have been developed to measure and control soil suction in the development of testing apparatus on unsaturated soils, including axis translation technique (ATT), osmotic technique (OMT), and vapour equilibrium technique (VET). Total suction of soil can be defined as the summation of matric suction, s, and osmotic suction, π [23]. Typical devices for measuring soil suction are listed in Table 1. Some of the newer methods include chilled-mirror hygrometer and electrical conductivity. The apparatuses and techniques used to measure soil suction vary widely in terms of limitation, time, cost, complexity, and testing range. Table 2 lists typical apparatuses using different techniques to control soil suction, among which the ATT is the most used one. However, the air pressure in ATT cannot represent the field atmospheric condition, and maximum controlled suction is only 1500 kPa [23], which might be low for measuring suction of unsaturated clay, such as bentonite. For the OMT, the field condition can be simulated due to lack of air pressure, and controlled suction can reach up to around 10 MPa [19]. However, the main limitation of OMT lies in the sensitive membranes which is easily attacked by bacteria. Thus, the polyethylene glycol (PEG) solution can infiltrate the specimen and hence the suction cannot be controlled [20]. The main drawback of VET is long period of moisture equalization since vapour transfers based on diffusion [20]. The ATT is adopted in this study for applying relatively low suction on the granular materials, which is adopted for the validation tests.

Table 1 Overview of the typical devices for measuring soil suction
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Table 2 Overview of testing apparatuses using different techniques to control soil suction
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Other necessities for the tests on unsaturated soils are the independent measurements of total volume and water content changes of a specimen. Total volume change is the main difficulty in unsaturated soil testing since it is related to the changes of pore air and pore water in a specimen. Several measurement techniques have been developed to tackle this problem, including direct air and water volume measurement [1, 35], direct measurement on samples [18, 32], and cell liquid measurement [5, 8, 16, 49, 68]. For the technique of cell liquid measurement, the total volume changes of the specimen are calculated based on volume changes of liquid in the cell. Bishop and Donald [8] proposed a double-cell system, in which mercury was used as the cell liquid in the inner cell. Wheeler [62] developed an improved apparatus with two cells by using a burette to measure the water volume changes of specimen. Yin [68] and Chen et al. [16] developed two new double-cell systems to continuously measure the volume changes of specimens under unsaturated condition and cyclic loading condition, respectively. However, the complexity of these double-cell systems might easily cause possible water leakage, and the Plexiglas of the cell water might absorb water and generate a greater creep effect in the long period in unsaturated soil testing. Agus et al. [2] used a stainless-steel cell to avoid the possible absorption of water. However, the specimen cannot be observed in the test because of the opaque stainless-steel cell. Aversa and Nicotera [5] and Ng et al. [49] proposed aluminium cells and measured water levels by differential pressure transducers. However, the fluid pressure might cause large immediate expansion, and the complexity of the double-cell systems might easily cause water leakage. Thus, it is still necessary to develop a new testing apparatus to tackle the challenges of accurate measurements of volume changes of unsaturated specimens.

Modular design (MD) is a design approach in which product components are produced following a standard and assembled as a system [60]. MD can be used to cope with the complexity of apparatus, massive customization, and expensive cost [6, 31]. So far, there has been little discussion about MD in the development of apparatus on unsaturated soils. Aversa and Nicotera [5] proposed a modular apparatus that can be configured to conduct oedometer and triaxial tests on unsaturated soils. Lauer and Engel [36] developed a triaxial device that can be used to determine shear strength, water retention curve (WRC), and hydraulic conductivity of unsaturated sand. However, these complex apparatuses on unsaturated soils have few functions, and the complexity might cause high cost. The expensive apparatus limits the engineering application of unsaturated soils. MD might help to remove the obstacle of high cost and obtain customization.

In this study, a novel multifunctional apparatus (MFA) on unsaturated soils is developed to conduct pressure plate test, oedometer test, direct shear test, and triaxial creep test for unsaturated soils. This system with stainless-steel cell overcomes the large creep deformation in other typical double-cell systems. Additionally, the MFA is designed in a manner to enable testing specimens with different dimensions and to control soil suction based on different techniques. Compared with a single-function device, an MFA can save a lot of money and space in manufacturing and time for calibration. The detailed set-up, calibration methods, and typical test procedures are introduced. Finally, some typical experimental results on a compacted granular fill are presented to illustrate the performances of this apparatus.

2 Descriptions for the multifunctional apparatus

2.1 General descriptions

A novel MFA for unsaturated soils has been designed, manufactured, and set up in the Soil Mechanics Laboratory of the Hong Kong Polytechnic University (Fig. 1). This apparatus is modular and can be configured to perform different types of tests on unsaturated soils, including pressure plate, oedometer, direct shear, and triaxial creep tests.

Fig. 1
figure 1

The multifunctional testing apparatus for unsaturated soils

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2.2 Control of matric suction and net normal stress

A steel hoop with a ceramic disc can be screwed on a custom-built pedestal which can be used in the oedometer-type modified pressure plate module (MPPM) and modified oedometer module (MOM) (Fig. 2a). For the modified direct shear module (MDSM), a steel square plate with ceramic disc can be screwed on a custom-built shear box base (Fig. 2b). In this study, the widely used ATT developed by Hilf [27] was adopted to apply and maintain relatively low matric suction (ua – uw) on the granular materials. Typically, pore-water pressure, uw, in unsaturated soils is negative when pore-air pressure, ua is atmospheric. For the triaxial-type MPPM and modified triaxial creep (MTCM), a steel hoop with ceramic disc can be screwed on a custom-built pedestal (Fig. 2c). The pore-air pressure can be applied and maintained on the coarse porous stone above the specimen through the air pressure pipe on the top of the pressure chamber in MOM and MDSM or air pressure valve on the base in MTCM. For MPPM, both valves on the top (similar to MPPM) and base (similar to MTCM) can be used. The pore-water pressure can be applied and measured by the water drainage system in the water chamber under the high air-entry value disc (HAEVD) which is screwed on the pedestals or shear box base. Exclusive drainage grooves (Fig. 2a to c) have been designed on the pedestals and shear box base to facilitate the circulation of water and the removal of air bubbles under HAEVD. The air-entry values of HAEVDs used in different moduli are 500 kPa. The procedures introduced by Chen [15] were used to prepare the HAEVD before each test.

Fig. 2
figure 2

a A custom-built ceramic disc, pedestal, and sample mould used in oedometer-type MPPM and MOM. b A custom-built ceramic disc and shear box base used in the MDSM. c A custom-built ceramic disc and pedestal used in triaxial-type MPPM and MTCM

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An axial force can be applied to the specimen by deadweight through the lever and load frame system. The ratio of hanger load to actual applied load on the specimen is 1:24. An inner load cell is linked to the loading piston to measure the axial force directly. A maximum axial force of 26 kN can be applied to the specimens. This force corresponds to stresses of 3.3 MPa on the cylindrical-shaped specimens in MPPM (diameter: 100 mm, height: 100 mm), MOM (diameter: 100 mm, height: 100 mm), and MTCM (diameter: 100 mm, height: 200 mm) or 2.6 MPa on a cuboid-shaped specimen in MDSM (length × width × height: 100.05 × 100.05 mm × 40 mm). A displacement transducer with a range of 50 mm is installed on the loading piston to measure the axial displacement of the specimen.

2.3 Modified oedometer module

The principle of modification for the proposed apparatus is similar to that of the previous relevant developments [5]. As shown in the MOM in Fig. 3, in general, an oedometer apparatus on unsaturated soils is a combination of conventional oedometer and system which can control suction and measure the water content change of specimen. The suction is controlled by the ATT and maintained in the whole loading stage, and load can be applied by the lever-arm frame. The actual load applied to the specimen can be measured by a calibrated inner load cell on the specimen. The deformation of the specimen can be measured by a displacement transducer installed on the loading piston on the specimen. The sample mould used in the specimen compaction can be used as the confining ring in tests. A HAEVD can be screwed on the pedestal at the bottom of the specimen, and a coarse porous stone can be placed on the specimen. The air and water pressures can be applied to the specimen located in the pressure chamber and water chamber under HAEVD, respectively. The drying and wetting of the specimen can be controlled by the changes of matric suction which is associated with water flow in the water chamber. An automatic volume change (AVC) device is connected to the water chamber beneath the HAEVD, and the inflow and outflow of water can be measured. The diffused air under HAEVD can be measured by a diffused air indicator (DAI). The axial force and net stress can be applied to the specimen by the dead weight on the hanger. Before the application of the next loading stage, the stabilization period between each suction or loading change shall be retained until both the water change and vertical displacement keep constant. The two sides of the water chamber are connected to components similar in MPPM. The inner diameter of the pedestal is 100 mm, which is suitable for tests on coarse granular materials. Other pedestals with different diameters can be easily installed on the base of the apparatus for tests on other types of materials.

Fig. 3
figure 3

A schematic layout of the modified oedometer module and oedometer-type modified pressure plate module

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Since the horizontal stress of soil specimen is not measured in the current oedometer module, the results shall be interpreted in terms of net vertical stress, \(\sigma_{{\rm v}}^{{\prime}}\), instead of net mean stress, \(\overline{p}\). Nevertheless, the experimental data can still be studied based on the constitutive behaviour of the soils. In any case, compared with other kinds of more sophisticated suction-controlled oedometer apparatus, this apparatus is relatively simple and easy to handle.

2.4 Modified triaxial creep module

The MTCM was designed following a testing apparatus described by Lai et al. [34]. Figure 4 shows the schematic diagram of MTCM. Both the constant shear stress and matric suction can be applied to the soil specimen in the MTCM. The constant shear stress can be applied using dead weights applied to the hanger of the lever-arm frame. To obtain accurate shear stresses, vertical loads applied to a specimen are monitored by an inner load cell in the pressure chamber, which is carefully calibrated before the tests. As stated in “Introduction”, based on the technique of cell liquid measurement, the total volume changes of specimen can be calculated based on volume changes of liquid in the pressure chamber. A pressure/volume controller connected to the pressure chamber is capable of recording flow-in/-out volume of water while maintaining constant water pressure in the pressure chamber. Thus, the total volume change of the specimen can be indirectly measured by the pressure/volume controller. The two sides of the water chamber are connected to components similar in MPPM. A maximum cell pressure of 2 MPa can be applied in the pressure chamber since the thickness of the pressure chamber is considerable.

Fig. 4
figure 4

A schematic layout of the modified triaxial creep module and triaxial-type modified pressure plate module

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2.5 Modified direct shear module

The MDSM was developed based on a soil-soil modified direct shear apparatus described by Hossain and Yin [29]. The fundamental concept of the MDSM is closely related to the previous widely used apparatuses proposed by other researchers [22, 24]. Figure 5 demonstrates the schematic diagram of MDSM. The direct shear box and specimen are installed in the steel pressure chamber. The two sides of the water chamber are connected to components similar in MPPM. The shear load is measured by a load cell in the horizontal direction which is carefully calibrated before the tests. The vertical load is applied by dead weights on the hanger of the lever-arm frame and measured by an inner load cell in the vertical direction. The displacements on horizontal and vertical directions are measured by two calibrated displacement transducers, respectively.

Fig. 5
figure 5

A schematic layout of the modified direct shear module

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2.6 Modified pressure plate module

Figure 3 presents the schematic layout of the oedometer-type MPPM developed as per apparatuses designed by other researchers [39, 51]. This type of MPPM can be used to obtain soil WRC with both drying and wetting curves and the drying and wetting scanning curves. Soil WRC affected by net normal stress can be obtained by the oedometer-type MPPM. As shown in Figs. 2a and 3, the samples used in the oedometer-type MPPM are compacted in the sample mould with a thickness of 10 mm. Figure 4 illustrates schematic layout of the triaxial-type MPPM designed following apparatuses proposed by other researchers [48]. Soil WRC affected by net confining pressure can be obtained by the triaxial-type MPPM. The samples used in this module are compacted in a specific mould and placed on the pedestal. Measurement of volume changes of soil during wetting and drying shall be carefully considered based on different soil types. For the expansive clays, lateral shrinkage can occur upon drying under null or low net normal stress in the oedometer-type MPPM. Therefore, the triaxial-type MPPM should be adopted for this specific type of soil, since the volume changes of specimens can be well recorded using the technique of cell liquid measurement described in the introduction section.

2.7 Combinations of different moduli

Figure 6 illustrates a simplified scheme of the pressure-control circuits and most of the pressure transducers. The different module can be easily demounted and installed for different tests. Particularly, the steel pressure chamber is fixed on the support frame and can be used by moduli (MOM and MDSA) in the maintenance of air pressure in unsaturated soil testing. De-aired water is used as the pressurizing medium and filled in the pressure chamber in the MTCM module for the total volume change measurement of specimen in the triaxial creep tests on unsaturated soils. The pressure chamber can be filled with air and de-aired water in oedometer-type MPPM and triaxial-type MPPM, respectively. The pressurized water was applied to the pressure chamber by a bladder air/water cylinder. The air and water pressures can be regulated by the pressure panel to deliver certain values of pressure to the system. The same transducers can be used in different moduli, and it is not necessary to demount and install these transducers for different types of tests.

Fig. 6
figure 6

Scheme of pressure control circuits and transducers of the multifunctional testing apparatus

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3 Calibration of the multifunctional apparatus

3.1 Calibration of conventional transducers used in the apparatus

Conventional transducers were calibrated following the relevant calibration procedures described in Head [26], including pore-air and pore-water pressure transducers, vertical and horizontal displacement load cells, vertical and horizontal displacement transducers, AVC, and DAI. The temperature during the calibration of apparatus and tests was maintained at 20 °C by several air conditioners in the laboratory. In addition, a dummy sample was used to eliminate the errors of elastic deformation of the frame and bedding effects on the contact surfaces, following the procedures introduced by Head [26] (Fig. 7a).

Fig. 7
figure 7

Calibration curves for a elastic deformation of apparatus frame, b immediate volume change induced by pressure, and c volume change with time

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3.2 Calibration of “immediate” volume change due to pressure increase and “creep” phenomenon

A dummy sample was placed on the pedestal, and the pressure in the pressure chamber was changed for two cycles and maintained for six days to calibrate the chamber expansion (Fig. 7b and c). Figure 7b shows that volume change induced by cell pressure below 100 kPa is relatively larger than those of other pressure values, and this phenomenon has also been observed by other researchers [16, 26, 48]. As shown in Fig. 7c, the volume change can be divided into two components: (i) immediate volume change due to the elastic deformation of the pressure chamber and drainage lines and (ii) volume change with time due to the creep effect of the system. The immediate volume change might be caused by compression of possible trapped air, water compressibility, deformation of membranes or pipelines, and minor pressure chamber distortion. Within common testing period, volume change due to creep effect can be assumed to be linear with time (Fig. 7c). This result agrees well with the previous studies [16, 49]. The volume change due to creep needs to be carefully calibrated and eliminated in the data analysis. The volume change due to the creep effect might result from the minor deformation of the chamber wall, water absorbed by the wall, possible water leakage at some connection parts of this system [16, 26]. The unstable volume change might be caused by the slight temperature changes in the laboratory.

4 Advantages of the multifunctional apparatus

Firstly, a stainless-steel cell has been used as the pressure chamber in the MFA. This steel pressure chamber can be used to measure the total volume changes of specimen in triaxial creep tests on unsaturated soils. Table 3 presents the comparison of calibration results on different testing apparatuses based on cell liquid measurement technique. The comparisons emphasize the ratios of errors to specimen volumes since the volumes of different systems are very different from each other. Compared with some typical double-cell systems [16, 49, 62, 64], the steel pressure chamber has an excellent performance in “creep” volume change under same constant pressure. The calibration coefficient regarding “creep” volume change per week for MFA is about half of the coefficient for a typical double-cell system. This might be due to the simple structure with less water leakage, less water absorption of steel, and greater stiffness of steel. This minor “creep” volume change is obviously advantageous to the long-period unsaturated soil testing. The performance of “immediate” volume change for the increase of cell pressure is also good, and this error can be easily removed by calibration. Apart from that, the temperature change effect on the steel wall might be less than that on the plexiglass wall. This minor effect might be beneficial in studies of temperature-dependent behaviour of testing materials. Additionally, a maximum cell pressure of 2 MPa can be applied in the pressure chamber because of the competent thickness of the pressure chamber wall. Thus, some triaxial creep tests with high cell pressure could be conducted on this apparatus to study particle breakage behaviour of testing materials. Furthermore, several high-strength and transparent plexiglass windows have been installed on the pressure chamber for real-time observation of the specimen.

Secondly, few studies have focused on the MD of testing apparatus on unsaturated soils. The conventional testing apparatus is very complex and has a lot of different components. Placing four single-function devices for performing different types of tests may take up a lot of space, whereas this MFA may only take up about a quarter of the space of other single-function devices. Furthermore, it is well known that the cost of unsaturated soil testing is high. A very important part of the cost is the expensive test equipment. The expensive test equipment is still a big obstacle for the researchers and engineers to apply the theories in unsaturated soil mechanics to engineering practice. In this MFA, many important parts can be shared in the different test moduli, including pressure chamber, lever-arm frame, support frame, and various transducers. Compared with a single-function device, an MFA can save a lot of money, and several MFAes can be produced at the same cost. It can greatly benefit the popularization of unsaturated soil tests. The utility rate of the MFA is higher than that of a conventional single-function device since it can be used in several different types of tests. Additionally, some calibration results can be shared in the different test moduli, and then, this apparatus can save a lot of time in the calibration. Overall, the apparatus is more feasible for application when compared to the specific single-function devices due to the intrinsic advantages such as space requirements, financial implications, ease of calibration, accuracy, and ease of usage.

Table 3 Comparison of calibration results on different testing apparatuses based on cell liquid measurement technique
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Thirdly, although the MFA is currently designed in a manner to enable testing coarse-grained granular materials, the base of the pressure chamber with changeable bottom pedestals on this apparatus can well accommodate specimens with various dimensions. In addition, despite the adoption of ATT in the current design for applying relatively low to medium high suction on granular materials, the apparatus can be potentially modified based on other suction-controlled techniques (e.g. VET) for application of wider suction ranges on clayey soils such as bentonite. Meanwhile, there are reserved channels on the apparatus for future transducers such as fiber bragg grating sensors [63, 64, 66]. Moreover, the pressure chamber is also removable for further improvements of larger chamber to test other large-grained materials.

5 Testing materials, test procedures, results, and discussion

5.1 Testing materials and specimen preparations

The soil utilized in this study was taken from an embankment fill material used for the new Chongqing Airport and categorized as poorly graded gravel with sand [40, 42]. Similar preparation procedures described by Liu et al. [42] were adopted to prepare specimens, including drying, aggregation separation, sieving, drying, water mixing, and compaction. According to the requirements in the Standard BS 1377 [13], the particles larger than 20 mm and 2 mm were removed to obtain a scaled-down curve for the pressure plate, oedometer, and triaxial creep tests and direct shear test (Fig. 8) [42, 55]. Dry density and water content of the prepared specimens were 1.87 Mg/m3 (88% of maximum dry density) and 5.75%, respectively.

Fig. 8
figure 8

Particle size distribution curves of the Chongqing granular fill samples used in different types of tests

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5.2 WRC

Only an oedometer-type pressure plate test was performed in this study. The test was carried out as per ASTM D6836 [4]. The procedures of pressure plate test generally included HAEVD preparation, set-up of specimen, saturation, drying of the specimen, wetting of specimen, demolition of the specimen, and measurement of water content. During the drying part of WRC, the soil suction was increased by steps of increasing the air pressure inside the pressure chamber (Table 4). In each step, the suction was maintained until the drainage of water reached the suction equalization criterion of a rate of 0.02%/day in water content. During the wetting part of WRC, the soil suction was decreased and maintained by steps of decreasing air pressure inside the pressure chamber.

Table 4 The suction, net normal stress, and deviatoric stress sequences adopted in different types of tests
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The filter paper method (FPM) can be used as a soil suction sensor to measure the matric and total suction of the soil. This method involves the placement of filter papers against soil specimen from which the pore water flows to the dry filter papers until the hydraulic equilibrium is reached in an airtight container [42]. After the equilibrium, the water content of filter paper is carefully measured, and this water content correlates with the soil suction. The soil suction can be calculated based on the calibration curve of the filter paper. To obtain the WRC of soil, specimens with different targeted water contents are prepared to reach considerable suction range.

WRCs of the granular fill were determined by PPT conducted on this novel MFA and FPM described in Liu et al. [42]. Figure 9 shows comparisons of WRC results obtained by these two methods. The data points obtained from FPM locate approximately in the middle of the drying and wetting paths obtained from PPT. The drying path might be a main draining curve, and this path might be a boundary. One FPM data point which is out of the boundary may be caused by the minor error in water content measurement in FPM. Despite imperfect agreement, the WRC results from different methods seem to be comparable. The differences in WRC results might be due to minor errors induced by sample preparations, test processes, and data analysis, such as slight difference in soil density, possible leakage on pipelines, weight of filter paper, and slightly inappropriate calibration curve of filter paper. The so-called “hysteresis” can be observed in the experimental result obtained from PPT. The “hysteresis” means that the drying path is different from the wetting path. The “hysteresis” might be due to several reasons, including differences in the soil–water contact angle between wetting and drying, entrapped air, and connectivity of pores [23]. In the soil pores, large pores can drain first when drying, whereas small pores can be filled first during wetting.

Fig. 9
figure 9

Comparisons of WRC results obtained by pressure plate test (PPT) and filter paper method (FPM)

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5.3 Unsaturated oedometer test

The main testing procedures described by Chen et al. [17] were adopted in this study, which included HAEVD preparation, set-up of the specimen, saturation, suction equalization, and compression. The rate of 0.02%/day in water content of the specimen was adopted as the equalization criterion in the oedometer test. As listed in Table 4, a series of stepwise increasing vertical loadings were applied on the specimen in a prescribed sequence using a lever-amplified dead weight. The vertical loadings were applied after ensuring the equalization of matric suction on the specimen. All the periods of loadings are at least 48 h and at least one week for the loadings to investigate time-dependent compression behaviour.

Figure 10a to e presents the variations in the void ratio versus time (logarithmic scale) for the specimen under matric suction of 40 kPa in the oedometer test. The net vertical stress, \(\sigma_{{\rm v}}^{{\prime}}\), is defined as follows:

$$ \sigma_{{\text{v}}}^{{\prime}} = \sigma_{{\text{v}}} - u_{{\text{a}}} $$
(1)

where \(\sigma_{{\rm v}}\) denotes the total vertical stress and ua denotes the air pressure.

Fig. 10
figure 10

Results of oedometer test on Chongqing granular fill under suction of 40 kPa: a \(\sigma_{v}^{{\prime}}\) is loaded from 50 to 400 kPa, b \(\sigma_{v}^{{\prime}}\) is unloaded from 400 to 50 kPa, c \(\sigma_{v}^{{\prime}}\) is reloaded from 50 to 400 kPa and loaded from 400 to 1200 kPa, d \(\sigma_{v}^{{\prime}}\) is unloaded from 1200 to 200 kPa, e \(\sigma_{v}^{{\prime}}\) is reloaded from 200 to 1200 kPa, and f void ratio versus net vertical stress

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As shown in Fig. 10a, c and e, the void ratio decreases with the increase of net vertical stress, and the change rate of void ratio increases with the increase of net vertical stress. The soil under different stress levels shows different responses. In general, the changes of void ratio in the secondary compression part are nearly linear with time when net vertical stresses are less than or equal to 400 kPa (Fig. 10a), and those of void ratio in the secondary compression part are nonlinear with time when net vertical stresses are greater than 400 kPa (Fig. 10c). This difference can be possibly explained by the different compression mechanisms of particles in the specimen. When net vertical stress is not large, the particle contacts between grains can remain stable since the particle friction might be great than the sliding forces at particle contacts. However, particle friction might not be sufficient to maintain the position of the particle if net vertical stress reaches a considerable stress level. At the same time, particle sliding and particle breakage might occur and lead to the rearrangement of soil fabric. Thus, considerable changes in void ratio might occur if net vertical stresses are great. As shown in Fig. 10b and c, the changes in the void ratio are not evident when the net vertical stress is less than the preconsolidation pressure, regardless of unloading or reloading conditions. It is worth noting that this phenomenon can be used to explain a high preconsolidation pressure applied in soil improvement projects can reduce the post-construction settlement of soil layers, especially for granular fills. As shown in Fig. 10b and d, the void ratio increases with the decrease of net vertical stress, and the change rate of the void ratio increases with the increase of net vertical stress. In general, the results agree with those results obtained by Chen et al. [17].

Figure 10f shows the relation of void ratio versus net vertical stress in constant-suction oedometer tests. The effective stress, \(\sigma_{{{\rm vp}}}^{{\prime}}\), was determined as 316 kPa by the interception point of two fitted lines on the e – log \(\sigma_{{{\rm vp}}}^{{\prime}}\) curve. This result is consistent with the result described by Chen et al. [17]. Table 5 lists the values of compressibility parameters for the testing materials. The compression index (Cc), and the recompression indices for unloading and reloading loops (Cr1, Cr2) are defined as follows:

$$ C_{c} ,C_{r1} \;{\text{or}}\;C_{r2} = - \frac{{{\rm d}(e)}}{{d(\log (\sigma_{v}^{{\prime}} ))}} $$
(2)

where e denotes the void ratio and \(\sigma_{v}^{{\prime}}\) denotes the net vertical stress.

The creep coefficient, Cαe, is defined by the equation as follows:

$$ C_{\alpha e} = - \frac{\text{d}(e)}{{\log ({t \mathord{\left/ {\vphantom {t {t_{0} )}}} \right. \kern-\nulldelimiterspace} {t_{0} )}}}}\;(t > t_{0} ) $$
(3)

where \(t_{0}\) denotes the time corresponding to the end of the transient period and is taken as 2 min in this study and d(e) denotes change of void ratio from the time \(t_{0}\). As listed in Table 5, the Cc, Cr1, and Cr1 values are 0.07, 0.002, and 0.004, respectively. The Cαe values for net vertical stresses of 200 kPa, 800 kPa, and 1200 kPa are 0.0003, 0.0011, and 0.0011, respectively. The slight differences between the compressibility parameters and those obtained by Chen et al. [17] might be caused by the inherent anisotropy induced by specimen preparation and the complex behaviour of coarse-grained granular materials [41]. In general, compared with the behaviour of fine-grained granular material, the behaviour of coarse-grained granular materials is very complex and highly heterogeneous, and this behaviour might easily cause non-uniform experimental results [54, 56, 58, 65, 67].

Table 5 Values of compressibility parameters for the testing materials based on oedometer test
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5.4 Unsaturated direct shear test

The testing procedures suggested by Borana et al. [9,10,11] were adopted in this study, which included HAEVD preparation, set-up of specimen, saturation, suction equalization, and drained shearing at constant suction and net normal stress. The calculated axial load, air pressure in the pressure chamber, and water pressure under HAEVD were applied sequentially in the suction equilibration stage (Table 4). Constant vertical deformation and water flow rate of 0.02%/day in water content of specimen were adopted as the equalization criteria. In the shearing stage, the specimen was sheared at a constant rate of 0.004 mm/min until the horizontal displacement reached 12 mm.

Figure 11 shows the result of the direct shear test on specimens under suction of 40 kPa and net normal stress of 100 kPa. Based on the relation between shear stress and horizontal displacement, soil shows gradually hardening behaviour. In the curve of vertical displacement and horizontal displacement, soil shows compression when the horizontal displacement is approximately less than 3%, followed by a little dilation. This dilation behaviour might be attributed to the application of suction on the specimen. Similar phenomena have been observed by Hossain and Yin [28] in a compacted completely decomposed granite soil. In general, the results agree with the results reported by Borana [9,10,11]. Under a certain level of net normal stress, the higher the suction, the more the shear dilation. Additionally, the softening and hardening behaviour of the soil is not evident with the changes of suction.

Fig. 11
figure 11

Results of direct shear test on Chongqing granular fill under suction of 40 kPa and net normal stress of 100 kPa: a shear stress versus horizontal displacement curve and b vertical displacement versus horizontal displacement curve

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5.5 Unsaturated triaxial creep test

The procedures introduced by Lai et al. [34] were adopted, which included HAEVD preparation, set-up of the specimen, equalization, isotropic consolidation, and loading under a certain matric suction. The termination criterion of the suction equilibration stage was the flow rate of 0.02%/day in water content. After the equalization stage, the isotropic consolidation was applied by increasing the confining pressure to obtain a desired net confining stress (150 kPa). The multi-stage loading method was adopted in this study, which was used by many researchers for the investigation of the creep behaviour of soils [34]. The deviatoric stresses for all the stages are listed in Table 4. When the axial deformation rate reached 0.005 mm/day, the stabilization of relevant axial deformation at certain deviatoric stress was obtained. The shear strength of specimens was determined as 500 kPa before the triaxial creep tests by the reanalysis of results from Liu et al. [42]. The deviatoric stress level, \(D{\rm = }\frac{{(\sigma_{1} { - }\sigma_{3} )}}{{(\sigma_{1} { - }\sigma_{3} )_{{\rm f}} }}\), is defined as the ratio of applied deviatoric stress, \((\sigma_{1} { - }\sigma_{3} )\), to maximum deviatoric stress, \((\sigma_{1} { - }\sigma_{3} )_{{\rm f}}\).

Figure 12a and b presents the curves of axial strain versus time and axial strain rate versus time for the specimen (s = 80 kPa; \(\sigma_{{\rm v}}^{{\rm ^{\prime}}}\) = 150 kPa) measured at different deviatoric stress levels. The axial strain rate, \(\dot{\varepsilon }_{{\rm a}}\), is defined by the equation as follows:

$$ \dot{\varepsilon }_{{\text{a}}} = \frac{{{\text{d}}\varepsilon_{{\text{a}}} }}{{{\text{d}}t}} $$
(4)

where dεa is the variation of axial strain measured over the corresponding period dt.

Figure 12a shows that, after 10 min, the axial strain increases linearly with time when the D is less than or equal to 0.6. However, the axial strain increases nonlinearly with time after 10 min when the D is at 0.8. A similar phenomenon can be observed in the oedometer tests. This might be due to the different compression mechanisms of particles explained in the section of explanation of oedometer test results. Figure 12b presents the variation of axial strain rate with time. It seems that the axial strain rate decreases linearly with time except for a few date points. The equation suggested by Singh and Mitchell [57] was used to calculate the linear trend of axial strain rate with time as follows:

$$ m = - \frac{{\Delta \log (\dot{\varepsilon }_{{\text{a}}} )}}{\Delta \log (t)} $$
(5)

where m denotes the slope of the linear trend line, \(\dot{\varepsilon }_{{\rm a}}\) denotes axial strain rate, and t denotes period.

Fig. 12
figure 12

Results of triaxial creep test on Chongqing granular fill under suction of 80 kPa and net confining pressure of 150 kPa: a axial strain versus time curve, b axial strain rate versus time curve, c axial strain versus stress level relationship, and d axial strain rate versus stress level relationship

Full size image

Based on the fitting results, the m-value for deviatoric stress levels ranging from 0.2 to 0.8 is 0.98, 1.02, 1.05, and 1.15, respectively. Singh and Mitchell [57] suggested that the slope was constant regardless of the variable deviatoric stress level and time for a given soil. However, Lai et al. [34] found the convergence of straight lines of the axial strain rate with elapsed time in an unsaturated clay. As shown in Fig. 12b, a similar convergent trend can be observed in different deviatoric stress levels, and this trend means that the slope increases with the increase of deviator stress level and is not constant with elapsed time. It agrees with the observations suggested by other researchers [34].

Figure 12c and d shows relationship between axial strain or axial strain rate and deviatoric stress level at period of 24 h. The axial strain increases with the increasing deviator stress level. Additionally, it appears that the axial strain rate increases linearly with the increase of deviator stress level. A similar trend was found by Mesri et al. [45] in saturated clay and Lai et al. [34] in unsaturated clay. In general, it is noted that the MFA works very well in establishing the creep parameters for unsaturated soils precisely.

6 Conclusion

A novel state-of-the-art modular-design-based MFA is designed and manufactured for performing a variety of tests such as pressure plate test, oedometer test, direct shear test, and triaxial creep test on unsaturated soils. The individual module, typical calibration results, and advantages are presented and discussed. A series of tests under different stress state variables have been conducted, and the testing process and methodologies are furnished. The calibration coefficient regarding “creep” volume change per week for MFA is about half of the coefficient for a typical double-cell system. Besides, the apparatus is more feasible for application when compared to the specific single-function devices due to the intrinsic advantages such as space requirements, financial implications, ease of calibration, accuracy, and ease of usage. Furthermore, the MFA is designed in a manner to enable testing specimens with different dimensions and to control soil suction based on different techniques. Overall, it is observed that MFA is suitable to perform any of the tests for unsaturated soils, as listed above.

The soil type and stress path of validation tests are relatively simple. In addition, other types of suction-controlled techniques can be adopted in the future modifications to apply and maintain a wider suction range on different types of soils. Moreover, the temperature effect on volume change shall be carefully considered if the apparatus is used in an environment without constant temperature control. Finally, there is a limitation in the determination of volume change of specimen under null or low net normal stress in the oedometer-type MPPM. Future studies shall be conducted to avoid this limitation in testing some special types of soils, especially for expansive clays which have lateral shrinkage during drying.