Introduction

Extensive areas throughout the world, mainly in arid and semi-arid regions, experience foundation problems caused by expansive soils (Radevsky 2001; Houston et al. 2011; Dafalla and Shamrani 2011, 2012). Expansive soils undergo significant volume change with change in water content. There are two main parameters that are used to evaluate the characteristics of expansive soils: swelling pressure and swelling strain [as per the American Society for Testing and Materials (ASTM) standard D4546]. These swelling characteristics are important for the design of several structures such as pavements, shallow foundations, shallow tunnels, retaining walls, canal linings and underground conduits. So far, one-dimensional oedometer testing has been widely used to evaluate these parameters where a specimen is laterally restrained with volume change occurring in one direction only (i.e., the vertical direction). Oedometer testing of expansive soils is conducted by constant stress and constant volume testing (ASTM D4546). For a constant stress test, the specimen is allowed to swell in the vertical direction under constant applied vertical stress. For a constant volume test, a specimen’s deformation is restrained in the vertical and lateral directions to determine swelling pressure. In “real life” engineering situations, swelling characteristics obtained from an oedometer is different than that recorded in the field. Factors contributing to this difference were summarized by El-Sayed and Rabbaa (1986) and included stress path (Komornik and David 1969), state of stresses, scale effects (Sing 1967; Chen 1975; Ranganatham and Satyanarayana 1965; Rabbaa 1975), boundary conditions (Kassif and Baker 1969), sample disturbance (Ofer et al. 1983), and degree of wetting (Dhowian 1990; Wray et al. 2005). In regard to boundary conditions and state of stresses, expansive soils in the field are not considered fully restrained in the lateral direction as simulated using the laboratory oedometer. Therefore, in situ behavior of expansive soil may involve swelling in a vertical as well as lateral direction. Previous research reported that the ratio of one-dimensional swelling as per oedometer tests to vertical swelling observed in the field was about three (Gizienski and Lee 1965; Erol et al. 1987; Dhowian 1990). In other words, the vertical swelling realized in the field represents about one-third of the volume change indicated by the oedometer.

Bearing the above in mind, several researchers have been motivated to investigate the swelling characteristics of expansive soils under various boundary conditions and stress states. Recently, Tang et al. (2013) and Lui et al. (2014) suggested that there are infinite possible boundary conditions besides constant volume and constant stress conditions under which specimens may undergo swelling. They devised a modified oedometer to investigate the swelling characteristics under various constant stiffness conditions in addition to constant stress and constant volume conditions. Constant stiffness imposes a boundary condition of increasing vertical stress with an increase in swelling strain. They concluded that the swelling characteristics of tested specimens significantly depended on boundary conditions applied with the swelling pressure evaluated under constant stiffness lying between constant stress and constant volume conditions. On the other hand, several researchers investigated the effect of stress state on the swelling behavior of expansive soils using a triaxial device under isotropic and anisotropic stress conditions (Dakshanamurthy 1979; Tisot and Aboushook 1983; Al-Shamrani and Al-Mhaidib 1995, 1999; Al-Shamrani and Dhowian 2003; Chen and Ng 2005). It was reported that the volumetric strain of expansive soils depends on the mean stress applied on specimens (Dakshanamurthy 1979; Tisot and Aboushook 1983). It was also noted that the there is a significant difference between the swelling pressure deduced from oedometer tests and that deduced from triaxial tests under isotropic conditions (Tang et al. 2013). Tests conducted on expansive soils during wetting using a suction-controlled triaxial device revealed that the variation of volumetric strain with suction showed a non-linear relationship (Chen and Ng 2005).

Most of the previous research on expansive soils focused on the evaluation of vertical and/or volumetric swell strain with little attention given to stresses developed in specimens during swelling. Furthermore, the volume change behavior of expansive clay under stresses greater than swelling pressures have been rarely discussed. In this study, a series of response-to-wetting triaxial tests were performed to evaluate the multi-directional (lateral and axial) stress and strain behavior of compacted, expansive clay under different boundary conditions. Boundary conditions simulated included: constant isotropic pressure (CIP), constant axial (CA) deformations and constant volume (CV). Strains and/or stresses evolved during specimen inundation were recorded. Moreover, a comparison between volume change behavior of expansive clay under triaxial and oedometer conditions was performed. Finally, the effect of the ratio of lateral stress (σ L ) to axial stress (σ a ; i.e., stress ratio, K) on the volume change behavior of tested expansive soils was investigated.

Soil used

Geological setting

The expansive clay used in this study was obtained from the city of Al-Qatif located in the eastern province of Saudi Arabia (latitude 26o56′N and longitude 50o01′E) along the shoreline of the Arabian Gulf coastal region (Fig. 1). This clay is part of sedimentary strata present in the Arabian Gulf which range in age from the Jurassic to the Eocene eras. These sedimentary strata dip toward the east and northeast at a mild slope of 1 m/km until they merge with the Arabian Gulf (Slater 1983). The geology in the eastern part of the Arabian Peninsula comprises argillaceous shale and calcareous sedimentary rocks such as dolomite, limestone, marl and chert from the Permian, Cretaceous, and Tertiary eras (Saint-Marc 1978). The expansive clays of the Al-Qatif region are derived from these geological materials by the actions of geological and weathering processes. Geological processes included deformational processes like glacial activity and successive transgression and regression cycles of gulf seawater that occurred during the late Pleistocene and Holocene ages (Al-Sayari and Zotl 1978; El-Naggar 1988). Subsequent physical and chemical weathering combined with favorable climatic and environmental conditions of the Arabian Gulf region have facilitated the evolution of the expansive clay minerals in Al-Qatif clay. Favorable environmental conditions include flat topography, an alkaline environment, hot and arid climates, an abundance of clay-forming ions (Na+, Ca2+, Mg2+, SO4 2+) in pore water of sediment materials (Mitchell 1993), and inhibited leaching due to restrained mobility of highly alkaline water (Azam and Al-Shayea 1999).

Fig. 1
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General layout of sampling area

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Soil sampling and characterization

Expansive clay samples were obtained from a test pit excavated to a depth of about 5.0 m below ground surface. The subsurface soil profile encountered during excavation is illustrated in Fig. 2. The expansive clay encountered at the site was classified as greenish gray, extremely fissured, highly overconsolidated clay, as shown in Fig. 3. Bulk soil samples were transported to the laboratory to perform routine geotechnical, physical, and mineralogical characterization. All geotechnical testing was conducted in accordance with ASTM test standards and using distilled water. Distilled water was produced using a water still device (model WSB/4, Hamilton Laboratory Glass, UK) . The liquid, plastic and shrinkage limits were 140, 60, and 20 %, respectively. The particle density of soil solids was 2.71 g/cm3. The grain size distribution of test soil constitutes 38 % silt-size particles (0.075–0.002 mm) and 56 % clay-size particles (<0.002 mm), as shown in Fig. 4. The soil is classified as CH according to the Unified Soil Classification System (USCS). The aforementioned characterization data were consistent with the results of previous studies conducted on the same clay (Abduljuawad et al. 1992; Azam et al. 1998; Al-Shayea 2001; Azam 2003).

Fig. 2
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Subsurface profile at test pit sampling location—Al-Qatif, Kingdom of Saudi Arabia (KSA)

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Fig. 3
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Photo documentation of sample obtained from sampling location

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Fig. 4
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Grain size distribution of Al-Qatif clay

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The mineralogical investigation of Al-Qatif soil conducted using X-ray diffraction (XRD) analysis revealed that the predominant clay minerals are montmorillonite and palygorsite which are typical expansive minerals. Quantitative analysis of Al-Qatif clay carried out by Abduljauwad (1994) revealed that the montmorillonite mineral constitutes about 52 % of its mineral composition.

Specimen preparation

To ensure repeatability and minimize variability in test data due to soil heterogeneity, compacted clay specimens were used in this study. Bulk clay samples were air dried, pulverized, and sieved using sieve no. 40 (mesh opening size of 0.420 mm) to remove oversized particles and to obtain clay powder. The soil was hand mixed with distilled water at a target water content. Mixing was conducted for about 30 min to ensure uniform distribution of water in the mixture. To ensure moisture homogenization, the mixture was placed in hermetic plastic bags and stored in a humid environment for not less than 24 h. Tested specimens were statically compacted to final dimensions at maximum dry density (γ d  = 12 kN/m3) and optimum moisture content (w op = 32 %) evaluated using standard compaction effort as per ASTM D698.

Specimen dimensions for oedometer testing were 20 mm high and 50 mm in diameter. Triaxial tests specimens were 30 mm high and 75 mm in diameter maintaining a height-to-diameter ratio similar to oedometer test specimens. It is worth noting that a specimen size smaller than that recommended in triaxial testing standards (i.e., height-to-diameter ratio = 2.0–2.5 as per ASTM D4767) was selected to reduce testing time. The specimen size recommended in triaxial standards was set to minimize the effect of friction between test specimens and triaxial platens (aka. end-platen friction) on shear strength. In this study, where the volume change behavior is of main interest, the end-platen friction effect is considered to have a minor effect. A discussion on the effect of end-platen friction on test results is provided later in this paper.

Equipment and test procedure

Triaxial tests

Triaxial testing was performed using a single-cell, computer-controlled stress path triaxial apparatus manufactured by GDS, UK. A schematic diagram showing the main components of the triaxial apparatus used in this study is shown in Fig. 5. The apparatus was equipped with two pressure volume controllers (PVCs) for the independent control of cell and back pressures. Specimen volume change was evaluated by noting the change in cell water volume recorded using cell PVCs. Axial loading and axial deformation were measured using a submersible load cell and external displacement transducer, respectively.

Fig. 5
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Schematic diagram of the triaxial system used in this study

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The general procedure for triaxial testing comprised three stages. In the first stage, compacted specimens were subjected to an isotropic confining pressure (σ c  = σ a  = σ L ; Fig. 6) and maintained until no volume change was recorded (typically for 30–60 min). Isotropic confining pressures (σ c ) considered were 50, 100, 200, 400, 600 and 800 kPa. In the second stage, specimens were inundated by admitting distilled water through the top drainage port under a nominal backpressure of 10 kPa with the bottom drainage port initially opened to allow the egress of air, which was then closed. The inundation process was maintained for 2–3 days to ensure full saturation of specimens and continued until equilibrium was attained (i.e., no change in specimen volume was recorded). Furthermore, back calculation of the degree of specimen saturation at the end of inundation revealed that the degree of saturation ranged between 96 and 100 %. The third stage constituted specimen unloading after attaining the final volume change. During the second stage, three test series were performed simulating volume change under different boundary and stress conditions as detailed below. A schematic diagram of test boundary and stress conditions before and at the end of inundation are provided in Fig. 6.

Fig. 6
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Stress and boundary condition a CIP, b CA and c CV specimens

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  • Constant isotropic pressure (CIP) test specimens were inundated under a constant isotropic confining pressure (σ c ) applied during the first stage. During inundation, the confining pressure remained constant and axial and volumetric strains developed were recorded (Fig. 6a).

  • Constant axial (CA) deformation tests specimens were inundated with a full restrained boundary in the axial direction and a free deformation boundary condition in the lateral direction (Fig. 6b). This condition was simulated by fixing the movement of axial loading ram while maintaining lateral stress (σ L ) constant. Under this condition, specimens were permitted to swell in the lateral direction only. Lateral swell strain developed was recorded using cell PVCs. Deviator stress q = (σ a – σ L ) generated during inundation was recorded using the load cell.

  • Constant volume (CV) tests In this test series, swelling of test specimens was restrained in both the axial and lateral directions by restraining the movement of the axial loading ram and cell PVC ram (Fig. 6c). Axial and lateral swell stresses were evaluated from the increase in deviator stress and cell pressure, respectively. It should be noted that specimens were not considered fully restrained in the lateral direction due to the compressibility of water, the flexibility of the plastic tubes connecting PVCs to the cell, and the cell volume change. Nevertheless, the maximum error in lateral strain measured was in order of 1.3 % (discussed later) which was deemed insignificant.

In addition to the above, a series of swell triaxial tests were conducted to investigate the effect of anisotropic stress conditions (i.e., σ a  ≠ σ L ) on the volume change behavior of expansive soils. In this test series (referred to herein as CAP), the stress and boundary conditions are similar to CIP tests with the exception that the specimen at inundation was subjected to an axial stress of 50 kPa with varying stress ratios (K = σ L /σ a ) of 0.5 and 1.5. A summary of all triaxial test conditions are presented in Table 1.

Table 1 Summary of triaxial tests conditions and results
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Triaxial calibrations

The cell PVCs were used to measure volume change of test specimens based on cell water ingress or egress with a transducer accuracy of 1.0 mm3. However, there are a number of factors that may affect the overall accuracy of the PVC volume change measurement. Error in PVC volume measurements (also referred to as apparent volume change) are attributed to: (1) immediate volume change due to the expansion/contraction of the cell wall, connecting tubes and cell water caused by the change in cell pressure; and (2) temperature-dependent volume change (Ng et al. 2002). To quantify the apparent volume change (AVC) for each error, a series of calibrations were performed. During calibrations, a stainless steel dummy specimen was used between the load platens of the triaxial apparatus to eliminate specimen volume changes. The first calibration involved increasing cell pressure up to the maximum value expected during testing (800 kPa) followed by unloading. For each cell pressure increment or decrement, the target pressure was ramped up within 2 min and the AVC was recorded using PVCs. The variation of AVC with applied pressure showed a linear relationship, as shown in Fig. 7. Moreover, conducting the calibration for two cycles showed that the data is repeatable with slight differences between the loading and unloading paths. This relationship was used to adjust volume change measurements recorded during the test.

Fig. 7
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Variation of immediate AVC with cell pressure

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To evaluate the temperature-dependent AVC, a second series of tests was performed in which cell pressure was applied and maintained for about 1 week. During this period, AVC and “on-cell” temperature were recorded. On-cell temperatures were recorded using a thermocouple sensor attached to the triaxial cell. Variation of “on cell” temperature and AVC with time is shown in Fig. 8. From Fig. 8, it is observed that the on-cell temperature and AVC vary in tandem with an 80-min response delay between AVC and on-cell temperature (see insert in Fig. 8). From this data, the error in PVC volume due to temperature was estimated to be in the order of 345 mm3/°C which is equivalent to volumetric strain of 0.22 %/°C for a specimen size 30 mm high and 75 mm in diameter.

Fig. 8
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Variation of AVC and on-cell temperature with elapsed time

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Oedometer testing

For the sake of comparison, a series of response-to-wetting tests using an oedometer was performed to evaluate the volume change behavior (whether swell or collapse) of tested specimens under lateral restraint conditions. Tests performed were in accordance with ASTM D4546 and included: (1) inundation under constant stress test (ASTM D4546—Method B) and (2) constant volume test (ASTM D4546—Method C). For method B tests, specimens were inundated under varying axial stresses of 50, 100, 200, 400, 600, and 800 kPa. All specimens were inundated using distilled water. For the convenience of reference, in the remainder of this paper, method B oedometer tests are labeled (O_B_Vt) where Vt symbolizes the vertical stress under which test specimens are inundated. The constant volume test is labeled (O_C). A summary of oedometer test conditions considered in this study is presented in Table 2.

Table 2 Summary of the conditions and the results for oedometer testing program
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Results and discussion

This section summarizes the results of the experimental program described earlier. The effect of boundary conditions on the response to swelling was evaluated with respect to multi-directional (i.e., axial, lateral and volumetric) strains and stresses. Furthermore, the effect of stress ratio, K, on volume change behavior of the tested soil was discussed.

Response-to-wetting curves

The aim of this section is to illustrate the different trends of response-to-wetting curves (stress–strain curves) observed as a result of inundation of swelling specimens under different boundary conditions considered in this study. These response-to-wetting curves are used to graphically portray the change in stress and strain for triaxial specimens as a result of dry loading, inundation, and unloading. Response-to-wetting curves for triaxial specimens shown in Figs. 9, 12 and 13 illustrate the variation of strain with the logarithm of stress. On the other hand, stress–strain curves for O_B and O_C specimens are illustrated in Figs. 10 and 11

Fig. 9
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Response-to-wetting curves for CIP specimens

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respectively. For the sake of clarity, only selected data sets were presented.

Fig. 10
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Axial strain versus axial stress for O_B samples

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Fig. 11
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Axial strain versus axial stress for the O_C method

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Response-to-wetting curves for CIP specimens under different applied stresses are illustrated in Fig. 9. Figure 9a depicts the relationship between the logarithm of axial stress (σ a ) and axial strain (εa), while Fig. 9b illustrates the relationship between logarithm of mean stress (p) and volumetric strain (ε v ). The mean stress (p) is calculated as (σ a  + 2σ L )/3. Because axial and lateral stresses remain constant during inundation of CIP specimens, the volume change behavior (whether swell or collapse) is represented by a vertical line on the σ a –ε a or p–ε v plots (e.g., line 1–1′ on Fig. 9).

During inundation, the response-to-wetting behavior for CA specimens in σ a –ε a coordinates is represented as a horizontal line (e.g., line 1–1′ in Fig. 12a). This horizontal line denotes the magnitude of change in axial stress that take place under no axial strain condition (i.e., CA test). Considering p–ε v representation, the response-to-wetting is delineated as an inclined line (e.g., line 1–1′ in Fig. 12b).

Fig. 12
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Response-to-wetting curves for CA specimens

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The response-to-wetting curves for CV specimens are illustrated in Fig. 13. Figure 13a shows the σ a –ε a relationship similar to that for CA specimens. For the p–ε v representation, it is expected that the inundation stage be represented as a horizontal line indicating an increase in stresses with zero volume change. However, when examining Fig. 13b, it was observed that some volumetric strain was recorded. This is attributed to lateral strains (ε L ) developed during inundation because of cell water compressibility imposing partial lateral restraint on the specimens. As stated earlier, the maximum error in lateral strain did not exceed 1.3 % (Table 1) which can be considered small.

Fig. 13
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Response-to-wetting for CV specimens

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Because of reduced specimen size considered in this study, it is important to assess the effect of end-platen friction on the quality of test results presented in Figs. 9, 12 and 13. For CV tests, the specimen was restrained in both lateral and axial direction. Hence, relative movement did not take place between the specimen and platen and end-platen friction is not relevant. In case of CIP and CA tests, radial strains in test specimens were permitted. Because of the axially restrained condition imposed during CA tests, the end-platen friction was of concern, especially when swelling was expected. In cases of CA specimens experiencing collapse, end-platen friction was considered to be negligible. A visual inspection of CA specimens that underwent swelling revealed that specimens showed small bulging. Based on this visual observation, end-platen friction was deemed to have a minor effect on test results.

Inundation strains

In order to assess the influence of boundary and stress conditions on the volume change behavior of expansive clay under O_B, CIP and CA test conditions, relationships between inundation strain and logarithm stress upon inundation for each test series are plotted as shown in Figs. 14 through 17. Inundation strain is defined as the maximum component of strain (whether axial, lateral, or volumetric) attained due to wetting. Figure 14 shows a linear relationship between axial inundation strain and the logarithm of axial stress upon inundation for O_B specimens. Depending on axial stress upon inundation, specimens may experience swelling or collapse behavior. A similar trend to that observed in the swelling zone of Fig. 14 was reported by Grob (1972) and is known as Grob’s law. The stress at which transition between swelling and collapse behavior occurs is considered the swelling pressure (defined by the intercept of the linear relationship with the horizontal axis). Similar conclusions can be derived from Fig. 15 showing linear variation of different components of inundation strain for CIP specimens with the logarithm of the confining pressure upon inundation (σ c ). From Fig. 15, it is observed that Grob’s law (1972) is also valid for lateral and volumetric swelling strains. Combining Figs. 14 and 15 into Fig. 16 clearly revealed that the magnitude of axial inundation strain depends on test conditions. Specifically, the axial swell strain deduced from O_B tests was greater than that deduced from CIP. This is attributed to the higher level of lateral restraint imposed on O_B specimens than CIP specimens. However, the volumetric swelling pressure (i.e., applied mean stress corresponding to zero volumetric strain) deduced from CIP and O_B specimens are almost the same.

Fig. 14
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Relation between axial inundation strain and axial stress upon inundation for O_B specimens

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Fig. 15
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Relations between inundation strains (volumetric, axial and radial) and confining pressure upon inundation for CIP specimens

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Fig. 16
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Comparison between inundation strain and stress for O_B and CIP specimens

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To investigate the effect of boundary conditions on the specimens’ lateral strains, the lateral inundation strains for CIP and CA specimens were computed using the following equations:

$$ \varepsilon_{L} = \frac{{\varepsilon_{v} - \varepsilon_{a} }}{2} $$
(1)

where ε v , ε a and ε L are volumetric, axial and lateral strain, respectively.

The variations of lateral inundation strains with confining pressure upon inundation for CIP and CA specimens are illustrated in Fig. 17. From Fig. 17, the lateral inundation strain in case of CA is observed to be significantly higher than that of CIP due to axial restraint imposed on specimens causing most of the swelling energy to be directed towards a lateral direction.

Fig. 17
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Lateral inundation strains for CIP and CA specimens

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Effect of stress ratio on swell strain

The response-to-wetting curves for CAP specimens under different stress ratios (K) are illustrated in Fig. 18. From this figure, it can be inferred that as the stress ratio applied on specimens increases, the axial swelling strain increases. Combining data obtained from CIP (representing K = 1.0) and CAP tests, the variation of axial and volumetric swell strains with stress ratio was plotted, as shown in Fig. 19. From Fig. 19, it is observed that the stress ratio has a significant effect on the axial and volumetric swell strains, with these strains increasing exponentially with stress ratio. The data in Fig. 19 was also combined to provide a relationship of swell ratio (SR)—defined as the ratio of the axial to the volumetric swell strain obtained from triaxial tests (i.e., CAP and CIP tests)—as a function of stress ratio, as shown in Fig. 20. Based on Fig. 20, the relative contribution of axial swell strain to volumetric strain ranged between 0.54 and 0.78 which is higher than that reported in the technical literature.

Fig. 18
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Effect of stress ratio on response-to-wetting curves at σL = 50 kPa

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Fig. 19
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Effect of stress ratio on axial and volumetric swell strain for CAP specimens

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Fig. 20
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Relationship between swell ratio and stress ratio

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Because conventional oedometers are routinely used to evaluate the swelling potential of expansive soils and due to discrepancies between oedometer measurements and in situ axial swell strain measurements, a heave reduction factor was proposed to estimate axial swell strain anticipated under given boundary and stress conditions. For the soil considered in this study, a heave reduction factor, R f , is defined as the ratio of the axial swell strain obtained from triaxial tests (i.e., CIP_50/Fig. 9 and CAP/Fig. 18) to that obtained from the oedometer test (i.e., O_B_50) under a constant axial stress of 50 kPa. A plot for the variation of R f with stress ratio is shown in Fig. 21. This figure revealed that R f increased exponentially with stress ratio and ranged between 0.25 and 0.85. A plausible explanation for this trend is as the stress ratio, K (i.e., lateral stress, σ L ) increases, the degree of lateral restraint in a triaxial specimen increases, causing the swelling potential to be favorably directed in the vertical direction. This figure can aid in estimating the in situ axial swell strain provided that the oedometric axial swell and in situ stress ratio are known.

Fig. 21
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Heave reduction factor versus stress ratio

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Stress state due to inundation

As stated earlier, CA tests simulate specimens that are restrained in axial conditions, while CV tests simulate specimens that are confined in both axial and lateral directions. The restraint imposed on the specimen will inhibit the development of strain and cause changes in specimen stresses. This section describes the stresses evolved during inundation of CA and CV specimens.

Constant axial (CA) deformation tests

Figure 22 shows the evolution of deviator stress (q = σ a –σ L ) as a function of time under selected confining pressures upon inundation (σ c ). The trends for q versus time curves were observed to depend on σ c . Under low confining pressure upon inundation, the gradual increase in deviator stress with time showed a “strain softening” behavior characterized by a definite peak value followed by reduction to a residual value. This phenomenon postulates that CA specimens experienced shear loss at the aggregate level due to an increase in deviator stress. This is evident by the reduction in K with time as presented in Fig. 23. As the confining pressure upon inundation increased (Fig. 22), the peak deviator stress decreased, reaching a negative value (extension stress) due to the specimen's tendency to collapse (at confining pressure upon inundation greater than 400 kPa). The summary of data illustrated in Fig. 24 shows that the confining pressure upon inundation had a significant effect on the maximum deviator stress generated.

Fig. 22
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Deviator stress development with time during CA specimens’ inundation

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Fig. 23
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Variation of stress ratio with time for CA tests

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Fig. 24
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Relationship between deviator stress (peak and residual) and confining pressure upon inundation for CA tests

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Constant volume (CV) tests

The change in mean stress (Δp) with time due to CV specimen inundation is depicted in Fig. 25. Similar to that observed for CA specimens, the change in mean stress with time was observed to be high under low confining pressures upon inundation. Further increase in confining pressure upon inundation (greater than 400 kPa) caused specimens to undergo collapse and the development of extension stresses (negative deviator stress). The effect of confining pressure upon inundation on the maximum deviator stress generated and lateral stress change is expressed as a linear trend, as shown in Fig. 26.

Fig. 25
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Change in mean stress with time during inundation of CV specimens

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Fig. 26
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Relationship between stress changes during inundation and confining pressure upon inundation during the CV inundation stage

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Stress paths during swell

For the full understanding of stresses imposed on specimens during swelling, the total stress paths followed by CA and CV specimens during swelling were plotted, as illustrated in Figs. 27 and 28, respectively. Both stress paths showed increasing deviator stress trends reaching a peak value followed by a decrease to a residual stress value. Under CA conditions, the increase and decrease in stress paths followed a single path as lateral stress acting on the specimen remained unchanged. Under CV conditions, the lateral stresses increased during swelling due to restraint imposed, and this is depicted by the increase and decrease in stress paths following different paths. Furthermore, the inclination of the increasing stress path (Fig. 27 and 28) indicates that the rate of increase in deviator stress is greater than the rate of increase in lateral stress due to anisotropy of the specimen.

Fig. 27
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Total stress path for CA specimens during swelling

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Fig. 28
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Total stress path for CV specimens during swelling

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Conclusions

This study experimentally demonstrated the influence of the stress and deformation boundary conditions on the multi-directional (i.e., axial and lateral) stress and strain behavior of compacted, highly expansive clay. Response-to-wetting curves were used as a simple representation to delineate the state of strains and stress in specimens before and after wetting. Different trends for response-to-wetting curves emerged depending on boundary conditions applied.

With respect to volume change behavior, it was observed that the axial swell strains for CIP and CAP specimens were less than that observed by oedometer specimens because of the full lateral restraint imposed on oedometer specimens during inundation. Furthermore, the stress ratio (K = σ L /σ a ) was observed to have a significant effect on axial and volumetric strain that increase exponentially with an increase in stress ratio. To quantify the effect of stress ratio (K; i.e., lateral restraint) on the axial swelling strain, the authors adopted the heave reduction factor, R f , which represents the ratio between the axial swell strain obtained from triaxial testing and that obtained from oedometer testing. By definition, R f will vary with stress ratio applied on a triaxial specimen. An increase in stress ratio (K) signifies an increase in lateral restraint, resulting in an increase in axial swell strain, as shown in Fig. 21. For the range of stress ratios considered in this study, the R f value was observed to range between 0.25 and 0.85. This factor can be used to estimate the axial swell in the field based on oedometer axial swell strain and provided that the stress ratio is known.

Plots for the variation of deviator stress with time and total stress paths plots for CA and CV specimens identified a strain-softening behavior characterized by a peak and residual stress values. This suggests that specimens underwent shear loss at the aggregate level due to specimen restraint to swelling.

In conclusion, this study highlights the importance of evaluating the behavior of expansive soils under realistic stress and deformation boundary conditions for the proper estimation of state of strains and stresses in the specimens.