Collapse Behavior of Compacted Clay in a Water Content-Controlled Oedometer Apparatus

Abstract

Assessing soil deformation leading to collapse is often conducted through a suction-controlled method, which can be time-intensive. In this study, the collapse deformation of compacted clay was investigated by conducting time-saving and convenient water content-controlled tests. The compacted clay specimens, each with a unique initial void ratio, were subjected to water retention experiments. The water content-controlled oedometer apparatus performed tests involving compression, wetting, and subsequent recompression. Observed experimental results indicate that water content has an inverse relationship with suction, with suction increasing as water content decreases, suggesting an inverse relationship between the two variables. In compression tests performed at a constant water content, water saturation increases and suction decreases as the void ratio decreases. Wetting leads to a decrease in void ratio as the saturation level rises, gradually declining along the wetting path until it aligns with the compression line of fully saturated soil. The compression lines at varying suction levels are established through theoretical analysis of water retention and water content-controlled compression test results. In addition, the collapse deformation is well predicted with a concise formula related to pore gas saturation. In this way, this study provides a quick and effective method for evaluating the hydro-mechanical properties of unsaturated soils.

1. Introduction

All over the world, unsaturated clayey soils are common. These soils are found in expansive clays in North and South America (United States, Brazil, and Argentina) [1], residual clays in Africa (South Africa and Nigeria) [2], loess-origin clays in Europe (Germany, Poland, and Czech Republic) [3], and expansive clays in Oceania (Australia and New Zealand) [4]. Given their worldwide presence, understanding the mechanics of unsaturated clayey soils is of great importance.

Unsaturated soils exhibit a hydro-mechanical coupled behavior, of which the collapsible response is crucial. This phenomenon presents a significant risk to the integrity and safety of geotechnical engineering projects. Despite comprehensive experimental and theoretical studies on the compressibility and collapsibility of unsaturated soils, the extended testing durations pose challenges for applying these experiments and theories in engineering practices.

Various studies have explored these phenomena through different experimental approaches. The investigation of compression characteristics began with Cui and Delage [5], who launched a study employing the suction control approach. This was followed by Sivakumar and Wheeler [6], who laid foundational insights into the topic, further developed by Estabragh et al. [7] through their detailed contributions. Subsequently, D’Onza et al. [8] provided significant observations that enriched the understanding of the subject. Building on this foundation, Burton et al. [9] offered valuable insights using the suction control method, while Estabragh and Javadi [10] further advanced this understanding through their research. More recently, Cai et al. [11] contributed significant findings that deepened the knowledge in this area. In parallel, Jotisankasa et al. [12] conducted significant research on wetting collapse tests, while Sun et al. [13] provided valuable insights that further enhanced the understanding of wetting collapse. All the previous researchers’ experimental findings provided a strong foundation for the sound establishment of the theory related to unsaturated soil mechanical characteristics. The method introduced by Hilf [14], known as axis translation, or by Cui and Delage [5], referred to as an osmotic technique, was utilized for managing suction. In these suction-controlled tests, achieving the target suction–equilibrium state requires significant time, particularly for clay soils. To further understand, Burton et al. [15] have taken a different approach of constant saturation Sr for the deformation experienced in unsaturated soil, which was further investigated by Xiong et al. [16]. The experimental instrument used is also a suction-controlled oedometer test apparatus or triaxial test apparatus. The pore water volume and loading rate were controlled during the Sr-controlled tests. The conduct of this experiment requires a high level of experimental skills.

Constitutive models were proposed to predict unsaturated soils’ compression and collapse deformation. Constitutive models have been developed within various frameworks, including the mean net stress–matric suction plane by Alonso et al. [17], Chiu and Ng [18], and Sheng et al. [19]. In contrast to the mean net stress–matric suction plane, Loret and Khalili [20] have taken an effective stress–matric suction plane, and this approach was followed by Wheeler et al. [21] and Sun et al. [22]. An additional approach based on the effective stress–water saturation plane was proposed by Zhang and Ikariya [23] and further refined by Zhou et al. [24], Li et al. [25], and Song et al. [26], while the most recent contribution is the effective stress–bonding function plane, introduced by Gallipoli et al. [27], Hu et al. [28], and Gallipoli and Bruno [29]. The compression and collapse theory summarized above commonly utilizes suction-controlled unsaturated tests to verify the theory. If it is possible to obtain the compression and collapse deformation of soils under various suctions by using the data from compression-wetting tests conducted under water content control and the soil water retention curve suggested by van Genuchten [30], Gallipoli et al. [31], and Li et al. [32], it will significantly shorten the time required for experiments and theoretical predictions.

This study aims to provide a rapid method for testing unsaturated soil collapse behavior. First, the effect of this change in suction is theoretically translated from a water content perspective using the soil water characteristic curve. Following these tests, compression and collapse tests are conducted under controlled initial water content conditions. Theoretically, the compression lines at various suctions are obtained based on the soil water characteristic curve and the water content-controlled compression test results. Afterward, a concise formula related to pore gas saturation is proposed to predict soil collapsible behavior.

2. Materials and Methods

2.1. Study Area

The research region is situated in the northwest of Beijing, namely, in Yanqing District. The site examined is represented in red in Figure 1 at 116°16′17″ E and 40°36′7″ N. Yanqing experiences a temperate continental monsoon climate with summer precipitation predominantly. Precipitation in the wider Beijing area varies between 372–683 mm, with over 70% falling in June to August, according to Zhang et al. [33]. The historical study reveals a declining trend in the total amount of wet season rainfall since the 1980s, while the frequency and intensity of short-duration extreme events have increased [33,34]. Such hydro-climatic states directly influence soil hydrology and soil deformation processes, which are central to this paleoenvironmental study.

2.2. Material

The soil composition used for research, Yanqing clay, was collected from a construction pit. The gathered soil was pulverized, air-dried, and then sieved through a 2 mm sieve as part of the experiment. Based on basic experimental observations, the plastic limit (PL) of Yanqing clay is 15.2%, while its liquid limit (LL) is presented in

Table 1. Basic properties of Yanqing clay.

Specific Gravity, Gs	Liquid Limit, LL (%)	Plastic Limit, PL (%)	Plasticity Index, IP
2.73	30.7	15.2	15.5

as index properties. According to the Unified Soil Classification System (USCS), this soil is categorized as clay of low plasticity (CL). The Yanqing clay grading curve is displayed in Figure 2. During standard Proctor compaction (593 kJ/m³), Yanqing clay achieved a maximum dry specific mass of 1.80 g/cm³, with a maximum moisture content of 17%, as shown in Figure 3.

2.3. Water Retention Tests

A test on water retention utilizing standard filter paper [35], along with the pressure plate method [36], was carried out to determine the matric suction. To establish a relationship between matric suction and moisture content, matric suction was measured. The initial three void ratios of 0.905, 1.01, and 1.10 were achieved through static compaction at 80%, 75%, and 70% of the maximum dry density, respectively. The standard cylindrical sample, with a diameter of 61.8 mm and a height of 20 mm, was taken for analysis. The soil sample was expertly saturated using the vacuum method and strategically placed in the pressure plate apparatus to conduct soil water retention tests effectively. Compacted samples of the same size as those used in the pressure plate method were prepared for the filter paper method, with eight different moisture contents for each void ratio to determine the suction.

Table 2. The water content of soil samples in filter paper tests.

Void Ratio	Water Content (%)
0.905	6.24	9.30	12.48	15.60	18.72	21.84	24.90	28.00
1.01	6.99	10.49	13.99	17.49	20.98	24.48	27.98	31.48
1.10	7.84	11.74	15.67	19.59	23.51	27.43	31.35	35.27

summarizes the water content values. For 14 days, the compacted soil samples were sealed at a regulated temperature of 25 °C after coming into contact with the filter paper, i.e., Whatman No. 42. Due to the requirement of high accuracy, 0.0001 g grade least count weighing balance was used to weigh the sample and filter paper; then the calibration curve equation was used to calculate the suction [37].

2.4. Compression Tests

ASTM [38] was followed when conducting compression tests. The samples taken for compression were prepared from the compaction with void ratios of 0.905, 1.01, and 1.10. The prepared sample had dimensions of 20 mm in height and 61.8 mm in diameter. For samples at each initial void ratio, eight water contents were set, summarized in

Table 3. The testing program for compression tests.

Test	Condition: w (%)
Compression	0.905	6.24	9.30	12.48	15.60	18.72	21.84	24.90	28.00
	1.01	6.99	10.49	13.99	17.49	20.98	24.48	27.98	31.48
	1.10	7.84	11.74	15.67	19.59	23.51	27.43	31.35	35.27

. During compression tests, the samples were ensured to have a constant water content by covering them with loose-fitting plastic membranes that prevent water evaporation. Oedometer tests were conducted in stepwise increments from an initial 5 kPa, doubling successively up to 1400 kPa over 24 h, with loading rates of approximately 4–125 kPa/h, allowing the sample height to stabilize at each step and minimizing pore pressure, thus ensuring accurate compression measurements. During the tests, the pore air pressure (${\mathrm{u}}_{\mathrm{a}}$) was atmospheric, and vertical stress was represented by net vertical stress. Vertical displacement was measured using a precision gauge (0.001 mm accuracy) and continuously recorded with a computer-connected data logger.

By calculating with the equation $\mathrm{e}={\mathrm{e}}_0+\left(1+{\mathrm{e}}_0\right)\mathrm{\Delta }\mathrm{h}/\mathrm{h}$, the soil sample’s void ratio following progressive pressure can be determined. The equation contains the designated initial void ratio (${\mathrm{e}}_0$); the initial sample height ($\mathrm{h}$), i.e., 20 mm; and the sample height change ($\mathrm{\Delta }\mathrm{h}$), respectively. Then, to effectively determine the degree of saturation, the relationship between Sr and w can be utilized Sr.: ${\mathrm{S}}_{\mathrm{r}}=\mathrm{w}{\mathrm{G}}_{\mathrm{s}}/\mathrm{e}$.

2.5. Wetting Collapse Tests

According to the ASTM [39], wetting tests were conducted on soil samples selected as per different void ratios after compression at the designated net vertical stress. This test’s key benefit is that it allows for the measurement and control of the three primary determinants of collapse potential: overburden stress, dry density, and saturation degree. The procedure Lawton [40] suggested, i.e., “soaked-after-loading method”, was adopted for the single-oedometer test in this instance. The soil was positioned in an oedometer, and a progressive net vertical stress was applied until the sample reached equilibrium in strain. Following strain equilibrium, the oedometer cell was inundated with distilled water for saturation. The vertical change in the dimension of soil specimens was continuously monitored using the displacement gauge during the soaking of distilled water. A total of five wetting tests were conducted for each void ratio and their respective water content, with the samples loaded in the same manner as in the compression tests; the details of these tests, including the net vertical stresses at which collapse was initiated during inundation, are presented in

Table 4. The testing program for compression wetting tests.

Test	Condition: (w, σv) (%, kPa)
Compression wetting	0.905	6.24, 800	9.30, 600	12.48, 400	15.60, 300	18.72, 200
	1.01	6.99, 600	10.49, 400	13.99, 200	17.49, 100	20.98, 50
	1.10	7.84, 300	11.74, 200	15.67, 100	19.59, 50	23.51, 30

. After wetting, the soil samples were reloaded to a net vertical stress of 1000 kPa to replicate the drainage condition. Additionally, the soil sample’s vertical displacement during recompression was continuously observed.

The saturation level and void ratio before the wetting path are comparable to the compression tests and can be obtained through calculation equations $e=e_0+\left(1+e_0\right)\Delta h/h$ and $S_{\mathrm{r}}=w{G}_s/e$, respectively. The saturation degree S_r was assessed by examining the moisture content w of the soil samples throughout the wetting process, and the saturated condition was verified following the wetting experiments.

3. Results and Discussions

3.1. Water Retention Test Results and the Parameter Calibration

Figure 4 shows the measured water retention curve test results. As suction (s) increases, it becomes evident that the degree of saturation Sr decreases. According to earlier research findings by Salager et al. [41] and Gao et al. [42], air entry value rises as the void ratio decreases. Zhang et al. [43] and Song et al. [44] also found a similar result in their research.

The measured WRC data were fitted with the van Genuchten [30]. The expression of the WRC model is

$$S_{\mathrm{r}}={\left[{\displaystyle \frac{1}{1+{\left(\alpha s\right)}^n}}\right]}^m$$

(1)

where $\alpha$ controls the variation of the air entry value with the void ratio, while $\mathrm{m}$ and $\mathrm{n}$ are two other model parameters. The calibrated parameters are $\alpha =0.011$, $m=0.241$, and $n=1.314$ for the soil specimen, with 0.905 as a designated initial void ratio. Similarly, the calibrated parameters are $\alpha =0.026$, $m=0.241$, and $n=1.314$ for 1.01 as a designated initial void ratio. Lastly, the calibrated parameters are $\alpha =0.080$, $m=0.241$, and $n=1.314$ for the soil specimen, with 1.1 as a designated initial void ratio.

3.2. Compression Test Results

Figure 5 illustrates how the void ratio evolved throughout the compression tests. As there is an increase in net vertical stress, there is a decrease in the void ratio. The compression curve’s slope is mild within a narrow range of net vertical stress; it becomes steeper as the net vertical stress rises above a particular threshold. In other words, the compression curve shows progressive yielding as the elastic state of the curve, brought on by the change from the elastoplastic state. During compression, all curves representing the driest soil specimen’s compression are positioned above those of all other moist soil specimens. With increasing water content, the yielding net vertical stress gradually decreases. As the void ratio of the soil specimens varies, the yielding zone appears to differ in the range of 50–800 kPa for void ratios of 0.905, 12–600 kPa for void ratios of 1.01, and 12–300 kPa for void ratios of 1.10. The test results of this study can be compared with the results published by Zou et al. [45]. In contrast to the findings of Zou et al. [45], this study definitively investigates the impact of initial void ratio and water content on soil compression.

The change in saturation level observed during the compression of the soil sample is illustrated in Figure 6. Reducing the initial water content reduces the initial degree of saturation. As the net vertical stress increases, the degree of saturation gradually increases first and then significantly increases. Before the significant increase in water saturation, the plot between the degree of saturation with the net vertical stress relationship is almost parallel for samples with varying water contents. This is related to the elastic compression deformation stage. The net vertical stress is large for a specimen with a small water content value when the water saturation change rate accelerates. This is consistent with the yield state of the compression test data. After the yielding state, the soil has reached the elastoplastic compression deformation stage. At this stage, the changing rate of water saturation with net vertical stress is larger than that at the elastic compression deformation state.

3.3. Compression–Wetting Collapse–Recompression Test Results

The alteration in the void ratio related to the volume change induced through the compression–wetting–recompression tests is illustrated in Figure 7. As the net vertical stress rises during the first stage of compression, the void ratio diminishes, demonstrating the significant impact of stress on soil structure. For soil samples that have elevated water content, the reduction in the volume of voids is more noticeable, as it experiences a significant decline during the wetting process, with the decrease becoming even more significant as the initial water content reduces. The void ratio gradually decreases in the drainage compression tests that come after the wetting test of the soil specimen. As the drainage compression stage advances, the void ratio and net vertical stress converge for various samples. This is because the soil samples have been saturated after the wetting test. In other words, the drainage compression test is a saturated soil compression procedure.

Figure 8 shows how the saturation level changes during the compression–wetting–recompression tests. With the reduction of initial water content, soil samples’ initial degree of saturation decreases. As the net vertical stress applied during the initial constant water compression tests increases, the saturation level progressively goes up. A near-parallel relationship exists between saturation level and net vertical stress for samples with different water contents. In the ensuing wetting tests, the saturation level then rises to 1. In the drained compression process that follows the wetting tests, the saturation level remains at 1, indicating that the compression curves for various soil samples coincide and match the compression curve of fully saturated soil.

3.4. The Variation of Suction During Compression and Compression–Wetting–Recompression Tests

A constitutive model for unsaturated soils is essential to predict soil collapse; however, most of these models are created and validated using suction-controlled tests. The water retention model (Section 3.1) and the degree of saturation shown in Figure 6 and Figure 8 were used in this study to determine the suction value. After that, the compression lines at different constant suction levels were determined using test data controlled by water content. Using the compression line at various fixed suctions, the compression index of the soil at various suctions was calibrated in the next section.

The suction variation during the water content-fixed compression tests is depicted in Figure 9. It is evident that when water content rises, suction diminishes, with a minor reduction in suction noted during compression. At large net vertical stress, suction significantly decreases as the vertical stress continues to increase. The primary cause is that the degree of saturation greatly rises as vertical stress increases in the high net vertical stress range (Figure 6). An analysis of outcomes for samples with various initial void ratios indicates that, at a specific water content, suction diminishes as the initial void ratio rises, which is consistent with the results from water retention experiments carried out at different initial void ratios.

Figure 10 depicts the variation in suction throughout the compression–wetting–recompression tests, indicating that, initially, suction declines as the water content rises, according to the findings shown in Figure 9. There is a decrease in suction as the initial void ratio increases at a specific water content, as shown in Figure 10a–c. The suction value somewhat decreases during the compression stage as the net vertical stress rises. Later in the wetting process, the suction value progressively drops to 0. During the subsequent drainage compression process, the suction value stays at 0 since the soil sample is saturated.

3.5. The Compression Lines at Constant Suctions

With the suction values in Section 3.4, the compression lines under various suction values are obtained from the water content-controlled compression test data. Figure 11 depicts the compression lines at various suctions and the test data during the water content-controlled compression tests. The compression index of the compression lines was analyzed using the compression equation proposed by Alonso et al. [17]:

$$e=N(s)-\lambda (s){\displaystyle \frac{{\sigma }_{\mathrm{v}}}{{\sigma }_{\mathrm{vc}}}}$$

(2)

where N(s) is the void ratio at σ_v = σ_vc, λ(s) is the compression index at the suction s, and σ_vc is the reference vertical stress. For the λ(s), it is assumed that Alonso et al. [17]

$$\lambda (s)=\lambda (0)\left[(1-r)\exp (-\beta s)+r\right]$$

(3)

where λ(0) is the compression index at a fully saturated state and r and β are two parameters controlling the variation of λ(s) with s. In the BBM model, it is assumed that λ(s) decreases with s, which was confirmed by the test data [46,47]. However, for some soils, it is also found that λ(s) increases with s [6,48]. Estabragh et al. [7] found that for the loose, silty soil samples, the compression index increases and then gently decreases with suction, which was also found in Raveendiraraj [49].

The calibrated values of λ(s) are shown in Figure 10. Interestingly, for the Yanqing clay compacted at three different initial void ratios, λ(s) = λ(0) = 0.11. That is, the compression lines of the compacted Yanqing clay at different suctions are parallel. This is a new finding on the compression curve of unsaturated soil under different values of suction.

3.6. The Prediction of Wetting Collapse Deformation

At fixed vertical stress, soil undergoes a sudden volume change when its moisture content increases (Figure 7). The collapse deformation (Cp) of each wetting-collapse test is calculated based on the following expression [50]:

$$Cp={\displaystyle \frac{\Delta e_{\mathrm{c}}}{1+e_{\mathrm{b}}}}$$

(4)

where Cp = collapse deformation, Δe_c = difference in void ratio after inundation, and e_b = void ratio before wetting.

Table 5. Collapse deformation (Cp) of each wetting-collapse test.

e0	w (%)	σv (kPa)	eb	Sr (%)	s (kPa)	Cp (%)
0.905	6.20	800	0.84	20.22	14,135.33	41.34
	9.30	600	0.79	32.14	3253.61	34.80
	12.48	400	0.81	41.99	1378.37	31.35
	15.60	300	0.79	53.82	605.25	25.94
	18.72	150	0.80	63.79	330.87	16.25
1.01	6.99	600	0.93	20.54	5694.66	46.06
	10.49	400	0.92	31.02	1540.44	41.37
	13.99	200	0.91	41.88	588.43	32.86
	17.49	100	0.93	51.61	295.26	24.20
	20.89	50	0.96	59.69	178.43	16.17
1.10	7.84	300	1.02	20.91	1747.00	34.14
	11.74	200	1.02	31.55	474.69	29.92
	15.67	100	1.03	41.67	194.28	23.72
	19.59	50	1.03	51.80	94.79	16.59
	23.51	30	1.04	61.89	50.87	11.29

shows the collapse deformation (Cp) values for the wetting-collapse tests, along with the degree of saturation and suction of the soil before the wetting test. The degree of saturation was calculated using the given equation S_r = wG_s/e_b. The matric suction s was obtained through the SWCC with the obtained Sr. Furthermore, it is also possible to obtain the degree of air saturation (1 − S_r) using S_r obtained previously.

Figure 12a,b depict the collapse deformation–matric suction relationship and the collapse deformation–degree of air saturation (1 − Sr) relationship, respectively. Figure 12a depicts that the collapse deformation increases nonlinearly with matric suction at a wide matric suction range. Under 1 MPa matric suction, collapse deformation increases rapidly with matric suction. In response to an increase in matric suction, the rate of collapse deformation slows down. Figure 12b depicts the variation of collapsible deformation with a degree of air saturation approaching linearity. Hence, the degree of air saturation may provide a more accurate prediction of collapse deformation than matric suction. Subsequently, the following expression can be proposed to predict the collapse deformation of soils within a wide air saturation range:

$$Cp=a(1-S_{\mathrm{r}})$$

(5)

where a is a parameter controlling the variation of collapse deformation and the degree of air saturation.

The parameter a in Equation (5) was calibrated with the test data. The calibrated values of a are 0.521, 0.556, and 0.406 for soils compacted at void ratios of 0.905, 1.01, and 1.10, respectively. After that, the collapse deformation of the compacted Yanqing clay was predicted with the proposed expression (Equation (5)). Figure 13 depicts the comparison between measured collapse deformation and predicted collapse deformation. R² values of 0.967, 0.901, and 0.900 are obtained, indicating that the collapsed deformation of the compacted Yanqing clay in a wide degree of air saturation range is well predicted by the proposed method.

4. Conclusions

A rapid method to measure the hydro-mechanical coupled behavior of unsaturated soils is proposed by conducting water retention tests, water content-fixed compression tests, and compression–wetting–recompression tests on Yanqing clay. The new findings are as follows.

The compression lines of soil at various suctions can be obtained with water retention tests and water content-controlled compression tests. For the compacted Yanqing clay, it is found that the compression index λ is the same for all suction magnitudes under three different initial void ratio conditions.

The collapse deformation increases nonlinearly with matric suction at a wide matric suction range. The collapse deformation increases rapidly at low matric suction levels and gradually at high suction levels as suction rises. The collapse deformation of compacted Yanqing clay shows a nearly linear relationship with the degree of air saturation over a wide range, and it can be effectively predicted using the expression a(1 − S_r).

The natural variability of soils is obviously not considered, as the scope of this study was focused on controlled lab experiments using compacted clays with defined void ratios. The use of tests on samples with water contents controlled, use of stepwise loading, and generally not very large samples might influence the found compression and collapse behavior. The authenticity of the findings and their broader applicability would therefore need to be further validated across other types of soil and field conditions.

The technique forms a means of testing faster than suction-controlled tests to assess compressibility and collapse of soil, which has practical benefit in foundation, embankment, and earth structures constructions.