Long-term consolidation behavior of solidified slurry-like muds subjected to various freezing–thawing cycles

Abstract

Solidification technology is widely used for treating slurry-like muds (MS) due to its efficiency and effectiveness. Numerous studies have investigated the mechanical properties of solidified MS, yet its long-term deformation behavior and the influence of freezing–thawing (FT) cycles remain ambiguous. This study presents an experimental investigation on the long-term consolidation properties of solidified MS subjected to various FT cycles. Three groups of solidified MS samples with different initial water contents and cementitious binder contents are subjected to 0, 1, 5, and 10 FT cycles. Then, a series of long-term oedometer tests and microscopic analyses are conducted accordingly. The results indicate that the increasing FT cycles lead to the degradation of the soil microstructure, thereby weakening the ability of solidified MS to resist long-term consolidation deformation. Specifically, after 10 FT cycles, the total strain increases by at least 1.12 times and the secondary consolidation coefficient (C_a) increases by 1.83 times, compared to solidified MS without FT cycles. It is found that the compression yield stress decreases exponentially as FT cycles increase, such decrease exhibits more pronounced for the samples with FT cycles smaller than 5. Based on the relationship between C_a and vertical effective stress for solidified MS subjected to different FT cycles, three distinct stages in the compression process are identified. As the number of FT cycles increases, the vertical stress required for the transition into the second stage decreases.

Graphical abstract

Keywords

solidified slurry-like MS / FT cycles / long-term oedometer tests / consolidation behavior / compression process

1 Introduction

Large amounts of slurry-like muds (MS) are dredged annually from ecological dredging projects and infrastructure construction [1–3]. Recent statistics indicate that over 100 million cubic meters of the dredged MS are produced every year in China [4]. The MS has a very high water content and extremely poor mechanical properties. Solidification technology is a safe and efficient treatment method that effectively reduces the water content of MS and enhances its strength through the addition of solidifying agents. These advantages make solidification technology highly suitable for treating MS [5,6]. Solidified MS has been widely employed in various engineering applications. Therefore, studying the long-term performance of solidified MS is crucial for ensuring the safety and stability of engineering projects.

Research has demonstrated that long-term deformations are commonly observed in various projects, such as tunnels, embankments, and foundations [7–9]. The current research primarily focuses on the long-term deformation of non-solidified soils [10–13]. In terms of solidified soils, extensive efforts have been dedicated to studying their short-term strength and compressive characteristics [14–17], whereas limited attention has been paid to its secondary consolidation behavior. Bobet et al. [18] highlighted that the creep deformation of soils can be reduced through cement treatment. By conducting oedometer tests, Venda et al. [19] demonstrated that the rate of secondary consolidation decreases with increasing binder content and identified the optimal binder type for stabilizing Portuguese soft soil. According to the results of creep tests on solidified soil under different confining pressures, a long-term strength prediction formula for solidified soil was proposed by Yang et al. [20]. Dredged MS with high water content exhibits relatively poor engineering properties [4,21–23], making the secondary consolidation of solidified MS an even more important concern. Current research is too limited to adequately elucidate the long-term characteristics of solidified MS.

More importantly, seasonally frozen ground covers approximately 35% of Earth’s terrestrial area [24]. Periodic temperature fluctuations in these regions lead to freezing–thawing (FT) cycles within the soil. In recent decades, the effects of FT cycles on soils have intensified due to global warming [25,26]. Numerous studies have been conducted to investigate the impact of FT cycles on the physical and mechanical properties of soils. By investigating the evolution of the soil-water characteristic curve, Zhao et al. [27] reported that FT cycles reduce the water retention capacity of expansive clay within the low suction range. Kong et al. [28] suggested that successive FT cycles continuously degrade the erosion resistance of soil, with the degradation stabilizing after approximately 10 FT cycles. Zou et al. [29] investigated the mechanical behavior of clay subjected to FT cycles and found that mechanical properties were reduced by 50%–70% during the first FT cycle, and by 65%–90% after 10 FT cycles. Based on the results of laboratory tests, Tang et al. [30] proposed a unified stress-strain relationship that incorporates the effects of FT cycles on the mechanical behavior of expansive soil. Regarding solidified soil, Kamei et al. [31] demonstrated that the presence and increase in the content of cementitious binders in the soil mixture significantly improve the strength and durability of samples subjected to FT cycles. Qin et al. [32] attributed the decrease in bearing capacity to water movement during the freezing process, which changes interparticle bonding and damages the internal structure of solidified soil. However, a systematic investigation into the long-term deformation characteristics of solidified soil subjected to FT cycles remains lacking.

The objective of this study is to investigate the long-term consolidation behavior of solidified MS subjected to various FT cycles. Long-term oedometer tests were conducted on solidified MS samples subjected to 0, 1, 5, and 10 FT cycles. A systematic investigation was then carried out to evaluate the effects of FT cycles on long-term consolidation characteristics, including compression yield stress ({\sigma }_{\mathrm{y}}^{\prime }), compression index (C_{\mathrm{c}}^{\ast }), secondary compression coefficient (C_a), and the microstructure of solidified MS. Finally, by identifying the three stages in the compression process under vertical effective stress, this study elucidates the long-term consolidation mechanism of solidified MS.

2 Experimental investigation

2.1 Materials and sample preparation

The MS used in this experiment was lake sediment collected from Jingyue Lake in Hubei Province, China, where temperatures range from below –15 °C in winter to over 35 °C in summer. The basic physical and engineering properties of the MS are listed in Table 1. Particle size distribution analysis indicates that the MS consists of 3.8% sand, 68.5% silt, and 27.7% clay (Fig. 1). Compositional analysis shows the presence of quartz, muscovite, calcite, and amesite in the MS. To achieve optimal solidification performance, 425# ordinary Portland cement (OPC) and ground granulated blast furnace slag (GGBS) were selected as the cementitious binders at a mass ratio of 1:1, based on previous experimental findings [33].

As shown in Fig. 2(a), solidified MS samples were prepared according to the following procedures:

1) Water was added to the MS and mixed to achieve the specified initial water contents of the MS (w_ei). Then, OPC and GGBS were thoroughly mixed with the MS according to the designated combination schemes to produce a homogeneous mixture of the cementitious binders and MS.

2) Two cutting rings, each with a diameter of 61.8 mm and a height of 20 mm, were taped together to form a cylindrical mold measuring 61.8 mm in diameter and 40 mm in height. A thin layer of petroleum jelly was applied to the inner walls of the mold before the mixture was added in three layers. The samples were then vibrated to prevent air entrapment and ensure uniformity.

3) The samples were wrapped in polyethylene film and cured in a standard curing room at (20 ± 3) °C and a humidity level exceeding 90% for 28 d. After curing, the upper cutting ring was removed, and the samples were trimmed into cylinders measuring 61.8 mm in diameter and 20 mm in height.

In this experiment, three groups of solidified MS samples with different w_ei and cementitious binder contents (w_c) were prepared as follows: group A (w_ei = 180%, w_c = 10%), group B (w_ei = 180%, w_c = 20%), and group C (w_ei = 120%, w_c = 20%). The values of w_ei and w_c were determined according to previous studies [16,34]. The water contents of the solidified MS samples were 144% for group A, 125% for group B, and 77% for group C.

2.2 Test methods

The solidified MS samples were subjected to FT cycles in a constant temperature and humidity test chamber, as illustrated in Fig. 2(b). A complete FT process consisted of freezing at –23 °C for 24 h, followed by thawing at 23 °C for another 24 h [35]. To prevent any water gain or loss, the samples were sealed with polyethylene film throughout the FT cycles. The number of FT cycles, denoted as n, was set to 0, 1, 5, and 10.

The long-term oedometer tests on solidified MS were conducted using a high-pressure consolidation instrument. A multi-stage loading method was employed, with vertical effective stress ({\sigma }_{\mathrm{v}}^{\prime }) of 12.5, 25 50, 100, 200, 400, 800, and 1600 kPa. Each stress was applied for a duration of 4320 min to ensure that the deformation reached a stable state [36]. Besides, scanning electron microscope (SEM) and nuclear magnetic resonance (NMR) tests were used to investigate the effects of FT cycles on the microstructure of solidified MS, as shown in Fig. 2(c). SEM analysis was performed using a GeminiSEM 500 field emission SEM manufactured by Carl Zeiss AG, Germany. The solidified MS sample was mounted on double-sided tape, sputter-coated with gold, and subsequently examined by SEM to characterize its morphology and surface features. NMR analysis was conducted on cylindrical samples using a MacroMR12-150H-I low-field NMR system manufactured by Niumag Analytical Instrument Co. Ltd., China.

3 Experimental results and discussion

3.1 Compressive strain

Based on the Boltzmann superposition principle [37], the compressive strain at each stress for samples in groups A, B, and C subjected to FT cycles is obtained, as shown in Fig. 3. In all three groups, the strain varies with vertical effective stress. For samples in group A, the strain values initially increase and then decrease as the stress rises, as shown in Fig. 3(a). For instance, when the number of FT cycles is 10, the strain values under eight stress levels are 1.21%, 2.21%, 4.28%, 7.87%, 9.20%, 9.77%, 8.78%, and 8.48%, respectively. The strain reaches its peak value of 9.77% at 400 kPa. For the samples in groups B and C, the strain values increase with vertical effective stress, and the highest value is observed at 1600 kPa for both groups.

FT cycles have an obvious impact on the compressive strain of solidified MS. Taking the samples in Group B as examples, under eight stress levels, the total compressive strains are measured as 20.1%, 24.4%, 27.5%, and 28.8% for samples subjected to 0, 1, 5, and 10 FT cycles, respectively. Besides, compared to samples without FT cycles, the total compressive strain increases by a factor of 1.12 in group A, 1.43 in group B, and 2.20 in group C after 10 FT cycles. The increase in the number of FT cycles induces internal structural damage to the soil, leading to an increase in the compressive strain of the samples. This suggests that when solidified MS is used as subgrade fill in seasonally frozen regions, the long-term settlement may be more severe than expected if FT effects are not considered in design.

Additionally, for a given number of FT cycles, the compressive strain of the samples is influenced by both the cementitious binder content and the initial water content of MS. A comparison between the samples in groups A and B shows that, with all other conditions constant, increasing the cementitious binder content from 10% to 20% significantly reduces the total strain under each FT cycle. Specifically, the strain decreases from 46.10% to 20.08% at 0 cycles, from 49.02% to 24.37% at 1 cycle, from 49.73% to 27.55% at 5 cycles, and from 51.77% to 28.75% at 10 cycles. Increasing the cementitious binder content enhances the cementitious structure of the samples, thereby improving their resistance to compressive deformation. A comparison between groups B and C indicates that reducing the initial water content from 180% to 120% markedly decreases the strain of the samples. The reduction in water content increases the internal friction and cohesion between soil particles, thereby improving the resistance of the soil to compressive deformation.

3.2 Long-term consolidation behavior of solidified muds subjected to various freezing–thawing cycles

3.2.1 Void ratio

To investigate the evolution of void ratio (e) over time, Figures 4–6 present the e–lgt curves of solidified MS samples subjected to various FT cycles in groups A, B, and C, respectively. The change in the void ratio of the samples increases with both time and vertical effective stress. It is observed that when the stress is below 50 kPa, the e–lgt curve approximates a straight line, showing no clear boundary between the primary and secondary consolidation stages. When the stress exceeds 100 kPa, the slope of the e–lgt curve gradually decreases over time, suggesting that the samples are easily compressed in the initial stages and exhibit increased resistance in the later stages. A boundary between the primary and secondary consolidation stages is evident. All samples demonstrate pronounced secondary consolidation deformation characteristics.

FT cycles lead to an increase in the void ratio of samples before compression. As the number of FT cycles increases from 0 to 10, the void ratios of the samples rise from 4.07 to 4.32 for group A, from 3.61 to 3.83 for group B, and from 2.24 to 2.40 for group C. Moreover, FT cycles have significant impacts on the variation in void ratio under compression. Taking the samples in group B as an example, as the vertical effective stress increases from 0 to 1600 kPa, the total changes in void ratio for samples subjected to 0, 1, 5, and 10 FT cycles are 0.93, 1.00, 1.30, and 1.39, respectively. After 10 FT cycles, the total change in void ratio for the sample is 1.49 times greater than that of the sample without FT cycles. The increase in void ratio variation indicates that the solidified MS becomes more compressible when subjected to FT cycles.

Moreover, the variation in the void ratio of samples under compression is influenced by the cementitious binder content and the initial water content of MS. A comparison between the samples in groups A and B shows that increasing the cementitious binder content reduces the variation in the void ratio under compression. Similarly, a comparison between the samples in groups B and C shows that increasing the initial water content increases the change in void ratio.

3.2.2 Compression yield stress

The compression yield stress, {\sigma }_{\mathrm{y}}^{\prime } of soils can be determined using a bilogarithmic approach proposed by Butterfield [38]. Following this method, the ln(1 + e)–lg{\sigma }_{\mathrm{y}}^{\prime } curves of solidified MS samples in groups A, B, and C are exhibited in Fig. 7. It is observed that most of the curves are characterized by two distinct linear segments. For the samples subjected to 10 FT cycles in group A, the two linear segments intersect at 66.25 kPa, indicating the onset of compression yielding. According to the bilogarithmic approach, the {\sigma }_{\mathrm{y}}^{\prime } value is therefore identified as 66.25 kPa.

The {\sigma }_{\mathrm{y}}^{\prime } value for the other samples can be determined, as shown in Fig. 7. It is noteworthy that for samples without FT cycles in group C, the ln(1 + e)–\lg {\sigma }_{\mathrm{y}}^{\prime } curve cannot be fitted with two distinct linear segments. This is because the maximum vertical effective stress of 1600 kPa in this experiment is insufficient for the sample to exhibit distinct compression yield characteristics. It can be inferred that the {\sigma }_{\mathrm{y}}^{\prime } of samples without FT cycles in group C is greater than 800 kPa.

Figure 8 illustrates the variation of {\sigma }_{\mathrm{y}}^{\prime } values with increasing FT cycles for samples in groups A and B. It can be seen that {\sigma }_{\mathrm{y}}^{\prime } values decrease exponentially with the increasing number of FT cycles, characterized by two distinct stages. Stage A: when the number of FT cycles is less than 5, the {\sigma }_{\mathrm{y}}^{\prime } values of samples decrease rapidly. Stage B: for the number of FT cycles exceeding 5, the decrease in {\sigma }_{\mathrm{y}}^{\prime } values slows down and tends to stabilize. Moreover, a damage factor, W_σy(n), is defined to quantitatively evaluate the impact of FT cycles on the {\sigma }_{\mathrm{y}}^{\prime } values. As shown in Eq. (1), a higher W_σy(n) value corresponds to a greater degree of damage to the {\sigma }_{\mathrm{y}}^{\prime } value. Figure 8 presents the variation of W_σy(n) with increasing FT cycles for samples in groups A and B. In stage A, the W_σy(n) values increases from 0 to 0.42 for group A and to 0.34 for group B, indicating that the degradation in {\sigma }_{\mathrm{y}}^{\prime } caused by FT cycles accounts for more than one-third of the total reduction relative to samples without FT cycles. After 10 FT cycles, W_σy(n) further increases to 0.47 for group A and 0.39 for group B. The rate of increase in the damage factor slows down in stage B.

(1)W_{\sigma \mathrm{y}}\left(n\right)=\frac{{\sigma }_{\mathrm{y}}^{\prime }\left(0\right)-{\sigma }_{\mathrm{y}}^{\prime }\left(n\right)}{{\sigma }_{\mathrm{y}}^{\prime }\left(0\right)},

where {\sigma }_{\mathrm{y}}^{\prime }(0) is the compression yield stress for samples without FT cycles, and {\sigma }_{\mathrm{y}}^{\prime }(n) is the compression yield stress for samples subjected to n FT cycles.

Furthermore, the {\sigma }_{\mathrm{y}}^{\prime } values are influenced by both the cementitious binder content and the initial water content of MS. A comparison between samples in groups A and B shows that a higher cementitious binder content corresponds to a greater yield stress. For example, for samples subjected to 1 FT cycle, the {\sigma }_{\mathrm{y}}^{\prime } value is 87.72  kPa in group A and 392.21  kPa in group B, showing a difference of 4.47 times. Besides, a comparison between the samples in groups B and C demonstrates that a lower initial water content leads to a higher yield stress for the solidified MS samples. At 1 and 5 FT cycles, the compression yield stress of group C is 1.67 times that of group B, and this value decreases to 1.55 at 10 FT cycles. As the cementitious binder content increases and the initial water content decreases, the water content of solidified MS decreases, and the proportion of cementitious structures within the soil increases. As a result, long-term deformation is reduced, and the yield strength is enhanced.

3.2.3 Compression index

The compression index, C_c, is defined as the slope of the linear segment of the e–lg{\sigma }_{\mathrm{v}}^{\prime } curve. Due to the nonlinear characteristics of the e–lg{\sigma }_{\mathrm{v}}^{\prime } curve obtained from the long-term consolidation tests of solidified MS, C_c can be determined stage by stage [11], and is denoted as C_{\mathrm{c}}^{\ast } (Eq. (2)). Results show that the C_c* value is influenced by the vertical effective stress, as exhibited in Fig. 9. For the samples in group A, as the stress increases, the C_{\mathrm{c}}^{\ast } value shows an initial increase followed by a decrease, with a maximum value at the stress of 400 kPa. This indicates that the compressibility of the sample is highest at 400 kPa. For the samples in groups B and C, the C_{\mathrm{c}}^{\ast } value increases as the vertical effective stress increases from 12.5 to 1600 kPa, indicating a continuous rise in the compressibility of the samples.

(2)C_{\mathrm{c}}^{\ast }=-\mathrm{\Delta }e/\mathrm{\Delta }\lg p.

The average C_{\mathrm{c}}^{\ast } values under eight vertical effective stress levels are obtained, and the influence of FT cycles on average C_{\mathrm{c}}^{\ast } values is shown in Fig. 10. As the number of FT cycles increases, the average C_{\mathrm{c}}^{\ast } values of samples in three groups show an increasing trend. A damage factor, W_c(n), is defined to quantitatively evaluate the impact of FT cycles on the C_{\mathrm{c}}^{\ast } values, as shown in Eq. (3). The W_c(n) values are all negative, indicating that the compressibility of the solidified MS increases after being subjected to FT cycles. As shown in Fig. 10(c), after 10 FT cycles, the W_c(n) value for the samples in group C reaches –1.48, whereas the values for the other groups are larger than –0.6. This suggests that FT cycles have the most pronounced effect on enhancing the compressibility of samples in group C, compared to other groups.

(3)W_{\mathrm{c}}\left(n\right)=\frac{C_{\mathrm{c}}^{\ast }\left(0\right)-C_{\mathrm{c}}^{\ast }\left(n\right)}{C_{\mathrm{c}}^{\ast }\left(0\right)},

where C_{\mathrm{c}}^{\ast }\left(0\right) is the compression index for samples without FT cycles, and C_{\mathrm{c}}^{\ast }\left(n\right) is the compression index for samples subjected to n FT cycles.

Furthermore, comparisons between samples in groups A and B, as well as between samples in groups B and C, show that an increase in initial water content and a decrease in cementitious binder content both result in greater compressibility of the solidified MS.

3.2.4 Secondary compression coefficient

Figure 11 presents the typical e–lgt curves of samples without FT cycles in group A under stress of 400, 800, and 1600 kPa. The curves illustrate two distinct stages of soil deformation in response to stress: primary consolidation and secondary consolidation [9,13]. During the secondary consolidation stage, the void ratio exhibits a linear relationship with time. The slope of the e–lgt curve at this stage is referred to as the secondary compression coefficient (denoted as C_a), which is calculated using Eq. (4). The C_a value characterizes the rate of secondary consolidation deformation.

(4)C_{\mathrm{a}}=-\mathrm{\Delta }e/\mathrm{\Delta }\lg t.

Figure 12 illustrates the relationship between C_a values and vertical effective stress for samples in groups A, B, and C. This relationship varies distinctly between different soil groups. For the samples in group A, C_a values range from 0.0017 to 0.022. As the stress increases from 12.5 to 400 kPa, the C_a value of samples without FT cycles rises from 0.0017 to 0.010, then decreases to 0.0091 as the stress increases from 400 to 1600 kPa. A similar trend is observed in samples subjected to 1, 5, and 10 FT cycles: the C_a value initially increases with rising vertical effective stress, reaching a peak before subsequently decreasing. The samples exhibit high void ratios and creep potential at lower stress levels. As stress increases, the cemented structure of the soil gradually breaks down, leading to a reduction in its resistance to deformation. The C_a value increases accordingly. When the stress reaches 400 kPa, the samples transition from a porous to a more compact state, reducing their deformation capacity and causing the C_a value to decrease. Besides, all four samples reach their peak C_a value at a stress of 400 kPa.

The influence of FT cycles on average C_a of samples in group A under eight vertical effective stress levels is shown in Fig. 13(a). An increase in FT cycles results in a higher secondary consolidation deformation rate. After 10 cycles, the average C_a value is 1.83 times higher than that of the sample without FT cycles. As shown in Eq. (5), a damage factor, W_a(n), is introduced to quantify the effect of FT cycles on C_a. The W_a(n) of samples in group A decreases with increasing FT cycles, indicating a progressively greater impact on C_a.

(5)W_{\mathrm{a}}\left(n\right)=\frac{C_{\mathrm{a}}\left(0\right)-C_{\mathrm{a}}\left(n\right)}{C_{\mathrm{a}}\left(0\right)},

where C_{\mathrm{a}}\left(0\right) is the secondary compression coefficient for samples without FT cycles, and C_{\mathrm{a}}\left(n\right) is the secondary compression coefficient for samples subjected to n FT cycles.

The variation in the long term consolidation behavior of solidified MS subjected to FT cycles is attributed to changes in microstructure. This can be illustrated using samples in group A as an example. The T₂ distribution curves of these samples, with different FT cycles, are shown in Fig. 14. For samples without FT cycles, the T₂ distribution curves display only a single peak. After being subjected to FT cycles, the curves exhibit both a primary and a secondary peak. The area of the secondary peak accounts for 0.68%, 1.51%, and 3.22% of the total T₂ spectrum for samples subjected to 1, 5, and 10 FT cycles, respectively, indicating that FT cycles enlarge the pore sizes within the soil. Additionally, Fig. 14 presents SEM images of samples from group A subjected to 0 and 10 FT cycles. These images show that FT cycles reduce soil compactness and increase porosity. During the cyclic rise and fall of temperature, the water within soil pores repeatedly transitions between liquid and solid states. The continuous formation and melting of ice crystals induce periodic volumetric expansion and contraction. This process induces an uneven stress distribution within the soil, resulting in the formation of new cracks, the disruption of cementitious structures, and an increase in porosity. Accordingly, the ability of solidified MS to resist long-term deformation under stress is reduced.

As shown in Fig. 12(b), the C_a values of samples in group B consistently increase with rising stress, which differs from the trend observed in group A. This difference is attributed to the higher cementitious binder content in group B (20%), which is twice that of group A. Moreover, samples in group B exhibit greater resistance to secondary consolidation deformation. The maximum stress applied in this test (1600 kPa) is insufficient to fully disrupt the cementation structure of the solidified MS. Therefore, the rate of secondary consolidation deformation continues to increase throughout the test. As shown in Fig. 13(b), the average C_a values of group B samples exhibit a progressive increase with the number of FT cycles. After 10 cycles, the deformation rate is more than twice that of samples without FT cycles. Correspondingly, the W_a(n) value decreases from 0 to –1.26 over this range, demonstrating that FT cycles markedly accelerate the long-term deformation rate of samples in this group.

An increase in cementitious binder content results in a decrease in the average C_a values of the solidified MS samples with fixed FT cycles. Specifically, the average C_a value of group B samples is lower than that of group A. This is attributed to the higher cementitious binder content, which promotes the formation of solid cementitious phases that bond soil particles, reduce the void ratio, and enhance resistance to deformation. As shown in the microstructural images (Fig. 15), rod-shaped ettringite is abundant in the samples of group A. For samples of group B, not only ettringite but also significant amounts of flocculent hydration products, such as CSH, CAH and CASH, are observed. These hydration products contribute to both cementation and the filling of the pores between soil particles, thereby reducing pore volume.

For the samples in group C, the C_a values exhibit a positive correlation with both increasing stress and the number of FT cycles, as illustrated in Figs. 12(c) and 13(c). The samples in group C reach the maximum C_a value at a stress of 1600 kPa, similar to those in group B. However, despite the more compact microstructure of samples in group C (Fig. 15(c)), the C_a value is higher compared to that in group B. The underlying reasons for this higher C_a value in group C will be elaborated in Subsection 3.3. Besides, when subjected to 0, 1, 5, and 10 FT cycles, the average C_a values of the samples in group C are 0.0079, 0.016, 0.019, and 0.023, respectively. After 10 FT cycles, the average C_a value is 2.91 times higher than that of the samples without FT cycles. The W_a(n) value decreases with an increasing number of FT cycles. As a result, the compressibility of the samples in group C increases under the influence of FT cycles.

Figure 16 illustrates the relationship between C_a and C_{\mathrm{c}}^{\ast } for samples from the three groups subjected to different FT cycles. The C_a and C_{\mathrm{c}}^{\ast } values of the samples in three groups show an approximately linear relationship. It is noteworthy that the C_a/C_{\mathrm{c}}^{\ast } ratio remains unchanged regardless of the number of FT cycles. This finding suggests that the C_a/C_{\mathrm{c}}^{\ast } ratio is influenced by the initial water content of MS and the cementitious binder content but is independent of the number of FT cycles.

Based on an analysis of secondary consolidation tests for 22 clay types, Mesri and Godlewski [39] concluded that, for a given soil, C_a/C_{\mathrm{c}}^{\ast } ratios remain constant, typically ranging from 0.025 to 0.10. In this experiment, the C_a/C_{\mathrm{c}}^{\ast } ratios for the samples in groups A and B are below this typical range. The C_a/C_{\mathrm{c}}^{\ast } ratio for the samples in group C is significantly higher than those of the other two groups due to the relatively high C_a values. These findings indicate that the C_a/C_{\mathrm{c}}^{\ast } ratios for solidified MS are comparatively low and fall outside the range suggested by Mesri and Godlewski [39]. In studies on other cement-stabilized soils, similar findings have also been reported [15,40].

3.3 Compression process of solidified muds

Suneel et al. [41] observed that the maximum C_a of marine clay occurred at a stress level higher than {\sigma }_{\mathrm{y}}^{\prime }. Similar observations have been reported in studies on natural sedimentary soils [42,43], reconstituted clays [11,44], hard clay shale [45], and solidified soils [46]. The underlying mechanism for this behavior was also discussed. {\sigma }_{\mathrm{y}}^{\prime } represents the stress point at which significant plastic deformation begins during compression [45]. When the applied stress is below {\sigma }_{\mathrm{y}}^{\prime }, large pores collapse and free water is expelled, while the soil structure remains intact. Once the stress exceeds {\sigma }_{\mathrm{y}}^{\prime }, structural degradation initiates. In Fig. 12, the positions of {\sigma }_{\mathrm{y}}^{\prime } are marked with red circles for clarity. With increasing stress, the soil structure progressively weakens, and the C_a reaches its peak when the structure is nearly destroyed [43]. Subsequently, the soil transitions into a new stable state, during which C_a decreases and gradually stabilizes [44].

In this study, the stress corresponding to the maximum C_a value on the C_a–p curve (denoted as {\sigma }_{\mathrm{m}}^{\prime }) is significantly larger than {\sigma }_{\mathrm{y}}^{\prime } (Fig. 12), which is consistent with the findings of the aforementioned studies. Wang et al. [46] pointed out that the cementation between soil particles contributes to the increase in the C_a of solidified soils when the applied stress exceeds {\sigma }_{\mathrm{y}}^{\prime }. Therefore, three stages in the compression process of the solidified MS can be identified: the initial compaction stage, the structure breakdown stage and the final compaction stage, as illustrated in Figs. 17 and 18.

Stage I (OA). The solidified MS undergoes initial compression when the applied vertical effective stress is below {\sigma }_{\mathrm{y}}^{\prime }. The volume of soil aggregates decreases, and the water content of the MS reduces. Besides, particle rearrangement results in a more compact soil structure. This stage is characterized by decreased porosity and a gradual increase in the C_a value.

Stage II (AB). The structure breakdown stage begins when the applied stress exceeds {\sigma }_{\mathrm{y}}^{\prime }. During this stage, cracks start to develop, and the cementitious structures within the solidified MS gradually break down, leading to a marked increase in both the deformation and deformation rate of the solidified MS.

Stage III (BC). When the stress exceeds {\sigma }_{\mathrm{m}}^{\prime }, the damaged soil undergoes the final compaction stage. Deformation becomes less sensitive to further increases in stress. The C_a value stabilizes, indicating the completion of the compaction process. This suggests that the soil has reached a fully compacted state, with minimal structural changes as stress continues to increase.

The identification of compression process stages in samples from groups A, B, and C shows that, as the stress increases from 12.5 to 1600 kPa, the samples in group A undergo all three stages. In comparison, the samples in groups B and C only progress through the first two stages, indicating that a stress level of at least 1600 kPa is required to fully destroy the soil structure. This explains why the variations of C_A and C_{\mathrm{c}}^{\ast } with {\sigma }_{\mathrm{v}}^{\prime } in group A differ from those in groups B and C. Additionally, with an increasing number of FT cycles, the {\sigma }_{\mathrm{y}}^{\prime } of the samples decreases, indicating that structural degradation initiates under lower stress levels, thereby accelerating the transition into the second stage.

Another noteworthy observation is that, although the total strain variations of the samples in group C under eight stress levels are smaller than those in group B, the average C_a value is higher, as shown in Figs. 13(b) and 13(c). To explain this, the ratio of secondary consolidation deformation to primary consolidation deformation under single-stage loading, ε_s/ε_p, is calculated and compared among groups. Since there is no clear boundary between primary and secondary consolidation in stage I, and the samples from groups B and C have not yet entered stage III, the ε_s/ε_p ratios of samples subjected to 1, 5, and 10 FT cycles in stage II are compared, as shown in Fig. 19.

In group C, the average ε_s/ε_p ratios for the samples subjected to 1, 5, and 10 FT cycles are 30.2%, 29.3%, and 20.3%, respectively. In comparison, the corresponding values for group B are 18.4%, 16.8%, and 15.9%, which are all lower than those in group C. This indicates that samples in group B exhibit significant primary consolidation deformation under the applied stress. In contrast, the samples in group C, with lower water content (125% in group B and 77% in group C) and a more compact structure with higher cementation, show limited primary consolidation deformation. As the loading duration increases, the cemented structure in group C deteriorates, leading to increased secondary consolidation deformation and a higher C_a value. This also explains the relatively high C_a/C_{\mathrm{c}}^{\ast } ratio for the samples in group C (Fig. 16). It is also observed that the ε_s/ε_p ratios of the samples in group A are lower than those in groups B and C, indicating that during stage II, the samples in group A are predominantly governed by primary consolidation.

Furthermore, the ε_s/ε_p ratio decreases with an increasing number of FT cycles for all three groups. This indicates that primary consolidation deformation is enhanced more by FT cycles than secondary consolidation deformation, highlighting the increased significance of instantaneous structural changes.

4 Conclusions

To provide new insights into the long-term deformation behavior of solidified MS and its changes under FT cycles, a series of long-term oedometer tests were conducted on solidified MS samples subjected to varying numbers of FT cycles. The main conclusions are as follows.

1) FT cycles significantly impact the strain of solidified MS samples. Compared to samples without FT cycles, the total strain of samples subjected to 10 FT cycles in groups A, B, and C increases by 1.12, 1.43, and 2.20 times, respectively. Besides, increasing the cementitious binder content and reducing the initial water content can enhance the resistance of solidified MS to compressive deformation.

2) The {\sigma }_{\mathrm{y}}^{\prime } value exhibits an exponential decrease as the number of FT cycles increases, with a pronounced reduction observed during the initial 5 cycles. Compared to samples without FT cycles, the rate of secondary consolidation for samples subjected to 10 FT cycles increases by at least 1.83 times. An increase in FT cycles results in the degradation of the soil microstructure, thereby diminishing the resistance of solidified MS to long-term consolidation deformation.

3) Three distinct stages in the compression process of solidified MS are identified: the initial compaction stage, the structure breakdown stage and the final compaction stage. As the number of FT cycles increases, the stress for solidified MS to transition into the structure breakdown stage decreases.

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