3.1 Effective friction coefficient
In the ring shear test, the normal stress exhibits continuous fluctuations, and systematic errors are difficult to directly avoid. In the subsequent data analysis, the effective friction coefficient \(\mu =\tau /P\) (where \(\tau\) and \(P\) are the shear stress and normal stress, respectively) of the granular system was used to describe the shear characteristics of the granular material. Figure 1 shows the variation curve of the effective friction coefficient of quartz sand over shear time with different saturation levels and particle sizes. The moving average method was employed for data filtering to achieve a smooth curve of effective friction coefficient versus shear time (indicated by a thick solid line).
As depicted in Fig. 1(a), the saturation level notably influences the effective friction coefficient curve of coarse quartz sand (1mm). At a saturation level of 40%, the peak friction coefficient, approximately 0.77, and the residual friction coefficient are markedly greater than those of quartz sand at other saturation levels. In contrast, for medium quartz sand (0.5mm), the impact of saturation on its effective friction coefficient curve is relatively minor, with differences only in the first half of the shearing process. In the latter half of the shearing process, the effective friction coefficient curves of quartz sand at different saturation levels tend to converge, as shown in Fig. 1(b). For medium sand, the peak friction coefficient is highest in a dry state (i.e., at 0% saturation), approximately 0.67. Compared to coarse and medium sand, the effective friction coefficient curves of fine sand at different saturation levels almost coincide, with only slight differences in the peak friction coefficient section, as shown in Fig. 1(c). The effective friction coefficient curve of fine sand demonstrates a notable smoothness with minimal observable fluctuations. A detailed discussion on the fluctuations in the friction coefficient is reserved for Section 3.2.
Figure 2 shows the relationship between the peak friction coefficient, residual friction coefficient, and saturation for quartz sand of different particle sizes. As illustrated in Fig. 2, for coarse quartz sand (1mm), the peak and residual friction coefficients demonstrate a trend of initially increasing and subsequently decreasing with the escalation of saturation levels. The inflection point occurs at a saturation level of 40%, where both the peak (approximately 0.77) and residual (approximately 0.67) friction coefficients reach their maximum values. Notably, the peak friction coefficient of coarse sand in a fully saturated state is inferior to that in a dry state, while the residual friction coefficients exhibit marginal variation. Regarding medium quartz sand (0.5mm), the variation in both peak and residual friction coefficients predominantly follows a unidirectional decrement with the escalation in saturation levels. In its desiccated state, the peak friction coefficient is quantified at approximately 0.67, and the residual coefficient at about 0.63, both reaching their zenith. The trajectory of the peak friction coefficient's reduction is notably steeper, signifying a heightened susceptibility to alterations in saturation, in contrast to the residual friction coefficient. In contrast to its coarser counterparts, fine sand (0.25mm) demonstrates a markedly attenuated responsiveness to saturation fluctuations. This is characterized by the sustained stability of both its peak and residual friction coefficients, which remain relatively unaltered across a spectrum of increasing saturation levels.
From the analysis presented, it becomes evident that the impact of saturation on the peak and residual friction coefficients of quartz sand exhibits a pronounced correlation with granulometry. This interrelation is intricately linked to the occurrence states of interstitial liquids among the particles. Subsequent discussions will be dedicated to an in-depth examination of the potential physical mechanisms involved.
Granular materials, contingent upon their liquid content (degree of saturation), are conventionally categorized into five discrete states: dry state, pendular state, funicular state, capillary state, and slurry state [39, 40], each delineated in Fig. 3. Quartz sand in a dry state is commonly regarded as a granular material lacking significant cohesive forces. During shear processes in dry conditions, the primary contributors to shear strength are the friction and interlocking forces between particles [41]. Microscopically, the influence of liquid in wet granular systems is twofold: firstly, the lubrication effect of the liquid diminishes friction between particles [26, 27]; and secondly, the capillary action of the liquid generates partial cohesive forces [22–24]. In the pendular and funicular states, liquid bridges at the contact points of quartz sand particles, formed due to liquid surface tension, generate capillary forces that substantially heighten the system's cohesiveness [39, 42, 43]. Here, capillary and surface tension forces take precedence, giving the wet granular agglomerates increased shear strength. In the capillary state, with the liquid filling the interstices and particle surfaces not fully wetted, the liquid assumes a continuous phase. Under these conditions, the liquid pressure in the particle voids falls below the gas pressure, leading to liquid surface concavity [44]. In this state, the absence of capillary forces within the wet granular system means that lubrication effects dominate, decreasing the agglomerates' shear strength. In the slurry state, where particles are entirely submerged in liquid and their external surfaces fully wetted, the concave capillary menisci become convex liquid surfaces, and the liquid pressure meets or surpasses the gas pressure. In this state, there is no cohesion between particles, and lubrication is the overriding factor [26]. Consequently, the presented outlined analysis may elucidate the underlying mechanism for the observed trend in coarse quartz sand, where its friction coefficient exhibits an initial increase followed by a decrease as saturation levels ascend.
For quartz sands with finer granulometry (medium and fine sands), their friction coefficient trends with respect to saturation deviate from the previously mentioned analysis. A plausible explanation is that, due to the finer particle size and smaller pore spaces, the dominant factors throughout the shearing process are the reduction in effective interparticle stress due to rising pore water pressure and the lubricating effect of the liquid. The capillary action is insufficient to significantly enhance the shear strength at any stage. It is imperative to acknowledge that the transition of wet particles from one state to another is contingent not solely on the liquid content but also on the intrinsic physical and geometric characteristics of the granular material. Hence, in future mechanical behavior investigations of wet granular materials, a differentiated quantitative description and analysis for various states are essential.
3.2 Particle system fluctuations
Figure 4–6 illustrates the variation of the standard deviation of the effective friction coefficient of quartz sand over time during shearing, considering different saturation levels and particle sizes. Herein, the standard deviation is methodically defined as the absolute value of the difference between each data point and the residual friction coefficient, evaluated once the effective friction coefficient reaches a stable state (after a shearing duration of 40 seconds). This metric serves to effectively and intuitively characterize the fluctuation dynamics within the particle system.
As delineated in Fig. 4, for coarse quartz sand at a saturation level of 40%, the system exhibits notably more pronounced fluctuations than at other saturation levels. This phenomenon is likely attributable to a complex dynamic equilibrium that manifests at this specific saturation level, resulting from the interplay between capillary effects and liquid lubrication. In this state of equilibrium, the partial presence of moisture among the particles engenders a nuanced interaction between capillary attraction and lubrication, leading to rapid alterations in interparticle contact points and frictional conditions [45], thereby inducing discontinuous and varied stress fluctuations. Concurrently, the heterogeneous distribution and movement of pore water during shearing may induce localized stress concentrations or relaxations, further intensifying the overall fluctuation in stress within the system.
In the case of medium and fine sands (referenced in Figs. 5 and 6), the observed system fluctuations are markedly lower compared to those in coarse sand, with a clear trend indicating that smaller particle sizes result in reduced system fluctuations. This phenomenon echoes the experimental findings reported by Wang and Huang [31, 32]. The more compact arrangement of finer particles diminishes their relative displacement during shearing. Concurrently, the diminished pore spaces between smaller particles restrict their reorganization, leading to a more uniform stress response. Furthermore, the higher particle count and increased contact points per unit volume in finer particle systems more effectively distribute and transmit stress, mitigating localized stress concentrations and fluctuations. Additionally, the reduced propensity for breakage in smaller particles lowers the stress variability caused by particle fragmentation. These factors collectively contribute to a trend where smaller particle sizes lead to lesser overall system fluctuations.
Moreover, in the context of finer quartz sands (referenced in Figs. 5 and 6), the fluctuations of the effective friction coefficient demonstrate a notable insensitivity to saturation changes. This observation aligns with the premise that finer particulate systems manifest markedly diminished fluctuations, attributable to their more compact particle arrangement and a lower propensity for fragmentation. Consequently, alterations in saturation levels fail to induce substantial variability in the fluctuations within fine particle systems. Additionally, the homogeneity of the pore structure and the uniformity of moisture distribution in finer sands minimally affect the dynamics of interparticle friction and stress dissemination.
3.3 Volumetric strain
Figure 7–9 illustrates the variation of the volumetric strain of quartz sand over time during shearing, considering different saturation levels and particle sizes. Volume strain quantitatively characterizes the changes in the overall volume of quartz sand samples subjected to shear, playing a critical role in elucidating the mechanical behaviors and deformation properties of granular materials. During the experiment, the base area of the sample remains constant, allowing for the calculation of volume strain by real-time monitoring of the sample's height.
Figure 7 delineates the changes in volume strain for coarse quartz sand (1mm) under varying degrees of saturation throughout the shearing process. Analysis of Fig. 7 reveals that the evolution of volume strain in quartz sand during shearing can be categorized into three distinct phases. During the initial stage of the experiment (Stage I), axial strains of samples across different saturation levels exhibit a minor increase, attributed to the rearrangement and compression of internal particles. This strain augmentation is more pronounced in wet particles compared to their dry counterparts, likely a consequence of the lubricative action of the liquid facilitating sample compaction. In the subsequent phase (Stage II), samples experience a marked expansion, with this volumetric expansion phenomenon being especially notable in dry samples. Throughout the first two stages of shearing, volumetric expansion is the dominant deformation mechanism in dry particle samples, whereas volumetric compression predominates in the deformation of wet particle samples.
During the third stage, discernible differences in volume strain become apparent between dry and wet particle configurations. Dry particles display continuous densification phenomena under elevated shear strains. This behavior aligns with observations made by Coop et al. [46], who ascribed such volumetric deformation characteristics to particle fragmentation within the shear zones. The topic of particle fragmentation will be elaborated upon in Section 3.4. Notably, the shear strain at the volumetric expansion's apex coincides with the peak in shear strength (as illustrated in Fig. 1). An escalation in shear strain results in the compaction of the specimen, reflected by a progressive increase in volume strain. In contrast, the volume strain of wet particles in this stage tends towards stabilization, indicating a distinct response to shearing compared to their dry counterparts.
Figure 8 depicts the changes in volume strain for medium sand (0.5mm) with different saturation levels during the shearing process. Similar to the coarse sand mentioned earlier, the volume strain changes in medium sand during shearing can also be broadly categorized into three stages. In the first and second stages, the volume strain changes in medium sand follow a pattern similar to that of coarse sand, undergoing a process of initial shear contraction followed by shear dilation. It is noteworthy that for wet particles (medium sand), the shear dilation phenomenon in the second stage is quite subdued. Particularly for samples at 20% and 40% saturation, the second stage exhibits continued shear contraction, albeit at a rate significantly lower than that of the first stage.
In the shearing process of medium sand, the volume strain changes observed in the third stage exhibit notable differences compared to those in coarse sand. For medium sand, the samples in a dry state do not display the sustained shear contraction characteristic of coarse sand in the third phase; instead, they approach a stable volume strain value. This preliminary observation suggests that dry medium sand does not experience continuous fragmentation during the shearing process. Furthermore, samples with varying degrees of saturation also gradually reach a stable volume after different extents of compression. It is posited that the volume compression observed in wet particles is not attributable to particle fragmentation but rather to the reduction in inter-particle friction facilitated by the presence of liquid, which promotes easier relative sliding and rearrangement of particles during shear [25, 27].
Figure 9 illustrates the volume strain changes of fine sand (0.25mm) with different saturation levels during the shearing process. The volume strain changes in fine sand during shearing are broadly similar to those observed in medium sand. A noteworthy difference is that, in the third stage, samples of wet particles with various saturation levels exhibit a continuous state of volume compression. This may indicate that particle rearrangement continues to occur throughout this shearing process.
3.4 Particle breakage
The process of particle breakage reflects the deformation and failure of granular materials under the action of force. By studying the behavior of particle crushing, a deeper understanding of the mechanical properties of granular materials, such as compressive strength, elastic modulus, and plastic deformation, can be gained. This provides important references for the engineering applications of granular materials. In this study, after each test, the post-test samples were carefully extracted from the ring shear box, and then the particle size distribution (PSD) of the particles was analyzed through manual wet sieving.
Figure 10 displays the mass percentages of particle size compositions for each sample set following the ring shear tests. As illustrated in Fig. 10(a), a pronounced phenomenon of particle fragmentation is observed in 1mm coarse sand during shearing, with about 50%-80% of particles remaining intact. The fragmentation is most significant in samples of dry particles, decreasing progressively with increasing saturation levels. The extent of fragmentation in 0.5mm medium sand and 0.25mm fine sand is considerably lower than that observed in coarse sand, as shown in Fig. 10(b) and (c). In the case of medium and fine sands, more than 90% of the particles are unfragmented. Under identical conditions, the smaller the particles, the more resistant they are to fragmentation. Additionally, the influence of saturation level variations on the fragmentation of finer particles is significantly reduced.
Figure 11 presents the PSD curves and the absolute particle breakage rates for each sample set after the ring shear tests, to provide readers with a clearer understanding of particle fragmentation within the samples. Here, to accurately capture the fragmentation information of particles within different samples, we introduce a new metric, the "absolute breakage rate \({w}_{a}\)", defined as follows:
$${w}_{a}=\frac{{m}_{t}-{m}_{r}}{{m}_{t}}\times 100\%$$
where \({w}_{a}\) is the absolute breakage rate of particles in a specific particle size range; \({m}_{t}\) is the mass percentage of initial particles in the particle size range before particle breakage; \({m}_{r}\) is the mass percentage of residual particles in the particle size range after particle breakage.
As depicted in Fig. 11(a), the PSD curves progressively ascend as saturation increases from 0–100%, signifying the ongoing creation of finer particles in 1mm coarse sand throughout the shearing process. In contrast, for both medium and fine sands (illustrated in Fig. 11(b) and (c)), their PSD curves exhibit a modest upward shift from the baseline gradation, with the PSD curves for different saturation levels nearly converging. Figure 11(d) distinctively elucidates the influence of saturation levels on the absolute crushing rates across quartz sands of varying granularities. For the coarse sand designated as PS1, there exists a pronounced negative correlation between saturation levels and absolute crushing rates, suggesting that the lubricative effect of the interstitial liquid mitigates the potential for particle fragmentation. Conversely, for medium (PS0.5) and fine sands (PS0.25), the effect of saturation levels on fragmentation is markedly reduced. This reduced susceptibility to fragmentation in finer particles, therefore, results in a minimal impact of saturation levels on their absolute crushing rates, underscoring the intrinsic resilience of finer particles to crushing, thereby diminishing the relative influence of saturation.