Rheology of Paste in Mine Backfilling: Mechanisms, Models, and Key Influencing Factors

1 Introduction

The continuous exploitation of mineral resources has imposed increasingly stringent requirements on underground stope management, tailings disposal, and environmental risk control [1,2,3]. Against this background, cemented paste backfill (CPB) has become an important technical approach for achieving safe and sustainable mining in mines, owing to its comprehensive advantages in tailings reutilization, underground stability control, and environmental risk reduction [4,5,6,7,8]. The engineering performance of paste backfill systems largely depends on the flow and deformation behavior of paste slurry during its preparation, transportation, and placement processes [4,6]. Consequently, paste rheology has emerged as one of the key scientific and engineering issues constraining the practical application and optimization of paste backfill technology [9,10].

Although paste backfill technology has been widely applied in engineering practice, a unified understanding of the physical nature of the rheological behavior of high-concentration paste is still lacking [6,11,12]. Existing studies generally indicate that paste is a structure-sensitive particulate–fluid composite system, whose flow behavior exhibits pronounced nonlinearity, time dependence, and path dependence [11,12,13,14]. However, rheological parameters obtained under different experimental conditions, testing methods, and material systems often show substantial discrepancies [15,16,17], which limits the comparability of experimental results and the general applicability of engineering models [12,16]. Such inconsistencies, to some extent, reflect the insufficient understanding of microstructural evolution processes and spatial interaction effects within paste systems in existing theoretical frameworks [11,18].

From a modeling perspective, although empirical and semi-empirical rheological models are widely used in engineering calculations due to their practical value [6,19], most of these models are based on local constitutive assumptions and therefore struggle to describe the spatially heterogeneous flow behaviors commonly observed in paste systems [20,21,22]. In recent years, nonlocal rheology, structural parameter evolution models, and multiscale modeling approaches have been proposed in an attempt to overcome the limitations of conventional models [23,24,25]. Nevertheless, these models still face challenges in terms of physical interpretability, parameter identification, and general applicability across different paste systems [26], and a unified and experimentally verifiable theoretical framework has yet to be established. This indicates that research on paste rheology is currently at a critical stage of transition from empirical descriptions toward physically constrained modeling.

Over the past two decades, research on paste rheology has shown a clear temporal evolution in the English-language literature, as reflected in the publication trend summarized in Fig. 1. Early studies were relatively sparse, whereas publication activity has increased markedly since 2017, indicating growing academic and engineering interest in paste-based backfilling systems. Recent work has shifted from single-factor rheological characterization toward multi-factor coupling, time-dependent structural evolution, sustainable binders and additives, and data-assisted optimization. This transition motivates the integrated, mechanism-oriented perspective adopted in this review, as discussed below.

Figure 1: Annual Publication Trend of Studies on Paste backfilling Rheology (2005–2025).

Against this background, recent advances in machine-learning approaches incorporating rheological physical constraints have emerged as a promising direction for addressing the complex behavior of paste in CPB systems [27,28,29]. These methods offer the potential to bridge empirical parameter prediction and mechanistic understanding, providing a more integrated framework for modeling paste rheology [30,31,32,33]. However, existing studies remain largely exploratory, and critical challenges persist regarding applicability, reliability, and integration with conventional rheological theories [34,35,36,37]. Unlike previous reviews that primarily emphasize empirical constitutive descriptions or isolated influencing factors, this review provides a critical synthesis of experimental observations, theoretical models, and emerging data-driven approaches from a structure-controlled perspective [38,39,40,41]. Particular attention is given to the roles of nonlocal effects and scale dependence in governing yield behavior, nonlinear flow response, and model applicability. Recent studies further indicate that integrating directly measurable operational variables and adopting robust learning and optimization strategies can enhance prediction stability and transferability under variable conditions [42,43,44,45]. To clarify the scope and logical structure of this review, a conceptual framework summarizing the rheology of paste in mine backfilling systems is presented in Fig. 2.

Figure 2: Conceptual framework summarizing the rheology of paste in mine backfilling.

2 Paste Rheological Properties

Paste is a high-concentration particulate-fluid composite, where macroscopic flow behavior is predominantly determined by the interactions between solid particles and the internal structural organization. Ideal paste backfill materials should contain at least 15% of particles smaller than 20 μm, along with sufficient water content [46,47]. Existing studies suggest that a saturation degree between 101.5% and 105.3% and a bleed water rate ranging from 1.5% to 5% can serve as additional performance indicators for paste materials [48]. Owing to the high solid volume fraction, such systems typically exhibit mechanical responses intermediate between those of solids and fluids, and are distinctly different from dilute suspensions or conventional non-Newtonian fluids. Under applied shear, paste systems may exhibit characteristic rheological features such as yield behavior, nonlinear flow response, and time-dependent effects. These macroscopic manifestations reflect the dynamic adjustment of internal particulate structures in response to changes in loading conditions, and represent common rheological features of dense particulate systems. Fig. 3 schematically summarizes typical experimental frameworks reported in the literature for rheological characterization of CPB, including the rheological testing apparatus, the standardized testing procedure, and representative shear stress–shear rate responses of paste slurries.

Figure 3: Schematic representation of the rheological testing framework for CPB and typical rheological curves of slurry under different admixture addition conditions: (a) Shear rate ascent stage; (b) Shear rate descent stage (adapted from Ref. [2]).

2.1 Yield Behavior and Structure-Controlled Solid–Liquid Transition

Yield behavior describes the mechanical response whereby a paste system exhibits solid-like characteristics when the applied shear stress remains below a critical value, undergoing only limited elastic or viscoelastic deformation. Once the applied stress exceeds this critical threshold, the internal load-bearing structure becomes unstable and collapses, leading to the onset of macroscopic flow [49]. This critical stress is commonly referred to as the yield stress, which distinguishes the solid-like and fluid-like states of paste systems [50]. As the applied shear stress approaches the yield stress, a pronounced change in shear rate is commonly observed, with the solid–fluid transition occurring at a finite shear rate, as schematically illustrated in Fig. 4 (adapted from Ref. [12]) based on representative observations reported in the literature. It should be noted that the sharpness of the transition and the associated shear rate at yielding may vary across studies, reflecting differences in particle size distribution, solid fraction, and testing geometry.

Figure 4: Representative solid–liquid transition behavior of paste systems reported in the literature, illustrating the yield process and structure-controlled transition under different solid volume fractions (adapted from Ref. [12]). (a) Shear stress–shear rate curves; (b) Apparent viscosity–shear stress curves.

From a physical perspective, the yield behavior of paste is not governed by the viscosity of the continuous phase but is primarily controlled by the particulate load-bearing structure formed under high solid volume fraction conditions. As the solid concentration increases, the average interparticle spacing decreases markedly, weakening hydrodynamic lubrication effects and promoting direct particle contacts and frictional interactions. These contacts collectively form a system-spanning mechanical network that enables the paste to sustain external loads in the absence of macroscopic flow [51].

The transition from a solid-like to a fluid-like state does not occur uniformly throughout the paste system but proceeds through progressive structural failure. With increasing applied shear stress, localized rearrangements and instabilities first develop in mechanically weaker regions, giving rise to shear localization. As the stress continues to increase, structural breakdown propagates through the load-bearing network, ultimately resulting in global yielding and sustained flow. This structure-controlled solid–liquid transition explains the spatial heterogeneity and abrupt nature commonly observed during yielding in paste systems. In CPB systems, this structure-controlled yielding is further coupled with cement hydration processes, which progressively modify interparticle bonding and network rigidity over time. This chemo-physical coupling distinguishes CPB from inert suspensions and leads to time-dependent evolution of yield behavior. The structure-controlled yielding of CPB is closely associated with the progressive evolution of particle networks, as schematically illustrated in Fig. 5 (adapted from Ref. [52]).

Figure 5: Schematic illustration of the structural evolution of fresh CPB, adapted from Refs. [53,54]. (A) Representative dispersed state of tailings and OPC particles after preshearing. (B) Stage I: flocculation of fine particles into larger agglomerates, accompanied by the initial formation of C–S–H bridges. (C) Stage II: progressive development of rigid interparticle links, leading to an increased number of large agglomerates and a transition from soft colloidal interactions to more rigid contacts. (D) Stage III: continued growth in the size and number of C–S–H bridges, resulting in an increase in system volume, while the overall packing density remains relatively stable due to the combined loosening and wedging effects [52].

Yield stress is not an intrinsic material constant but reflects the instantaneous structural state of the paste. Even for systems with identical compositions, measured yield stress can vary substantially with resting time, preshear history, and loading protocol, highlighting the sensitivity of yield behavior to structural evolution. Across the reviewed studies, reported yield stress values for CPB slurries span several orders of magnitude, primarily due to variations in solid concentration, particle gradation, cement content, curing time, and testing methodology. Under standard rheometer measurements, yield stress values are most commonly reported in the range of 10–100 Pa, whereas substantially higher values, reaching the order of 100–1000 Pa or above, have been observed under specialized conditions such as very high solid contents or fiber-reinforced CPB systems [55,56,57].

2.2 Shear-Rate-Dependent Nonlinear Rheological Response

Once the applied shear stress exceeds the yield threshold, paste slurry enters a flowing regime in which the apparent viscosity becomes strongly dependent on shear rate, exhibiting pronounced nonlinear rheological behavior. Within most engineering-relevant shear-rate ranges, paste systems predominantly exhibit shear-thinning behavior, characterized by a continuous decrease in apparent viscosity with increasing shear rate [12]. Accordingly, shear-thinning should be regarded as the dominant rheological response of CPB slurries under typical operational conditions, whereas shear-thickening represents a regime-specific behavior that emerges only under extreme combinations of solid fraction, particle contact state, and shear-rate level.

This behavior can be rationalized from the perspective of shear-induced structural evolution. At low to moderate shear rates, the load-bearing structures formed by particle contacts and flocculated aggregates are progressively disrupted by shear, leading to a continuous reduction in the number of structural units capable of transmitting stress and, consequently, a decrease in macroscopic flow resistance. In this regime, shear primarily weakens the internal structure, and structural breakdown dominates the rheological response. In contrast, for pastes with extremely high solid volume fractions or pronounced friction-dominated contact interactions, a transition to shear-thickening behavior has been reported at sufficiently high shear rates [58,59,60,61]. Under such conditions, the frequency of instantaneous direct particle contacts increases significantly, accompanied by enhanced frictional dissipation and collisional interactions, resulting in an increase in flow resistance. These observations indicate that the dominant mechanisms governing paste rheology can shift across different shear-rate regimes and material conditions [51].

The coexistence of shear thinning and shear thickening within the same paste system across different shear-rate regimes reflects the competition between structural breakdown mechanisms and particle contact–dominated interactions. This competition gives rise to pronounced nonlinearity and strong system dependence in the rheological response of CPB slurry, making it challenging to describe the flow behavior using a single dominant mechanism or a unified constitutive relation.

2.3 Thixotropic Behavior and Time-Dependent Structural Evolution

Thixotropy refers to the time-dependent and reversible evolution of rheological properties under shear, arising from the breakdown and rebuilding of the internal particle network. In CPB systems, thixotropic behavior is particularly pronounced due to the combined effects of particulate structuring and time-dependent cement hydration.

A key characteristic of thixotropic paste systems is the strong asymmetry between rapid shear-induced structural breakdown and much slower structural rebuilding during rest. Under applied shear, load-bearing particle networks are quickly disrupted, leading to a reduction in apparent viscosity and yield stress. Upon cessation of shear, the internal structure progressively rebuilds, resulting in a gradual recovery of rheological strength. At short time scales (minutes to hours), thixotropic evolution is primarily governed by physical restructuring of the particle network, including flocculation and contact reformation. At longer time scales (hours to days), cement hydration and setting progressively introduce irreversible chemical bonding, which further increases yield stress and viscosity and may eventually suppress reversibility. This coexistence of reversible physical restructuring and irreversible chemical evolution distinguishes CPB from inert suspensions [62], and is schematically illustrated in Fig. 6 (adapted from Ref. [63]).

Figure 6: Representative comparison of yield stress and viscosity obtained using constant shear rate (CSR) and flow curve (FC) methods in CPB systems, illustrating the dependence of measured rheological parameters on shear protocol and structural state (adapted from Ref. [63]). (a) Yield stress; (b) Apparent viscosity.

From an engineering perspective, thixotropic structural rebuilding during rest periods can lead to a substantial increase in restart pressure and flow resistance, posing significant challenges for intermittent operation, pipeline restart, and blockage prevention in paste backfill transport systems. This pronounced time dependence underscores the limitations of purely time-independent rheological models and motivates the adoption of structural-parameter-based constitutive frameworks capable of capturing thixotropic evolution and shear-history effects in paste systems.

2.4 Shear History Effects and Differences between Static and Dynamic Yield

The rheological behavior of paste systems is strongly dependent on shear history due to their thixotropic and time-dependent nature. Different shear protocols and resting conditions can therefore lead to substantially different apparent yield stresses, even for identical material compositions [64,65,66].

Static yield stress is commonly defined as the stress required to initiate flow from a fully rested and structurally rebuilt state, whereas dynamic yield stress corresponds to the stress required to sustain flow after prior shearing has partially disrupted the internal structure. The difference between static and dynamic yield stress reflects distinct structural states induced by different shear histories rather than measurement artifacts [67,68]. Experimental studies consistently report higher static yield stresses than dynamic values, particularly after extended resting periods, owing to progressive structural rebuilding during rest [69,70].

From an engineering perspective, static yield stress is most relevant for pipeline restart, intermittent operation, and blockage risk assessment, while dynamic yield stress is more appropriate for steady-state flow and pressure-drop calculations [71]. This strong dependence on shear history highlights the limitations of time-independent rheological models and motivates the incorporation of structural evolution into constitutive descriptions of paste backfill flow [72,73].

3 Rheological Models for Paste

The rheological behavior of paste slurry is typically non-Newtonian, influenced by factors such as solid particle concentration, binder type, and chemical additives. Commonly used models, such as the Bingham plastic and Herschel-Bulkley models, are effective in describing the flow characteristics of paste under various conditions. Paste flow is governed by yield-stress behavior and, under specific regimes, shear-thickening behavior, where viscosity increases at high shear rates. These models offer practical insights into the paste’s flow behavior, which is crucial for applications like mine backfilling and pipeline transport [74,75].

3.1 Bingham Plastic Model

The Bingham plastic model is one of the most widely used rheological models for describing yield-stress fluids [76,77,78,79]. This model assumes that the material behaves as a rigid solid when the applied shear stress is lower than a critical yield stress, and begins to flow only after the shear stress exceeds this threshold. The mathematical expression of the Bingham model is given as: τ=τy+Kγ˙(1) where τ is the shear stress, τ y is the yield stress, K is the plastic viscosity, and γ ˙ is the shear rate. The Bingham model characterizes the flow behavior of paste by introducing a yield stress and is widely used to analyze and predict the flow of backfill slurry during pipeline transport.

3.2 Herschel-Bulkley Model

The Herschel–Bulkley model is another widely used rheological model for describing non-Newtonian fluids, particularly those exhibiting yield behavior combined with shear-thinning or shear-thickening characteristics over different shear-rate regimes. The model is expressed as: τ=τy+Kγ˙n(2) where τ is the shear stress, τ y is the yield stress, K is the consistency index, γ ˙ is the shear rate, and n is the flow behavior index. Compared with the Bingham model, the Herschel–Bulkley model provides greater flexibility in describing the flow behavior of CPB slurry across a wide range of shear rates, particularly in capturing shear-thinning or shear-thickening phenomena at high shear rates. Consequently, this model has been widely applied in the analysis and prediction of paste flow behavior, especially in studies concerning flow resistance and pumping performance.

Experimental studies indicate that paste slurry typically behaves as a yield-stress fluid, and its yield stress is closely related to solid volume fraction, particle morphology, and the presence of chemical additives. Rheological models not only facilitate the optimization of pumping efficiency during pipeline transport but also enable the prediction of slurry flow behavior under different operating conditions. However, because paste rheology is influenced by multiple factors—including solid concentration, binder type, additive usage, particle shape, and particle size distribution—selecting an appropriate rheological model and accurately determining its parameters remain critical for achieving stable and efficient paste backfilling operations.

3.3 Applicability and Limitations of Rheological Models

The applicability of rheological models for paste systems depends on flow conditions, shear history, material composition, and engineering objectives, common non-Newtonian fluid rheological models are presented in Table 1. Model parameters should not be interpreted as intrinsic material constants, but rather as effective descriptors reflecting the instantaneous structural state of the paste under specific testing and operating conditions. Similar conclusions have been drawn in recent slurry pipeline studies, where rheological parameters were shown to vary systematically with solid concentration, particle size distribution, and operating regime, directly affecting pressure loss and energy consumption during transport [80,81].

Conventional viscoplastic models, such as the Bingham and Herschel–Bulkley formulations, remain widely used due to their simplicity and computational convenience. The Bingham model is generally applicable to low shear-rate regimes near yielding, whereas the Herschel–Bulkley model provides greater flexibility in representing nonlinear shear-rate dependence over broader operating ranges [82,83]. These models have been successfully applied to pipeline transport analysis and pressure-drop estimation in dense slurry systems [84]. However, they are inherently local and time-independent, limiting their ability to capture structural evolution, shear-history effects, and transient phenomena such as flow stoppage and restart.

Under flow regimes dominated by time-dependent structural evolution and pronounced thixotropy, structural rheological models incorporating a time-dependent structural parameter (λ) provide a more appropriate framework for describing the progressive build-up and breakdown of internal load-bearing particle networks. Such models have been widely used to interpret stress decay, hysteresis, and flow onset behavior in cementitious and granular suspensions [85,86]. Nevertheless, their application at the pipeline scale remains limited by parameter identifiability and experimental validation, and they should therefore be regarded as complementary rather than universal alternatives to empirical viscoplastic models.

4 Factors Influencing the Rheological Properties of Paste

4.1 Effect of Particle Gradation on the Rheological Properties of Paste

Particle gradation plays a significant role in determining the rheological properties of paste, particularly in terms of yield stress and viscosity [57]. From a microstructural perspective, particle size distribution controls packing efficiency, interparticle contact density, and the balance between lubrication and frictional interactions. Finer particles, with higher specific surface area, tend to increase yield stress by strengthening particle networks. In contrast, coarser particles contribute less to yield stress but predominantly affect the flow resistance at higher shear rates. Accordingly, rheological behavior reflects the combined effects of particle size distribution and solid concentration rather than particle size alone [91].

Experimental studies show that, at comparable solid contents, particle gradation significantly affects both the magnitude and shear-rate dependence of rheological parameters. Incorporation of fine particles (typically <10 μm) has been reported to increase yield stress by approximately 30–40%, while larger particles (≈100 μm and above) primarily influence high-shear flow resistance. Well-graded systems generally exhibit more pronounced shear-thinning due to progressive structural breakdown under shear, whereas poorly graded systems tend to display higher low-shear resistance and weaker shear-thinning behavior [92,93].

From an engineering perspective, particle gradation serves as a practical control parameter for optimizing paste flowability in mine backfilling and pipeline transport. Increasing fines content can improve pumpability and reduce apparent yield stress within appropriate limits, while excessive fines may increase water demand and thixotropy. For cemented paste backfill systems, fines contents on the order of 15–30 wt.% below approximately 20 μm are commonly reported to provide a favorable balance between flowability and structural stability, indicating that optimal gradation design requires balancing improved flow behavior against structural buildup during rest.

4.2 Effect of Temperature on the Rheological Behavior of Paste

Temperature is an important external factor influencing the rheological behavior of cemented paste backfill, particularly yield stress and apparent viscosity. In general, increasing temperature leads to reductions in both yield stress and viscosity at early ages, primarily due to decreased pore fluid viscosity and enhanced particle mobility. Experimental studies have reported that a temperature increase of approximately 10°C can reduce yield stress by 15–20%, although the magnitude of this effect depends on paste composition, solid content, and curing conditions [91]. These observations indicate that temperature directly affects the ease of microstructural rearrangement within the paste [94,95].

From a rheological perspective, the temperature dependence of paste viscosity is often described by Arrhenius-type relationships, reflecting the role of temperature in lowering the energy barrier for structural disruption under shear. At elevated temperatures, particle networks are more readily broken down, resulting in lower apparent viscosity and more pronounced shear-thinning behavior. Conversely, at lower temperatures, reduced thermal motion and stronger interparticle interactions promote higher resistance to flow and may suppress shear-thinning tendencies. These trends highlight that temperature modifies rheological response by regulating the balance between structural stability and shear-induced breakdown [96].

From an engineering standpoint, the influence of temperature on paste rheology has direct implications for mine backfilling and pipeline transport operations. Moderate temperature increases can improve flowability and pumpability during mixing and transport, while prolonged exposure to elevated temperatures accelerates cement hydration and structural buildup, potentially increasing yield stress and thixotropy over time. Accordingly, temperature effects should be interpreted within a time-dependent framework, recognizing that short-term rheological benefits may diminish during extended transport or delayed placement. Effective temperature management therefore represents an important consideration for maintaining consistent paste performance under varying operational conditions [97].

4.3 Effect of Additives on the Rheological Behavior of Paste

Chemical additives and binder-related modifications constitute one of the most extensively studied approaches for controlling CPB rheology [98,99,100]. Chemical additives, including superplasticizers, dispersants, and mineral admixtures, play an important role in modifying the rheological behavior of paste systems by regulating interparticle interactions and flocculation state [93,101,102,103]. In general, the addition of suitable chemical admixtures reduces yield stress and apparent viscosity by weakening attractive forces between particles and improving particle dispersion. This effect is particularly pronounced in cemented paste backfill systems, where electrostatic repulsion and steric hindrance introduced by admixtures can significantly alter the load-bearing particle network and promote shear-induced structural breakdown.

Experimental studies consistently report that the effectiveness of additives is strongly dosage-dependent. Within appropriate dosage windows, yield stress reductions on the order of several tens of percent are commonly observed, accompanied by improved shear-thinning behavior and enhanced flowability [67]. However, increasing dosage beyond these optimal ranges often results in diminishing rheological benefits and may induce adverse effects such as segregation, bleeding, or excessive retardation of hydration [63]. These observations highlight that additive performance depends not only on chemical type but also on paste composition, solid concentration, and hydration state. The associated microstructural refinement, characterized by reduced pore connectivity and modified interparticle networks induced by chemical admixtures, is schematically illustrated in Fig. 7 (adapted from Ref. [101]).

Figure 7: Representative pore-structure refinement induced by superplasticizer addition in cemented paste backfill systems, illustrating changes in pore-size distribution. (a) Incremental pore-size distribution; (b) Cumulative pore-size distribution (adapted from Ref. [101]).

From an engineering perspective, chemical additives provide a practical means for fine-tuning paste rheology to meet specific operational requirements in mine backfilling and pipeline transport. Rather than relying on universal dosage values, the literature emphasizes the importance of dosage optimization tailored to material characteristics and transport conditions. Methodologically, this dosage-design problem can be formulated as a coupled multi-objective optimization task, where rheological controllability, process efficiency, and sustainability-related constraints are balanced simultaneously [104]. When applied within appropriate ranges, additives can effectively enhance pumpability and transport stability, whereas improper selection or overdosing may compromise paste uniformity and long-term performance.

5 Challenges and Emerging Directions in Paste Rheology

5.1 Challenges of Nonlocal Effects in Paste Rheology Behavior

A large body of experimental and numerical studies has demonstrated that paste materials often exhibit pronounced spatially heterogeneous flow behaviors under shear, including shear localization, plug flow, and the coexistence of flowing regions with quasi-static zones. Although these phenomena have been extensively observed, their underlying formation mechanisms and their influence on macroscopic rheological behavior remain poorly unified. Existing studies generally agree that such spatially heterogeneous flows cannot be adequately explained solely by local shear rate or stress conditions, but are closely related to the spatial distribution and evolution of the internal microstructure of the system [14]. Local structural rearrangements and changes in particle contact states may influence neighboring regions through stress transmission, thereby inducing strong spatial coupling in the flow behavior [21,105]. In this context, traditional rheological models based on purely local constitutive assumptions often fail to effectively capture these heterogeneous flow characteristics in highly concentrated paste systems [106]. In recent years, some studies have attempted to address this issue by introducing structural evolution variables or gradient correction terms, however, the physical interpretability and applicability range of these models still require further validation. Consequently, the development of a rheological theoretical framework capable of consistently describing both structural evolution and spatially heterogeneous flow remains one of the key challenges in this field.

5.2 Scale Effects and Experimental–Model Consistency

Previous studies have consistently shown that the rheological response of paste materials is highly sensitive to experimental scale, shear configuration, and loading history, which is widely recognized as a major factor limiting the general applicability of yield-stress-based rheological models [107,108,109,110]. Even for paste systems with identical material compositions, substantial variations in macroscopic parameters, such as yield stress and apparent viscosity, can emerge under different geometrical dimensions, shear modes, and boundary conditions [108,111]. Mechanistically, these discrepancies are generally attributed to the coupling between internal structural length scales and external flow or observation scales [112,113,114,115,116]. When the system size approaches or falls below the dominant structural length scale, local heterogeneities are amplified, and the macroscopic response may deviate markedly from classical continuum assumptions; by contrast, at larger scales, local structural effects are partially averaged out, resulting in apparently more homogeneous flow behavior [117,118,119,120]. Therefore, explicitly incorporating the interactions among structural length scales, temporal scales, and experimental observation scales is a central scientific challenge for achieving cross-condition consistency and improving predictive capability [121,122,123,124,125]. Recent advances in multiscale constitutive modeling and predictive rheological frameworks further support this direction [126,127,128,129,130].

5.3 From Empirical Descriptions to a Unified Physical Framework

Overall, research on the rheology of highly concentrated pastes is gradually shifting from predominantly empirical, curve-fitting-based descriptive models toward unified theoretical frameworks constrained by physical mechanisms [131,132,133,134]. Existing studies indicate that this transition does not rely on continuously increasing model complexity, but rather requires the rational incorporation of the intrinsic relationships among key physical factors such as microstructural evolution and scale effects during model development. The literature suggests that merely introducing more complex constitutive formulations often fails to fundamentally enhance model applicability across different material systems and flow conditions [135]. A complementary strategy is to use dual-perspective influence screening to detect key interaction pathways among variables prior to model fitting, which helps reduce redundant complexity while retaining dominant system-level effects [136]. In contrast, describing the formation, breakdown, and reorganization of dominant internal structures using a limited number of state variables with clear physical meaning is considered a more promising pathway toward achieving both model unification and experimental verifiability. Consequently, future developments in paste rheology should focus on establishing a reasonable balance between experimental observability and model simplicity, and on this basis, constructing physically consistent frameworks capable of capturing flow behavior across multiple scales. This research direction is widely recognized as a critical foundation for advancing paste rheology from empirical analysis toward quantitative prediction [137,138,139,140,141].

5.4 Applications of Artificial Intelligence in Paste Rheology

In recent years, data-driven methodologies have been increasingly introduced into the rheological study of complex fluids and dense particulate systems as a complement to traditional physics-based modeling approaches [142,143,144]. Machine learning techniques are particularly effective in handling high-dimensional input spaces and strongly nonlinear relationships, enabling the establishment of empirical mappings between material composition, microstructural characteristics, and macroscopic rheological responses. In paste rheology, supervised learning models have been widely applied to correlate mixture proportions and experimental conditions with key rheological parameters such as yield stress and apparent viscosity, thereby reducing experimental workload and improving parameter-screening efficiency [145]. In addition, data-driven frameworks have been used to jointly analyze experimental data and numerical simulation results, allowing multivariate sensitivity assessment and identification of dominant factors governing flow behavior [146,147].

To enhance physical consistency and practical relevance, recent studies have increasingly integrated machine learning with rheological principles by embedding physical constraints or structural descriptors into learning frameworks. Such physics-constrained approaches, including physics-informed neural networks (PINNs), aim to preserve mechanically plausible trends while improving predictive robustness, and are particularly attractive for multiscale rheological problems that are difficult to capture using conventional constitutive models alone [148,149]. In applications relevant to paste and CPB systems, these frameworks typically rely on multi-source data integration, combining laboratory rheometry, field-scale transport records, and routine operational variables such as solid concentration, temperature, resting time, and shear history, thereby improving reproducibility and transferability across material systems and operating conditions [150,151]. Physical bounds and rheological consistency constraints are introduced to control extrapolation behavior and suppress nonphysical predictions beyond the training domain [152,153].

Recent developments further emphasize interpretable feature construction, structured learning strategies, and optimization-based calibration to enhance model stability and identifiability under industrial data conditions [154,155]. From an engineering perspective, uncertainty quantification and reliability-oriented validation have become essential components for deploying data-driven rheological models in mine backfilling operations. Model outputs are increasingly linked to decision-oriented tasks, including mix-design screening, pumpability-window identification, pressure-loss risk monitoring, and restart-risk assessment following flow interruption, forming an integrated “input–learning–validation–decision” workflow [156,157]. Representative data-driven and physics-informed modeling frameworks reported in the literature, including sequence-based learning models and physics-informed neural networks, illustrate transferable strategies for linking complex rheological responses with underlying physical constraints [158].

Fig. 8 summarizes commonly reported elements in the literature, including multi-source inputs, physics-constrained learning, unified validation, and engineering mapping, and organizes them into a conceptual framework relevant to paste rheology. Despite their demonstrated potential, existing studies also highlight limitations of artificial intelligence approaches, particularly with respect to interpretability, extrapolation capability, and dependence on data quality. Addressing these challenges will require further development of hybrid modeling strategies that more tightly integrate data-driven techniques with fundamental rheological principles, thereby improving both predictive reliability and mechanistic understanding in practical applications [159,160].

Figure 8: Representative data-driven and physics-informed modeling frameworks reported in the literature for complex geophysical and rheological systems (adapted from Ref. [157]). (a) A bidirectional long short-term memory (BiLSTM)–based model for debris-flow rheology prediction, illustrating sequence-based learning of shear-rate–shear-stress relationships. (b) A physics-informed neural network (PINN) framework for rock-strength prediction, in which data-driven learning is coupled with mechanics-based constraints to ensure physically consistent predictions.

6 Conclusions and Future Perspectives

Paste rheology in mine backfilling systems is governed by the coupled effects of particulate structure, time-dependent structural evolution, spatial heterogeneity, and scale dependence. From a structure-controlled perspective that accounts for nonlocal effects and observation scale, this review synthesizes experimental evidence, rheological models, and emerging data-driven approaches, highlighting the challenges of reconciling results across different material systems and testing conditions. The main conclusions and future perspectives can be summarized as follows.

• (1)The macroscopic flow behavior of paste is primarily controlled by the formation and evolution of internal particle networks, rather than by the properties of the liquid phase alone.
• (2)Empirical constitutive models widely used in practice provide useful engineering approximations under specific flow conditions, such as steady-state transport in shallow or well-controlled mining systems. However, they are limited in describing structural evolution, time dependence, and spatially heterogeneous flow behavior that commonly arise in deeper or more complex mining operations, where high pressure, flow interruption, and restart conditions are prevalent.
• (3)Rheological parameters are strongly influenced by testing protocols and observation scale, underscoring the need for improved experimental consistency and scale-aware interpretation.
• (4)Particle gradation, temperature, and additives modify paste rheology by altering interparticle interactions and hydration processes, offering practical means of rheological control for optimizing pumpability and transport stability when applied appropriately.
• (5)There remains a lack of rheological models capable of consistently linking microstructural evolution with macroscopic flow behavior across relevant length and time scales, particularly in capturing structure-controlled yielding, spatial heterogeneity, and scale dependence.
• (6)Data-driven and physics-informed approaches show promise for modeling history-dependent rheological behavior, but their broader application is limited by challenges in interpretability, robustness, and integration with physical mechanisms.