Experimental investigation of evolutive mode-I and mode-II fracture behavior of fiber-reinforced cemented paste backfill: Effect of curing temperature and curing time

Abstract

The curing temperature-dependent cement hydration causes the nonlinear evolution of fracture behavior and properties of fiber-reinforced cemented paste backfill (CPB) and thus influences the stability of mine backfill materials in deep mines. Therefore, the coupled effect of curing temperature (20, 35, and 45 °C) and cement hydration at different curing times (3, 7, and 28 d) on the mode-I and mode-II fracture behavior and properties of fiber-reinforced CPB is investigated. A comprehensive experimental testing program consisting of semicircular bend tests, direct shear tests, measurement of volumetric water content and matric suction, TG/DTG tests, and SEM observation is carried out. The results show that the coupled thermochemical effect results in strongly nonlinear development of pre- and post-peak behavior of fiber-reinforced CPB. Moreover, the results discover a positive linear correlation between fracture toughness and shear strength parameters and also reveal the vital role played by matric suction in the formation of fracture toughness. Furthermore, predictive functions are developed to estimate the coupled thermochemical effect on the development of K_Ic and K_IIc. Therefore, the findings and the developed mathematical tools have the potential to promote the successful application of fiber-reinforced CPB technology in deep underground mines.

Graphical abstract

Keywords

fiber reinforcement / cemented paste backfill / fracture behavior / underground mine / cement hydration

1 Introduction

Cemented paste backfill (CPB, an engineered mixture of mine tailings, binder, and water) is one of the most widely used mine backfill technologies [1,2]. The component and corresponding proportion have been documented by many previous works of literature [3,4]. Characterized with a rapid strength acquisition, CPB can provide prompt support in the mined-out stope [5,6]. This will shorten the mining cycle and thus increase the productivity of mines. However, the reliability of the CPB support is determined by many factors, such as the mining interval, underground temperature, and permeability of the country rock [7]. However, due to the brittle behavior of CPB materials, many failures still took place when it was exposed to mining disturbances even with sufficient mechanical strength [8,9]. In addition, the poor tensile strength and weak ductility of CPB allow rib falls easily, which worsens the ore dilution [10–12]. Hence, to improve CPB’s engineering performance, the incorporation of fiber into CPB is turned out to be an effective and economical approach [13–15]. Specifically, the addition of fibers into the CPB matrix can improve the unconfined compressive strength (UCS) by 70%–90%, depending on the fiber content [16,17]. Moreover, Yi et al. [18] found that the usage of fiber contributes more to UCS improvement in comparison with that contributed by cement hydration. In other words, given the fact that the cost of cement accounts for 20% to 40% of the mining activities, replacing certain cement with fibers can considerably decrease the cost of CPB [19]. Indeed, fiber has already been increasingly used for the reinforcement of civil engineering structures [20,21]. For example, the addition of fiber can reduce the lateral strain in gravel, which is important to railway ballast [22], and the usage of fiber arrests the propagation of fracture in concrete [23]. In addition, the adoption of fiber benefits the improvement of the mechanical properties of cemented soil [24]. Likewise, the fiber-reinforced CPB is considered a promising mine backfill technique in the mining community as well.

To implement mine backfill technology, the strength-based design method has been extensively used. However, intact CPB mass without defects is commonly assumed during the process of engineering design. It should be emphasized that both intrinsic and induced defects coexist in CPB mass. Specifically, due to the mixing operation and underground transportation, the entrapped air bubbles together with capillary pores, form the intrinsic defects in the hardened CPB [25]. Moreover, CPB mass is confined by surrounding rock walls with rough surfaces. Consequently, the stiff and rough rock walls cause the generation of micro- and macro-notches (i.e., induced defects) along the surfaces of CPB mass [26]. Therefore, when subjected to complex quasi-static and dynamic loadings, the intrinsic and induced defects in CPB act as stress concentrators to trigger the crack initiation, propagation, and coalescence, which indicates CPB failure is actually a fracture mechanics problem. Correspondingly, a well understanding of fracture behavior and properties of fiber-reinforced CPB is the prerequisite for the successful application of the fiber reinforcement technique in the mine backfilling operation. In terms of fracture behavior of CPB, Libos and Cui [26] have confirmed that the linear elastic fracture mechanics is valid for CPB materials. Correspondingly, cracks initiate and propagate at the moment as the stress intensity factor hits the fracture toughness [27]. Therefore, fracture toughness can be adopted as the key fracture property to evaluate the fracture response of CPB. Moreover, it should be noted that both tensile stress and shear stress can develop in CPB under field loading conditions. For example, CPB sill beams act as the temporary stope roof for further extraction and lead to the formation of tensile stress near the bottom of the CPB body [28]. Meanwhile, when ore pillars are extracted, the exposed CPB surface is subjected to a biaxial compressive loading condition. Consequently, tensile stress can also develop near the exposed surfaces. In addition, unequal principal stresses commonly exist in CPB mass due to the combined effect of self-weight stress and external loading from surrounding rock mass, which causes the development of shear stress in CPB mass. Based on the fracture-mechanics principles, the crack propagation is governed by the tensile and shear stress concentration near the crack front [29]. Hence, it is essential to study the tensile and shear fracture behavior and properties of mine backfill materials.

Owing to the ongoing cement hydration (i.e., chemical effect), the mechanical behavior and properties of cementitious materials evolve with curing time [30]. Consequently, the acquisition rate of mechanical properties of mine backfill materials directly affects the progression of extraction of secondary stopes and thus the mining cycles [31]. Meanwhile, due to the geothermal gradient, CPB materials are commonly subjected to various thermal loadings in the deep underground mines [32]. The resultant warmer underground temperatures (i.e., thermal effect) influence the in situ cement hydration rates. Therefore, the coupled thermochemical effect plays a critical role in the development of in situ mechanical behavior and properties of CPB. However, only a few studies [26,28,33] have been conducted to investigate the curing time-dependent fracture behavior of fiber-free CPB materials at room temperature only, i.e., without consideration of the coupled thermochemical effect. Moreover, no studies have been specifically designed to study the fracture behavior and property of fiber-reinforced CPB. The existing research gap prevents a well understanding of the field behavior of CPB mass under complex thermochemical loadings. Therefore, the main objectives of the current study are to 1) experimentally investigate the coupled thermochemical effect on the development of fracture behavior and property of fiber-reinforced CPB under mode-I and mode-II loadings; and 2) establish predictive mathematical tools to estimate the coupled thermochemical effect and thus facilitate the engineering application of fiber-reinforced CPB technology.

2 Materials and experimental program

2.1 Materials

It is well known that 70 wt.%–85 wt.% of CPB is made of natural tailings. The tailings adopted at the laboratory level thus play a critical role in mimicking the in-site characteristics and performance of CPB. Two perspectives, namely rheological and mechanical properties, should be considered in determining the selection of tailings. The rheological characteristic is mainly determined by the particle size distribution (PSD), while the mechanical property is up to the PSD and mineral component [34]. Given the high similarity in PSD and mineral components with natural tailings [35,36], silica tailings are selected for the preparation of CPB specimens in the laboratory. Various types of fibers can be used for the reinforcement of cementitious materials, depending on the desired function (strength or ductility improvement). In this study, polypropylene (PP) fibers were adopted owing to the wide commercial availability and low cost and wide. The adopted PP fibers have a diameter of 80 μm and a length of 13 mm, and the detailed material properties of PP fibers are summarized in Tab.1. As for the binding agent, GU Portland cement (which is manufactured by the CRH group) is used because of its widespread application in backfill formulation [37]. To eliminate the uncertainty in interpretation, distilled water is used for the mixing process.

2.2 Mixture recipe and specimen preparation

The mixture recipe of all samples is consistent. The cement and fiber content are set to 4.5 wt.% and 0.5 wt.%, respectively (with reference to the total mass of the solid phase), and the water-to-cement ratio is controlled as 7.6. To avoid the fiber floating and ensure the homogeneity of the mixture, fiber was added after the beginning of the mixing, and the mixing operation lasted for 7 min. To release the air trapped during mixing and sample preparation, all samples were vibrated manually. Then, the fresh paste was cast into cylindrical molds (10 cm (width) × 20 cm (height)) and respectively cured at ambient temperature (around 20 °C), 35 and 45°C up to 28 d. To maintain the warmer curing temperature (i.e., 35 and 45 °C), an Espec ESI-3CA temperature and humidity chamber is adopted. After the target curing age was met, the cylindrical specimens were further trimmed into the test specimens. Detailed information about the fabrication of test specimens will be presented in Subsection 2.3.

2.3 Experimental study program

To discover the coupled thermochemical effect on the evolutive fracture behavior and properties of fiber-reinforced CPB, an experimental testing program consisting of semicircular bend (SCB) tests, direct shear tests, a monitoring program, and microstructural analysis (including scanning electron microscopy (SEM), thermo-gravimetric and differential thermo-gravimetric test (TG/DTG)) were conducted in this study. The SCB test results can directly reveal the evolutive mode-I and mode-II load−displacement behavior, which can be used to further derive the key fracture property (i.e., fracture toughness). Moreover, direct shear tests can be used to identify the associated shear strength parameters, including cohesion and friction angle. The conventional shear strength parameters can be linked to the material resistance to the tensile and shear crack propagation, which can not only facilitate the identification of different contributors to the development of fracture toughness, but also has the potential to simplify the determination of fracture property of fiber-reinforced CPB. In terms of auxiliary analysis, the monitored matric suction and moisture content, SEM images, and TG/DTG results can be used to confirm the coupled thermochemical effect at the material level.

2.3.1 Semicircular bend tests

The SCB tests were conducted in accordance with ASTM D8044. For the SCB specimen fabrication, the cylindrical samples were trimmed into the semicircular samples (10 cm (width) × 5 cm (height)) through a Bosch GCM12SD miter saw. After that, a straight-through notch with a length of 2.5 cm was introduced to the semicircular disc samples and thus maintained a notch-to-radius ratio of 0.5. The initial notch was aligned with the centerline of CPB specimens under mode-I SCB tests, while the notch inclination angle of 54° was adopted by the CPB specimens under mode-II SCB tests [38]. The detailed information about the SCB specimens is shown in Fig.1. During the SCB tests, an axial force is applied at a rate of 1 mm per minute until failure occurs. The load−displacement curves were continuously recorded through a load cell (with a nonlinearity of less than 0.03%) and a displacement transducer (with a resolution of 0.01 mm), respectively. Three SCB specimens were tested under each curing temperature and curing time to yield repeated test results.

The fracture toughness can be used to evaluate the material resistance to fracture propagation. Correspondingly, crack growth will occur when the stress intensity factor approaches the fracture toughness. Through the load−displacement curves measured from SCB tests, the peak load P_m can be used to calculate the fracture toughness. According to the previous studies [39–41], the mode-I & mode-II fracture toughness K_Ic and K_IIc can be calculated as follows:

(1)K_{\mathrm{I}\mathrm{c}}=\frac{P_{\text{m}}\sqrt{\text{π}a}}{2Rt}{Y}_{\text{I}}\left(\frac{a}{R},\frac{S}{R}\right),

(2)K_{\text{IIc}}=\frac{P_{\text{m}}\sqrt{\text{π}a}}{2Rt}{Y}_{\text{II}}\left(\alpha ,\frac{a}{R},\frac{S}{R}\right),

where t denotes the thickness of the specimen (cm), Y_I and Y_II are the normalized stress intensity factor (dimensionless) which are associated with the notch inclination angle α (°), the notch-to-radius ratio a/R, and the half span-to-radius ratio S/R [42]. The values of Y_I and Y_II have been identified by previous studies [43–45]. It should be noted that the stress intensity factor is sensitive to the notch width [46,47]. To introduce a notch into SCB samples, a diamond blade (thickness: 1.5 mm) was unitized, and the resultant notch had a width of approximately 2 mm. Moreover, it has been found that the shape of the notch on the fracture toughness measurement [48–52] and the thickness of SCB samples exerts very limited effects on the stress intensity factor Y_I [53] and mode-I fracture toughness K_Ic [54]. Considering the relatively lower tensile strength of CPB materials, a thickness of 50 mm was adopted in this study. The detailed information about the adopted value of each parameter is summarized in Tab.2.

2.3.2 Measurement of shear strength parameters

The matrix cohesion and frictional resistance play dominant roles in the crack propagation in the cementitious materials [35,55]. Therefore, the determination of shear strength parameters can facilitate the recognition of mechanisms for the development of tensile (i.e., mode-I) and shear (i.e., mode-II) fracture behavior and properties of fiber-reinforced CPB. Correspondingly, direct shear tests were carried out in compliance with ASTM D3080/D3080M-11 with the ELE direct shear device to obtain the cohesion and friction angle. The ELE direct shear device consists of upper and lower shear boxes. Through the lower shear box, the CPB sample is sheared in the horizontal direction at a rate of 1 mm per minute. The shear/normal displacement and force are recorded by the usage of two displacement transducers (with a maximum run of 25 mm) and a load cell (with a measurement capacity of 4.5 kN). For the specimen fabrication, the cylindrical samples were first cut into three disc-shaped samples. As shown in Fig.2, the obtained disc-shaped samples were further trimmed into three cuboidal specimens (6 cm × 6 cm × 3 cm) through a professional dual-bevel 12-inch mitre saw. For each curing condition, three normal stresses (50, 100, and 150 kPa) are respectively applied. To maintain the repeatability of test results, three cuboidal specimens were tested for each curing condition and each normal stress. As a result, 81 cuboidal specimens were fabricated and tested under direct shear tests.

2.3.3 Matric suction and volumetric water content measurement

The pore water consumed by curing temperature-dependent cement hydration causes complex changes in VWC and matric suction in the CPB matrix. The water content changes inevitably influence the interparticle friction [56] and thus the resistance to crack propagation [57], while the enhanced matric suction has the potential to improve the apparent cohesion [58]. Therefore, it is of great importance to monitor the evolution of VWC and matric suction under the coupled thermochemical effect and identify their contribution to the evolution of fracture behavior and property of fiber-reinforced CPB. The monitoring program was carried out through the cylindrical specimen (10 cm (width) × 20 cm (height)) as well and thus ensures the recorded VWC and matric suction are compatible with the load−displacement behavior and fracture property measured from consistent curing conditions. As shown in Fig.3, two well-sealed molds were submerged in the Humboldt H-1392 water bath (with an accuracy of ±0.1%) to ensure a consistent temperature (35, 45°C), and one mold was directly placed in the laboratory room to capture the effect of room temperature. Two types of sensors, including T5X and 5TE, were installed into the molds to respectively measure the matric suction and VWC. The monitoring outcomes were recorded by a data logger (Meter Environment ZL6).

2.3.4 Microstructure analysis and thermogravimetric analysis

Scanning electron microscope (SEM) observation is carried out to probe into the coupled thermochemical effect on microstructure change of CPB matrix. Considering moisture can lead to damage to the device (Hitachi Su-70), the specimen needs to be oven-dried at 45 °C for 2 d prior to the observation. Because the cement hydration is assumed to be ceased after the removal of pore moisture, the SEM images obtained are still considered representative of the state before the drying process, even after 2-d drying. Unlike the SEM, the TG/DTG test is carried out on powdered cement paste (without silica tailings and fiber) with a thermogravimetric analyzer (Q5000IR). The temperature range is from 30 to 1000 °C. According to the weight loss at different thermal periods, the amounts of various cement hydration products can be determined. The weight loss is induced by the dehydration and/or decomposition of cement hydration products, and the appearing time of the dehydration or decomposition varies with products.

3 Results and discussion

3.1 Evolutive load−displacement behavior of fiber-reinforced cemented paste backfill

The coupled thermochemical effect on the mode-I load−displacement curves of fiber-reinforced CPB is presented in Fig.4. For the pre-peak branch, fiber-reinforced CPB demonstrates a linear load−displacement behavior, despite the ages of specimens. This confirms the validity of linear elastic fracture mechanics for fiber-reinforced CPB materials. Moreover, when the warmer curing temperature is applied, the linear pre-peak branch is further enhanced and shows a higher material stiffness. The improved stiffness under the higher temperature enables CPB mass to offer more effective group support to limit the stope convergence under field loading conditions. For the peak load, it can be found that the early-age fiber-reinforced CPB is more sensitive to the variations in temperature. For instance, the 3-d peak load respectively increases by 57.6% (27.1 N) at 35 °C and 98.2% (34.1 N) at 45 °C relative to the counterpart (17.2 N) at 20 °C. However, the 28-d peak load was only improved by 21.7% (74.5 N) at 35 °C and 32.4% (81 N) compared with that (61.2 N) at 20 °C. The weakened improvement of peak load with curing time can be interpreted by the limited cement in CPB. Specifically, owing to the dependency of cement hydration on curing temperature [36], a warmer temperature can accelerate the cement hydration and yields a higher chemical reaction rate. As a result, more hydration products, such as calcium silicate hydrate (C-S-H) and calcium hydroxide (CH), are generated inside the early-age CPB, which will form a stronger cohesive strength between tailings at a particular curing time. As a consequence, the early-age CPB is able to offer a higher resistance to crack propagation under warmer curing temperatures. However, it is noteworthy that the hydration kinetics also depends on the diffusion rate of pore water between the exterior of hydration products and internally anhydrous cement grains [59]. Correspondingly, the accelerated formation of hydration products under warmer curing temperature unavoidably prevents moisture diffusion and thus reduce the cement hydration rate at advanced ages. Therefore, the peak load demonstrates a descending growth rate with curing time. For the post-peak branch, a residual load was measured from all fiber-reinforced CPB under mode-I loading conditions. It is acknowledged that the tensile stress governs the mode-I crack extension in the matrix. When the tensile crack surfaces are generated, the associated cohesive strength between particles cannot be mobilized along the crack surface. Therefore, the residual load of fiber-reinforced CPB under mode-I loading can only be attributed to the inclusion of fibers in CPB matrix. Therefore, the measured residual load further confirmed the effectiveness of fiber reinforcement.

The load−displacement curves under mode-II loading are plotted in Fig.5. It is noticeable that a warmer temperature can improve material stiffness under mode-II loading, and the temperature-induced difference in the stiffness narrows with curing time. Moreover, the peak load of the fiber-reinforced CPB also increases with curing temperature and the curing age. This increasing peak load and stiffness under the thermochemical effect coincide with the findings of the conventional geomechanical behaviors [36]. Furthermore, the displacement at the peak load under mode-II loading shows a stronger dependency on the curing temperature and curing time. For example, the displacement at which the load of the 28-d specimen peaks reaches 0.33 mm (an increase of 31.7%) at 35 °C and 0.37 mm (an increase of 50%) at 45 °C compared with that (0.25mm) cured at 20 °C. Similar improvement of displacement associated with peak load is measured from 3-d and 7-d specimens as well. Since the stope contraction is inevitable under high geostress, improvement of tolerance of fiber-reinforced CPB to the displacement under the thermochemical effect contributes to the mechanical stability of rock stope under field loadings. Similarly, the mode-II peak load also shows a significant improvement with the increase in curing temperature and time. This is because, besides the contribution of cohesion and bridging effect, the frictional resistance also contributes to the development of the mode-II peak load [18,36]. Moreover, the interparticle friction resistance is able to mobilize along the shear crack surface and thus results in a higher mode-II residual load (see Fig.5) relative to the counterpart under mode-I loading (see Fig.4).

Moreover, as shown in Fig.4 and Fig.5, a consistent residual load exists in the post-peak region when fibers are included in CPB production. The existence of the residual loads of fiber-reinforced CPB is due to the fiber bridging effect posed by the interface friction between tailings particles and fibers. The fiber bridging effect can be clearly observed along the crack paths in the SCB specimens, as shown in Fig.6. In other words, in the post-peak region, it is only the fiber that arrests the propagation of the cracks, and the crack-arresting ability enhances with time. Most importantly, the different magnitudes of material resistance (including both peak and residual loads) under mode-I and mode-II loadings clearly indicate the critical roles played by the shear strength parameters. A specific discussion on the development of shear strength parameters is demonstrated in Subsection 3.3. In addition, as shown in Fig.4(c), Fig.5(b) and Fig.5(c), the post-peak resistance of advanced-age fiber-reinforced CPB becomes weaker under a warmer curing temperature. This can be attributed to the sudden release of strain energy corresponding to the peak load. It can be observed that larger strain energy (i.e., area beneath the load−displacement curves) can be accumulated inside fiber-reinforced CPB under warmer curing temperatures. Correspondingly, matrix failure occurring at the peak load will suddenly release a considerable amount of strain energy and thus may cause additional matrix damage due to the inertial effect. Consequently, a weaker post-peak resistance was measured from fiber-reinforced CPB under warmer curing temperatures.

3.2 Evolutive notch fracture toughness of fiber-reinforced cemented paste backfill

Fig.7 depicts the development of K_Ic & K_IIc of fiber-reinforced CPB under coupled thermochemical effect. It is concluded that both K_Ic & K_IIc show a continuous improvement with curing time and curing temperature. Prior to the further probe into the change in the notch fracture toughness, it is necessary to understand the mechanisms that dominate the development of the mechanical properties of fiber-reinforced cementitious material: 1) the cement hydration and 2) fiber-induced bridging effect. As a major product of cement hydration, C-S-H acts as the principal binding agent, and the binding ability is normally proportional to its quantity and distribution [60]. The quantity of C-S-H is up to the degree of cement hydration, which is sensitive to the curing temperature and curing time. Specifically, a warmer temperature and longer curing time benefit the acceleration of cement hydration, and accordingly, the amount of C-S-H is increased. In contrast, the distribution quality of C-S-H is determined by the capillary structure, and a finer pore structure promotes the migration of C-S-H [33]. As for the fiber-induced bridging effect, the magnitude is ascribed to the interaction (cohesion and friction angle) between fiber and tailings particles as well as the lubricant effect of pore water.

It is noticeable from Fig.7 that as the temperature increases from 20 to 45 °C, the K_Ic of the 7-d specimen rises from 9.1 to 18.4 kPa∙m^1/2 while the K_IIc increases from 6.1 to 8.5 kPa∙m^1/2. The positive contribution of curing temperature is mainly brought about by the enhanced degree of cement hydration and self-desiccation. In detail, as a result of intense binder hydration, a considerable amount of C-S-H is generated. In addition, the refinement of extra amounts of byproducts (ettringite, gypsum) of the enhanced reaction leads to a denser pore structure, and this allows C-S-H to migrate easily [32]. Consequently, the binding force is considerably improved. The finer pore structure is evident in the SEM images of fiber-reinforced CPB, as shown in Fig.8. Compared with the microstructure of specimen cured at 20 °C, less capillary is seen in specimen cured at 35 °C, and a comparatively denser pore structure is observed in sample cured at 45 °C. In addition, a higher degree of cement hydration means extensive consumption of pore water, and this is manifested as an improved self-desiccation. The lubricant effect caused by water is accordingly weakened. On the other hand, the matric suction is also increased because of the loss of pore water. The reduced VWC and the build-up matric suction under the thermochemical effect are shown in Fig.9. For example, when the temperature rises from 20 to 45 °C, VWC decreases from 0.48 to 0.3 while the matric suction experiences an increase from 19.3 to 72.6 kPa.

As for the curing time-dependent evolution of the fiber-reinforced CPB’s notch fracture toughness, it is noticed that for specimens cured at 20°C, the K_Ic & K_IIc are 6.1 and 3 kPa∙m^1/2 on the third day. However, after 25 d of curing, they respectively jump to 22 and 7 kPa∙m^1/2. The processes that lead to the significant improvement in notch fracture toughness with curing time are attributed to the combined effect of the more considerable quantity of C-S-H, denser pore structure as well as intensified self-desiccation. Many previous studies have already demonstrated the contribution of cement hydration to the improvement of time-dependent mechanical properties of CPB [61,62]. With the elapse of time, an extensive quantity of C-S-H and gypsum are generated, which have twofold effects on notch fracture toughness improvement. First, the refinement of the larger amount of gypsum results in a finer capillary structure, thereby facilitating the migration of C-S-H. Secondly, the increasing amount of C-S-H with curing time benefits the cohesion (between cement particles as well as that between cement matrix and fiber) acquisition. The argument that more C-S-H and gypsum are generated with time is attested by the outcomes of the TG/DTG test (Fig.10) on cement paste with curing ages of 3-, 7-, and 28-d. It is well acknowledged that the weight loss situated at 50–160 °C is attributed to the dehydration of C-S-H and gypsum [63]. It is observable from the figure that the weight loss of the 7-d specimen is lower than that of the 28-d sample but higher than that of the 3-d sample. This indicates that compared with the 28-d specimen, less C-S-H and gypsum are produced in the 7-d sample, and the least products are generated in the 3-d sample. The finer pore structure with time is certified by the comparison of the microstructure of 7- and 28-d fiber-free CPB [33] (the addition of fiber poses no influence on the cement hydration process [18,36]). It can also be seen from the SEM images that after 28 d of curing, more C-S-H is discovered at the surface of the cement particles, which further proves the ongoing cement hydration with time. Moreover, the monitoring results in Fig.9 depict an increasing matric suction and decreasing VWC in fiber-reinforced CPB with time. This also accounts for the rising notch fracture toughness, as shown in Fig.7.

3.3 Correlation between notch fracture toughness and shear strength parameters and matric suction

The determination of notch fracture toughness is the prerequisite for the evaluation of tensile and shear crack extension in the CPB matrix. Therefore, the predictive functions of mode-I & mode-II notch fracture toughness can be used as valuable mathematical tools for the quantitative description of fracture behavior of fiber-reinforced CPB. Moreover, the SCB test results confirm the critical roles played by the shear strength parameters and matric suction. Compared with specimen fabrication for the notch fracture toughness tests, it is more convenient for researchers and backfill designers to prepare the specimens for conventional direct shear tests. Meanwhile, multiple techniques, such as the axis translation technique [64] and the dew-point technique [65], are available for the in situ measurement of matric suction in porous media. Therefore, the development of predictive functions through the conventional mechanical properties and measurable pore-water state variable can significantly simplify the evaluation of the key fracture property (i.e., notch fracture toughness) and thus promote the engineering application of linear elastic fracture mechanics to the mine backfill design.

3.3.1 Determination of the friction angle, cohesion, and regularized matric suction

Based on the obtained results in Subsections 3.1 and 3.2, it can be concluded that the development of the K_Ic of fiber-reinforced CPB is related to the cohesion and the matric suction, while the K_IIc is contributed by the cohesion, matric suction as well as the frictional resistance between tailings particles. To reveal the specific correlation between these parameters, direct shear tests are carried out on fiber-reinforced CPB, which are cured at the same thermochemical conditions. With the adoption of the Mohr−Coulomb criterion, the cohesion and friction angle of fiber-reinforced CPB are obtained, as presented in Fig.11. The comparison between Fig.7 and Fig.11 shows that the cohesion experience an evolutionary tendency similar to that observed from K_Ic. In contrast, the gradual growth in K_IIc is a result of the monotonously-rising cohesion and comparatively-stable friction angle (especially for 7- and 28-d specimens).

Compared with shear strength parameters, the effect of matric suction is relatively complex. This is because the matric suction only acts on the solid surface that is in contact with water. As the cement hydration proceeds, the quantity of pore water undergoes a continuous decrease, and as a result, the contact area between water and solid particle is inevitably reduced. Therefore, the contribution of matric suction to notch fracture toughness is limited by the water content. To evaluate the combined effect of matric suction and VWC on notch fracture toughness, a regularized matric suction is proposed:

(3)\overline{\psi }=\theta \cdot \psi ,

where \overline{\psi } is regularized matric suction (kPa), θ is VWC (dimensionless), and ψ is the matric suction (kPa).

3.3.2 Dependency of notch fracture toughness on shear strength parameters and matric suction

As mentioned above, the notch fracture toughness of fiber-reinforced CPB is contributed by the shear strength parameters and regularized matric suction. Fig.12 illustrates the dependency of K_Ic on the cohesion and regularized matric suction. It can be observed that there exists an approximately linear correlation between K_Ic and cohesion (see Fig.12(a)), which clearly indicates the key role played by the cohesive strength among tailings particles and the fiber/matrix interface. However, as shown in Fig.12(b), a nonlinear relationship was observed between K_Ic and regularized matric suction. More precisely, a strengthened improvement of K_Ic appears when regularized matric suction reaches a critical suction value (approximately 32 kPa). This can be interpreted by the existence of air entry value for the porous media. In other words, the moment the matric suction hits the air entry value, the air begins to enter the porous media and thus leads to the transition from a fully to partially saturated condition. When the matrix is in the unsaturated state, the increased matric suction intends to pull the tailings particles together, which not only improves the particle contact area (i.e., interparticle friction resistance), but also yields a denser matrix. Most importantly, the lower water content associated with the unsaturated state will significantly enhance the interparticle friction resistance. Therefore, compared with matric suction in a saturated zone (i.e., matric suction less than air entry value), the changes in matric suction greater than this critical value are able to cause an enhanced improvement of notch fracture toughness in the unsaturated CPB.

Fig.13 depicts the correlation between the K_IIc and friction angle, cohesion, and regularized matric suction. From Fig.13(a) and Fig.13(b), a positive linear correlation between K_IIc and shear strength parameters is observed, which indicates that the effect of shear strength parameters on the development of notch fracture toughness is similar to those on the shear strength defined by the Mohr−Coulomb criterion. Correspondingly, the criterion can be utilized as a reference to define the predictive function for K_IIc. In terms of regularized matric suction (see Fig.13(c)), a critical suction value (approximately 32 kPa) can also be observed for the development of K_IIc. This is because the pore air and pore water cannot sustain shear stress. Correspondingly, no shear stress component exists in the matric suction which is defined by the difference between pore-air pressure and pore-water pressure. As a result, matric suction inevitably exerts a similar contribution to the development of K_Ic and K_IIc.

According to the dependency of notch fracture toughness on the shear strength parameters and regularized matric suction, two rules can be identified for the definition of predictive functions: 1) the contribution of shear strength parameters to notch fracture toughness is similar to the counterparts defined by Mohr−Coulomb failure criterion (i.e., linear relationship between notch fracture toughness and shear strength parameters); and 2) the regularized matric suction exerts a similar contribution to the development of K_Ic and K_IIc. Correspondingly, two predictive functions are proposed to quantitatively evaluate the dependency of mode-I & mode-II notch fracture toughness on the cohesion, angle of internal friction, and regularized matric suction, respectively:

(4)K_{\text{Ic}}\left(c,\psi \right)=A_{1}c+A_2{\left(\frac{\overline{\psi }}{{\psi }_{\text{R}}}\right)}^{A_3\left(\frac{{\overline{\psi }}_{\text{C}}}{{\psi }_{\text{R}}}\right)},

(5)K_{\text{IIc}}\left(c,\varphi ,\psi \right)=B_{1}c+B_2\tan \varphi +B_3{\left(\frac{\overline{\psi }}{{\psi }_{\text{R}}}\right)}^{B_4\left(\frac{{\overline{\psi }}_{\text{C}}}{{\psi }_{\text{R}}}\right)},

where c and ϕ refer to the cohesion (kPa) and friction angle (°) of fiber-reinforced CPB, \overline{\psi } is regularized matric suction (kPa), ψ_R is a reference matric suction (ψ_R = 1 kPa), \overline{\Psi }_C is the critical regularized matric suction (kPa), and A_i (i = 1 to 3) and B_j (j = 1 to 4) are fitting constants. Based on the correlation between regularized matric suction and notch fracture toughness (see Fig.12(b) and Fig.13(c)), the critical suction \overline{\psi }_C = 32 kPa is adopted. Meanwhile, through regression analysis on the measured notch fracture toughness, A₁ = 0.05 m^1/2, A₂ = 0.75 kPa∙m^1/2, A₃ = 0.02, B₁ = 0.02 m^1/2, B₂ = 3.44 kPa∙m^1/2, B₃ = 0.15 kPa∙m^1/2, and B₄ = 0.004 are obtained.

As shown in Eqs. (4) and (5), the notch fracture toughness is linearly related to the cohesion and friction coefficient (i.e., tanϕ), and similar regularized matric suction terms were adopted. Correspondingly, the two rules associated with the effects of shear strength parameters and regularized matric suction can be satisfied. Moreover, it should be noted that the evolution of notch fracture toughness is mainly induced by the progression of cement hydration. The chemical reaction contributes to the formation of particle bond strength [66], pore-water loss [67], and macroscale notch fracture toughness [68]. Most importantly, cement hydration is curing-temperature sensitive [69]. Therefore, the changes in shear strength parameter (cohesion and friction angle) and matric suction already incorporates the thermochemical effect associated with cement hydration. Correspondingly, the good agreement between the estimated and measured notch fracture toughness (Fig.14) confirms that the proposed predictive functions can well capture the evolution of K_Ic and K_IIc. Besides, the high regression ratios (R² = 0.93 and R² = 0.97) further indicate the dependency of notch fracture toughness on the cohesion, friction angle, and regularized matric suction in fiber-reinforced CPB. Therefore, the proposed predictive functions have the potential to evaluate the coupled thermochemical effect on the development of notch fracture toughness of fiber-reinforced CPB in deep underground mines.

4 Conclusions

The coupled thermochemical effect on the evolution of fracture behavior and property of fiber-reinforced CPB is experimentally investigated in the current study. According to the experimental results and analytical outcomes, the following conclusions are drawn.

1) Both pre-peak stiffness and peak load of fiber-reinforced CPB increase with curing temperature and curing ages. Moreover, the inclusion of fiber makes residual load observable in both mode-I & mode-II load-displacement curves.

2) The increasing K_Ic and K_IIc under the thermochemical effect are mainly because of the enhanced cement hydration and strengthened bridging effect. In other words, the larger quantity of C-S-H increases the binding force while the decreasing VWC and the associated changes in matric suction enhance the frictional resistance between fiber and tailings particles.

3) A positive linear correlation between notch fracture toughness and shear strength parameters was uncovered under the coupled thermochemical effect. Therefore, the contributions of shear strength parameters are similar to the counterparts defined by the Mohr−Coulomb failure criterion.

4) When the regularized matric suction is greater than the critical value, an enhanced improvement of notch fracture toughness appears, which can be attributed to the existence of air entry value and associated changes in the saturation conditions.

5) Since there is no shear stress component in matric suction, the regularized matric suction exerts a similar contribution to the development of K_Ic and K_IIc under thermochemical effect.

6) Two predictive functions are proposed to demonstrate the dependency of notch fracture toughness on cohesion, regularized matric suction, and the friction angle. The high regression ratio indicates the proposed equations can well capture the coupled thermochemical effect on the development of notch fracture toughness of fiber-reinforced CPB, which can simplify the evaluation of the key fracture properties through conventional mechanical properties and a measured pore-water state variable.

References

[1] Yılmaz T, Ercikdi B. Predicting the uniaxial compressive strength of cemented paste backfill from ultrasonic pulse velocity test. Nondestructive Testing and Evaluation, 2016, 31(3): 247–266

[2] Sari M, Yilmaz E, Kasap T, Guner N U. Strength and microstructure evolution in cemented mine backfill with low and high pH pyritic tailings: Effect of mineral admixtures. Construction & Building Materials, 2022, 328: 127109

[3] Ercikdi B, Külekci G, Yılmaz T. Utilization of granulated marble wastes and waste bricks as mineral admixture in cemented paste backfill of sulphide-rich tailings. Construction & Building Materials, 2015, 93: 573–583

[4] Libos I L S, Cui L. Time- and temperature-dependence of compressive and tensile behaviors of polypropylene fiber-reinforced cemented paste backfill. Frontiers of Structural and Civil Engineering, 2021, 15(4): 1025–1037

[5] Yılmaz T, Ercikdi B. Effect of construction and demolition waste on the long-term geo-environmental behaviour of cemented paste backfill. International Journal of Environmental Science and Technology, 2022, 19(5): 3701–3714

[6] Cavusoglu I, Yilmaz E, Yilmaz A O. Sodium silicate effect on setting properties, strength behavior and microstructure of cemented coal fly ash backfill. Powder Technology, 2021, 384: 17–28

[7] Qi C, Guo L, Wu Y, Zhang Q, Chen Q. Stability evaluation of layered backfill considering filling interval, backfill strength and creep behavior. Minerals (Basel), 2022, 12(2): 1–16

[8] Zhang H, Cao S, Yilmaz E. Influence of 3D-printed polymer structures on dynamic splitting and crack propagation behavior of cementitious tailings backfill. Construction & Building Materials, 2022, 343: 128137

[9] Li J, Cao S, Yilmaz E, Liu Y. Compressive fatigue behavior and failure evolution of additive fiber-reinforced cemented tailings composites. International Journal of Minerals Metallurgy and Materials, 2022, 29(2): 345–355

[10] Xue G, Yilmaz E, Song W, Cao S. Mechanical, flexural and microstructural properties of cement-tailings matrix composites: Effects of fiber type and dosage. Composites. Part B, Engineering, 2019, 172: 131–142

[11] Yi X W, Ma G W, Fourie A. Centrifuge model studies on the stability of fibre-reinforced cemented paste backfill stopes. Geotextiles and Geomembranes, 2018, 46(4): 396–401

[12] ZhaoZCaoSYilmazE. Effect of layer thickness on flexural property and microstructure of 3D printed rhomboid polymer reinforced cemented tailings composites. International Journal of Minerals Metallurgy and Materials, 2023, 30: 236–249

[13] Chakilam S, Cui L. Effect of polypropylene fiber content and fiber length on the saturated hydraulic conductivity of hydrating cemented paste backfill. Construction & Building Materials, 2020, 262: 120854

[14] Cao S, Yilmaz E, Yin Z, Xue G, Song W, Sun L. CT scanning of internal crack mechanism and strength behavior of cement-fiber-tailings matrix composites. Cement and Concrete Composites, 2021, 116: 103865

[15] Wang A, Cao S, Yilmaz E. Effect of height to diameter ratio on dynamic characteristics of cemented tailings backfills with fiber reinforcement through impact loading. Construction & Building Materials, 2022, 322: 126448

[16] Chen X, Shi X, Zhang S, Chen H, Zhou J, Yu Z, Huang P. Fiber-reinforced cemented paste backfill: The effect of fiber on strength properties and estimation of strength using nonlinear models. Materials (Basel), 2020, 13(3): 1–20

[17] Wang Y, Yu Z, Wang H. Experimental investigation on some performance of rubber fiber modified cemented paste backfill. Construction & Building Materials, 2021, 271: 121586

[18] Yi X, Ma G, Fourie A. Compressive behaviour of fibre-reinforced cemented paste backfill. Geotextiles and Geomembranes, 2015, 43(3): 207–215

[19] Wang C, Ren Z, Huo Z, Zheng Y, Tian X, Zhang K, Zhao G. Properties and hydration characteristics of mine cemented paste backfill material containing secondary smelting water-granulated nickel slag. Alexandria Engineering Journal, 2021, 60(6): 4961–4971

[20] Torabi A R, Pirhadi E. Extension of the virtual isotropic material concept to mixed mode I/II loading for predicting the last-ply-failure of U-notched glass/epoxy laminated composite specimens. Composites. Part B, Engineering, 2019, 176: 107287

[21] Torabi A R, Majidi H R, Cicero S, Ibáñez-Gutiérrez F T, Fuentes J D. Experimental verification of the Fictitious Material Concept for tensile fracture in short glass fibre reinforced polyamide 6 notched specimens with variable moisture. Engineering Fracture Mechanics, 2019, 212: 95–105

[22] Ajayi O, Le Pen L, Zervos A, Powrie W. A behavioural framework for fibre-reinforced gravel. Geotechnique, 2017, 67(1): 56–68

[23] Jahanbakhsh P, Saberi K F, Soltaninejad M, Hashemi S H. Laboratory investigation of modified roller compacted concrete pavement (RCCP) containing macro synthetic fibers. International Journal of Pavement Research and Technology, 2022, 1–15

[24] Wang W, Kang H, Li N, Guo J, Girma D Y, Liu Y. Experimental investigations on the mechanical and microscopic behavior of cement-treated clay modified by nano-MgO and fibers. International Journal of Geomechanics, 2022, 22(6): 04022059

[25] Dong Q, Liang B, Jia L, Jiang L. Effect of sulfide on the long-term strength of lead-Zinc tailings cemented paste backfill. Construction & Building Materials, 2019, 200: 436–446

[26] Libos I L S, Cui L. Effects of curing time, cement content, and saturation state on mode-I fracture toughness of cemented paste backfill. Engineering Fracture Mechanics, 2020, 235: 107174

[27] Liu J, Li Y, Qiao L. Analytical solutions of stress intensity factors for a centrally cracked brazilian disc considering tangential friction effects. Rock Mechanics and Rock Engineering, 2022, 55(4): 2459–2470

[28] Xu W, Cao P. Fracture behaviour of cemented tailing backfill with pre-existing crack and thermal treatment under three-point bending loading: Experimental studies and particle flow code simulation. Engineering Fracture Mechanics, 2018, 195: 129–141

[29] Wang X, Yu J, Li Q, Yu Y, Lv H. Study on the crack evolution process and stress redistribution near crack tip in soil. International Journal of Geomechanics, 2022, 22(1): 04021255

[30] Liu J, Zhao L, Chang F, Chi L. Mechanical properties and microstructure of multilayer graphene oxide cement mortar. Frontiers of Structural and Civil Engineering, 2021, 15(4): 1058–1070

[31] Raffaldi M J, Seymour J B, Richardson J, Zahl E, Board M. Cemented paste backfill geomechanics at a narrow-vein underhand cut-and-fill mine. Rock Mechanics and Rock Engineering, 2019, 52(12): 4925–4940

[32] Fang K, Fall M. Effects of curing temperature on shear behaviour of cemented paste backfill-rock interface. International Journal of Rock Mechanics and Mining Sciences, 2018, 112: 184–192

[33] Fang K, Ren L, Jiang H. Development of Mode I and Mode II fracture toughness of cemented paste backfill: Experimental results of the effect of mix proportion, temperature and chemistry of the pore water. Engineering Fracture Mechanics, 2021, 258: 108096

[34] YilmazEFallM. Paste Tailings Management. Cham: Springer International, 2017

[35] Fang K, Fall M. Chemically induced changes in the shear behaviour of interface between rock and tailings backfill undergoing cementation. Rock Mechanics and Rock Engineering, 2019, 52(9): 3047–3062

[36] Libos I L S, Cui L, Liu X. Effect of curing temperature on time-dependent shear behavior and properties of polypropylene fiber-reinforced cemented paste backfill. Construction & Building Materials, 2021, 311: 125302

[37] Koohestani B, Belem T, Koubaa A, Bussière B. Experimental investigation into the compressive strength development of cemented paste backfill containing nano-silica. Cement and Concrete Composites, 2016, 72: 180–189

[38] Ayatollahi M R, Aliha M R M. Fracture parameters for a cracked semi-circular specimen. International Journal of Rock Mechanics and Mining Sciences, 2004, 41: 20–25

[39] Lim I L, Johnston I W, Choi S K. Stress intensity factors for semi-circular specimens under three-point bending. Engineering Fracture Mechanics, 1993, 44(3): 363–382

[40] MatsudaS. Theoretical approach to determine dynamic fatigue strength characteristics of ceramics under variable loading rates on the basis of SCG concept. International Journal of Fracture, 2019, 215(1−2): 175−182

[41] Torabi A R, Jabbari M, Akbardoost J. Scaling effects on notch fracture toughness of graphite specimens under mode I loading. Engineering Fracture Mechanics, 2020, 235: 107153

[42] Huang S, Yan E, Fang K, Li X. Effects of binder type and dosage on the mode I fracture toughness of cemented paste backfill-related structures. Construction & Building Materials, 2021, 270: 121854

[43] Feng G, Kang Y, Wang X. Fracture failure of granite after varied durations of thermal treatment: An experimental study. Royal Society Open Science, 2019, 6(7): 190144

[44] Ayatollahi M R, Aliha M R M. Wide range data for crack tip parameters in two disc-type specimens under mixed mode loading. Computational Materials Science, 2007, 38(4): 660–670

[45] Torabi A R, Jabbari M, Akbardoost J. Mixed mode notch fracture toughness assessment of quasi-brittle polymeric specimens at different scales. Theoretical and Applied Fracture Mechanics, 2020, 109: 102682

[46] Torabi A R, Pirhadi E. Translaminar notch fracture toughness expressions for composite laminates. Theoretical and Applied Fracture Mechanics, 2022, 119: 103332

[47] Fang K, Cui L. Experimental investigation of fiber content and length on curing time-dependent mode-I fracture behavior and properties of cemented paste backfill and implication to engineering design. Fatigue & Fracture of Engineering Materials & Structures, 2022, 45(11): 3302–3318

[48] Torabi A R, Rahimi A S, Ayatollahi M R. Tensile fracture analysis of a ductile polymeric material weakened by U-notches. Polymer Testing, 2017, 64: 117–126

[49] Torabi A R, Rahimi A S, Ayatollahi M R. Fracture study of a ductile polymer-based nanocomposite weakened by blunt V-notches under mode I loading: Application of the Equivalent Material Concept. Theoretical and Applied Fracture Mechanics, 2018, 94: 26–33

[50] Torabi A R, Rahimi A S, Ayatollahi M R. Elastic-plastic fracture assessment of CNT-reinforced epoxy/nanocomposite specimens weakened by U-shaped notches under mixed mode loading. Composites. Part B, Engineering, 2019, 176: 107114

[51] Torabi A R, Rahimi A S, Ayatollahi M R. Mixed mode I/II fracture prediction of blunt V-notched nanocomposite specimens with nonlinear behavior by means of the Equivalent Material Concept. Composites. Part B, Engineering, 2018, 154: 363–373

[52] Rahimi A S, Ayatollahi M R, Torabi A R. Ductile failure analysis of blunt V-notched epoxy resin plates subjected to combined tension-shear loading. Polymer Testing, 2018, 70: 57–66

[53] Aliha M R M, Saghafi H. The effects of thickness and Poisson’s ratio on 3D mixed-mode fracture. Engineering Fracture Mechanics, 2013, 98: 15–28

[54] Yuan X, Tian Y, Liu Q, Liu S, Dou Q, Aliha M R M. K_Ic and K_IIc measurement for hot mix asphalt mixtures at low temperature: Experimental and theoretical study using the semicircular bend specimen with different thicknesses. Fatigue & Fracture of Engineering Materials & Structures, 2021, 44(3): 832–846

[55] Vizini V O S, Futai M M. Mode II fracture toughness determination of rock and concrete via Modified Direct Shear Test. Engineering Fracture Mechanics, 2021, 257: 108007

[56] Holthusen D, Batistão A C, Reichert J M. Amplitude sweep tests to comprehensively characterize soil micromechanics: Brittle and elastic interparticle bonds and their interference with major soil aggregation factors organic matter and water content. Rheologica Acta, 2020, 59(8): 545–563

[57] Barani O R, Khoei A R, Mofid M. Modeling of cohesive crack growth in partially saturated porous media: A study on the permeability of cohesive fracture. International Journal of Fracture, 2011, 167(1): 15–31

[58] Shen Z, Jiang M, Thornton C. Shear strength of unsaturated granular soils: Three-dimensional discrete element analyses. Granular Matter, 2016, 18(3): 1–13

[59] Rahimi-Aghdam S, Bažant Z P, Abdolhosseini Qomi M J. Cement hydration from hours to centuries controlled by diffusion through barrier shells of CSH. Journal of the Mechanics and Physics of Solids, 2017, 99: 211–224

[60] Dong P, Allahverdi A, Andrei C M, Bassim N D. Liquid cell transmission electron microscopy reveals C-S-H growth mechanism during Portland cement hydration. Materialia, 2022, 22: 101387

[61] Jiang H, Fall M, Li Y, Han J. An experimental study on compressive behaviour of cemented rockfill. Construction & Building Materials, 2019, 213: 10–19

[62] Yilmaz E, Belem T, Bussière B, Mbonimpa M, Benzaazoua M. Curing time effect on consolidation behaviour of cemented paste backfill containing different cement types and contents. Construction & Building Materials, 2015, 75: 99–111

[63] Pane I, Hansen W. Investigation of blended cement hydration by isothermal calorimetry and thermal analysis. Cement and Concrete Research, 2005, 35(6): 1155–1164

[64] Ahmadinezhad A, Jafarzadeh F, Sadeghi H. Combination of water head control and axis translation techniques in new unsaturated cyclic simple shear tests. Soil Dynamics and Earthquake Engineering, 2019, 126: 105818

[65] Lu S, Lu Y, Peng W, Ju Z, Ren T. A generalized relationship between thermal conductivity and matric suction of soils. Geoderma, 2019, 337: 491–497

[66] Cui L, Fall M. An evolutive elasto-plastic model for cemented paste backfill. Computers and Geotechnics, 2016, 71: 19–29

[67] Cui L, Fall M. A coupled thermo–hydro-mechanical–chemical model for underground cemented tailings backfill. Tunnelling and Underground Space Technology, 2015, 50: 396–414

[68] Fang K, Fall M. Shear behaviour of rock–tailings backfill interface: Effect of cementation, rock type, and rock surface roughness. Geotechnical and Geological Engineering, 2021, 39(3): 1753–1770

[69] Cui L, Fall M. Mechanical and thermal properties of cemented tailings materials at early ages: Influence of initial temperature, curing stress and drainage conditions. Construction & Building Materials, 2016, 125: 553–563

RIGHTS & PERMISSIONS

Higher Education Press