Time- and temperature-dependence of compressive and tensile behaviors of polypropylene fiber-reinforced cemented paste backfill

Abstract

The understanding of compressive and tensile behaviors of polypropylene fiber-reinforced cemented paste backfill (FR-CPB) play crucial roles in the successful implementation of reinforcement technique in underground mine backfilling operations. However, very limited studies have been performed to gain insight into the evolution of compressive and tensile behaviors and associated mechanical properties of FR-CPB under various curing temperatures from early to advanced ages. Thus, this study aims to investigate the time (7, 28, and 90 d)- and temperature (20°C, 35°C, and 45°C)-dependence of constitutive behavior and mechanical properties of FR-CPB. The obtained results show that pre- and post-failure behaviors of FR-CPB demonstrate strongly curing temperature-dependence from early to advanced ages. Moreover, the pseudo-hardening behavior is sensitive to curing temperature, especially at early ages. Furthermore, the mechanical properties including elastic modulus, material stiffness, strengths, brittleness, cohesion, and internal friction angle of FR-CPB show increasing trends with curing temperature as curing time elapses. Additionally, a predictive model is developed to capture the strong correlation between compressive and tensile strength of FR-CPB. The findings of this study will contribute to the successful implementation of FR-CPB technology.

Graphical abstract

Keywords

cemented paste backfill / fiber reinforcement / constitutive behavior / temperature / tailings

1 Introduction

To provide effectively and reliably secondary ground support to the underground excavations (called stopes) generated during natural minerals extraction process, cemented paste backfill (CPB, a man-made construction material consisted of total mill tailings or other wastes, cement, and mixing water) has been increasingly employed in the modern underground mines around the world [ 1, 2]. However, underground mining activities can reach a depth greater than 1000 m [ 3]. Due to the geothermal gradient (approximately (25°C−45°C)/km [ 4]), the mine backfill materials are commonly exposed to warmer curing temperatures in the deep underground stopes. As a result, the warmer curing temperature accelerates cement hydration [ 5] and generates more hydration products including calcium hydroxide, calcium silicate hydrate and ettringite in the pore space for a given curing period [ 6]. Consequently, a more cohesive and denser CPB matrix can be formed at warmer curing temperatures as curing time elapses, which significantly increases the mechanical strengths including unconfined compressive strength (UCS) [ 7], tensile strength [ 8], and shear strength [ 9]. Therefore, the time- and curing temperature-dependence of CPB must be fully considered in the mine backfill design.

As a type of cementitious materials, the weak tensile strength of CPB relative to its compressive strength imposes safety risks on underground mining activities [ 10, 11]. For instance, in the deep underground mine with narrow and steeply dipping veins of ore, the underhand cut-and-fill stopping method is widely adopted [ 12]. Correspondingly, the massive CPB beam must provide sufficient tensile strength to ensure the safety of personnel and mining equipment under the hardened CPB mass. To improve the mechanical behavior of CPB materials, polypropylene (PP) fiber reinforcement has been considered a promising technique in CPB design [ 13, 14]. Several experimental studies have been carried out to experimentally investigate the tensile strength of fiber-reinforced CPB (FR-CPB). For example, through splitting tensile strength (STS) tests, it has been proven that PP fiber can improve the tensile strength of FR-CPB to a greater extent [ 10, 15]. Apart from the improvement of tensile strength, it has also been found that fiber inclusion can effectively enhance the compressive strength of CPB and thus reduce the usage of costly cement [ 16]. Additionally, the fiber reinforcement can significantly enhance the ductility of CPB materials through its crack bridging effect [ 17].

The previous experimental studies have significantly improved our understanding of the compression and tension behavior of FR-CPB. However, it should be noted that the effectiveness of fiber reinforcement is dependent mainly on the fiber-CPB matrix interfacial interaction. Consequently, the more cohesive and denser CPB matrix formed at warmer curing temperatures affects the extent of fiber reinforcement and the evolutive mechanical behaviors of FR-CPB as curing time elapses. However, as a key design concern, the curing time and curing temperature sensitivity of compressive and tensile behavior of FR-CPB has not been studied yet. Therefore, a series of UCS tests and STS tests were conducted to 1) investigate the effect of curing temperature (20°C, 35°C, and 45°C) on the evolutive constitutive behavior (i.e., stress-strain behavior from UCS tests and force-displacement behavior from STS tests) and mechanical properties (elastic modulus, material stiffness, UCS, STS, material brittleness, cohesion, and internal friction angle) of FR-CPB at 7, 28, and 90 d; and 2) quantitatively evaluate the correlation between UCS and STS of FR-CPB, which can make it easier for backfill engineers to assess the mechanical strengths of FR-CPB based on limited testing data.

2 Materials and methods

2.1 Materials

Silicon dioxide has been identified as the major mineral in hard rock mines in Canada [ 18]. Due to its chemically inert nature, the usage of silicon dioxide can effectively minimize the uncertainties (e.g., sulfate effect on pore structure and mechanical properties of CPB [ 19, 20]) associated with natural tailings. Therefore, quartz tailings (consisted of 99.8% silicon dioxide, manufacturer: US Silica company) were chosen in this study. Based on the results of particle size distribution analysis (Fig. 1), the D-values including D₁₀ = 1.9 μm, D₃₀ = 8.5 μm, and D₆₀ = 25.7 μm were determined and thus uniformity coefficient ( C_U = D₆₀/ D₁₀ = 13.7), and coefficient of gradation ( C_c = D₃₀²/( D₁₀ × D₆₀) = 27.2) were obtained. For the binding agent, GU Portland cement (manufacturer: CRH group) was adopted due to its relatively low cost, wide availability and versatility, which has been extensively used in backfill formulation [ 21, 22]. Tap water was used as mixing water. The water chemistry can influence cement hydration and thus the mechanical properties and behavior of CPB materials. The effect of mixing water has been investigated in a previous study [ 23]. The PP fibers are thermoplastic polymer which can effectively reduce the segregation and offer high crack control in cement-based materials [ 15, 17, 24]. Moreover, compared with other synthetic fibers including polyacrylonitrile and glass fiber, it has been found PP fibers can improve the compressive strength of CPB to a greater extent [ 25]. Therefore, monofilament PP microfibers (Manufacturer: Euclid Chemical company) were utilized. The material properties of the PP microfibers are listed in Table 1.

2.2 Mix ratios and specimen preparation

FR-CPB specimens were prepared with a water to cement ( w/ c) ratio of 7.6, a cement content ( C_m) of 4.5% and a fiber content of 0.5% (measured with reference to the weight of solid phase). Since the objective of this study is to uncover the time- and temperature dependence of mechanical behaviors of FR-CPB, the effects of fiber types and contents were not considered in the present study. Detailed information about the effects of fiber parameters can be found in the published work [ 13, 16, 26, 27]. Moreover, the previous study [ 13] found FR-CPB with a fiber content of 0.5% and a cement content of 5% is able to enhance material strength by 70%–90%, which is similar to the mix recipe adopted in this study. A group of control CPB specimens without addition of fibers was also prepared for comparative analysis. According to ASTM C192 [ 28], the mixing operation was conducted by two phases, including dry and wet mixing. Based on previous experimental studies on CPB [ 5, 29, 30], the mixing time greater than three minutes were commonly adopted to ensure the material homogeneity. Therefore, the dry mixing of GU cement, tailings, and PP fibers was first conducted for five minutes. Then, tap water was added to the dry materials and mixed for eight minutes. Then, the fresh paste was poured into plastic cylinder molds with two different sizes: 1) 5 cm (D) × 10 cm (H) for UCS tests, and 2) 10 cm (D) × 20 cm (H) for STS tests. The smaller molds can be used to obtain standard CPB specimens with a height-to-length ratio of 2, and the specimens obtained from the larger molds will be trimmed into circular disk-shaped specimens with a thickness of 5 cm and a diameter of 20 cm. Therefore, the height of specimens for UCS tests is same to the diameter of specimens for STS tests, which will further limit the size effect on the testing results. The molds were covered by matching lids and attached by waterproof tapes. After that, the prepared samples were cured at 20°C (room temperature), and oven-controlled warmer curing temperatures including 35°C and 45°C for 7, 28, and 90 d curing periods, respectively. The adopted mix recipe and curing conditions are summarized inTable 2.

2.3 Testing methods

2.3.1 Unconfined compressive strength tests

To study the compression behavior of FR-CPB cured at different temperatures, UCS tests were performed on FR-CPB and control specimens according to ASTM C39 [ 31]. A linear variable differential transformer (LVDT, 25-mm capacity from A-Tech Instruments Ltd.) was used to record the axial displacement. The displacement rate was set to 1 mm/min. A 1000-lbs capacity load cell (Manufacturer: ARTECH Industries, Inc.) was used to measure the axial load. To improve the accuracy and reproducibility of the UCS tests, three replicate specimens were tested for each curing condition. Based on the obtained results from UCS tests, the material properties (elastic modulus and UCS) and compression behavior (i.e., stress-strain curves) were retrieved from the measured data.

2.3.2 Splitting tensile strength tests

According to ASTM 3967−16 [ 32], STS tests were performed on FR-CPB and control specimens. For each curing condition, STS tests were conducted a minimum of three times to ensure repeatability of testing results. To maintain the comparability of measured results from UCS and STS tests, the same displacement rate (1 mm/min) was adopted in STS tests. Moreover, the applied vertical load and loading point displacement were measured through the same load cell and LVDT used in UCS tests. Through the experimental data from STS tests, the tension behavior (force-displacement curves) and material stiffness (slope of straight-line portion of the stress-displacement curve) were obtained.

2.3.3 Long-term monitoring program

The progression of cement hydration is accompanied by the pore-water consumption [ 33]. The resultant self-desiccation process inevitably weakens the pore-water induced lubricant effect between tailings particles and fibers. Moreover, the transition from fully to partially saturated states also causes the development of matric suction in CPB, which contributes to the evolution of mechanical behavior and properties of FR-CPB. To clearly demonstrate the changes in the moisture content and matric suction, a long-term monitoring program (see Fig. 2) was conducted on FR-CPB specimens under different curing temperatures (20°C, 35°C, and 45°C) for 90 d. A water bath (model: Humboldt H-1392) was adopted to accurately control the warmer curing temperatures during the monitoring period. The matric suction sensor (model: T5X) and volumetric water content sensor (model: 5TE) were employed in this study. A ZL6 data logger was used to collect the monitoring data.

2.3.4 Scanning electron microscopy (SEM) analysis

The changes in the microstructure of 7 d FR-CPBs cured at 20°C, 35°C, and 45°C were investigated through a Hitachi Su-70 Schottky Field Emission SEM (Manufacturer: Hitachi High-Tech Global). The selected FR-CPB samples were first oven-dried at 45°C for 24 h to remove the pore water from CPB matrix. The oven-drying operation below 50°C for 24 h has been widely adopted in previous studies [ 11, 34, 35] to limit the influence of drying temperature on the microstructure of CPB matrices. Then, the obtained dry FR-CPBs were cut into small cuboid samples (approximately 1 cm ³) for the SEM observation.

3 Results and analysis

3.1 Evolutive constitutive behavior of FR-CPB under different curing temperatures

3.1.1 Early-age compressive and tensile behavior of FR-CPB under different curing temperatures

The comparison of constitutive curves of early-age (7 d) FR-CPB subjected to various curing temperatures is presented in Fig. 3. From this figure, it can be observed that curing temperature significantly affects the pre- and post-failure behavior of FR-CPB subjected to axial compressive and tensile stresses. Specifically, at the pre-failure stage, the hardening behavior becomes more evident with the increased curing temperature. Correspondingly, the slopes (i.e., elastic modulus in Fig. 3(a), and material stiffness in Fig. 3(b)) of the loading curves become steeper as curing temperature increases. This is because, as shown in Fig. 4, a more cohesive and denser CPB matrix can be formed at warmer curing temperatures. Therefore, the resultant stiffer and stronger CPB resists the deformation to a higher extent and thus causes an enhanced hardening behavior. However, it should be noted that the loading portions of FR-CPB and control CPB cured at the same temperature (20°C) are close to each other, which indicates the relatively limited effect of fiber inclusion on the pre-failure behavior.

In the post-peak region, softening behavior can be observed in both compressive and tensile unloading processes and becomes more apparent as curing temperature increases. The strain corresponding to peak stress (Fig. 3(a)) and displacement corresponding to peak loads (Fig. 3(b)) decrease with the increased curing temperature, which implies the reduced tolerance capacity of plastic deformation and the loss of material ductility at warmer curing temperatures. However, there exist some distinct aspects of the compressive and tensile behaviors of FR-CPB at the post-failure stage. First, early-age FR-CPB shows inconsistent residual compressive strengths, while similar residual tensile resistance forces are observed in the STS tests. This is because, as shown in Fig. 5, the shear cracks are commonly observed in FR-CPB specimens under compressive tests. Correspondingly, frictional resistance can be mobilized along the shear crack surfaces [ 36] and contributes to the residual compressive strength. Moreover, due to the lubricant effect of pore water between solid particles [ 37], a larger interparticle shear resistance can develop when more pore water is consumed by the accelerated cement hydration at a warmer curing temperature. Consequently, a higher residual compressive strength is obtained from FR-CPB cured at a warmer temperature. However, no friction mobilization occurs along tensile cracks, which indicates only the fiber bridging contributes to the residual tensile resistance forces across the tensile cracks. Therefore, compared with residual compressive strengths, the difference among residual tensile resistance forces becomes unnoticeable in FR-CPB under STS tests. Second, as shown in Fig. 3(b), it is interesting to find that an enhanced pseudo hardening behavior (i.e., a second peak force) appears at the post-failure stages. The pseudo hardening behavior can be explained by the progressive development of passive fiber bridging effect in the post-failure region [ 38, 39]. As discussed previously, the warmer curing temperature contributes to a more cohesive and denser CPB matrix which can hold the fibers to a greater extent. Consequently, an improved pseudo hardening behavior is obtained from FR-CPB cured at a warmer temperature.

3.1.2 Advanced-age compressive and tensile behavior of FR-CPB under different curing temperatures

Figure 6 presents the typical constitutive curves of advanced-age (90 d) FR-CPB cured at various temperatures. From this figure, it can be clearly seen that the constitutive behavior of advanced-age FR-CPB still shows strong temperature-dependent hardening behavior at the pre-failure stage and softening behavior at the post-failure stage. However, compared with the early-age constitutive behavior (see Fig. 3), advanced-age FR-CPB illustrates noticeable differences in the post-failure regimes. First, for the post-failure compressive behavior, FR-CPB shows similar residual compressive strengths. This is because cement hydration consumes large amounts of pore water at advanced ages [ 40, 41]. As a result, the lubricant effect of pore water becomes weaker at advanced ages. Therefore, similar friction mobilization takes place along the shear failure surfaces in advanced-age FR-CPB, and thus yields similar residual strengths. Second, the pseudo hardening behavior becomes relatively unnoticeable compared with those observed in early-age FR-CPB under STS tests. The weakened pseudo hardening behavior can be interpreted by the combined effect of cohesion loss along tensile crack surfaces and fiber pullout from CPB matrix after the peak force. Specifically, advanced-age CPB cured at a warmer temperature possesses a higher cohesion. Consequently, the loss of higher cohesion along tensile cracks after peak force directly causes the comparatively weak pseudo hardening behavior induced by the fiber bridging effect. The detailed discussion on the cohesion of FR-CPB specimens is presented in Subsection 3.2.3. Moreover, the abruptly released strain energy after the peak resistance force is partially dissipated by the tensile crack propagation and partially consumed by the stress redistribution around fibers (see Fig. 7). For the latter, the loss of large cohesion and the associated release of large strain energy may cause the fiber pullout and thus weaken the fiber bridging effect in CPB matrix and the pseudo hardening behavior.

3.2 Evolutive mechanical properties of FR-CPB under different curing temperatures

Based on the obtained results (see Figs. 3 and 6), it has been found the curing temperature can affect pre- and post-failure constitutive behavior of FR-CPB from early to advanced ages. Therefore, it is necessary to investigate the curing temperature sensitivity of the associated mechanical properties, including resistance to elastic deformation (elastic modulus and material stiffness), peak compressive and tensile strength, material brittleness, cohesion, and internal friction angle. The detailed discussion about the effect of curing temperature on the mechanical properties of FR-CPB is presented in the following subsections.

3.2.1 Elastic modulus and material stiffness of FR-CPB

The material resistance to being deformed elastically can be quantitatively evaluated by the elastic modulus from compressive stress-strain curves and material stiffness from the tensile load-displacement curves. To ensure the comparability of material resistance to elastic deformation, the secant modulus at 50% peak stress and secant stiffness at 50% peak force are determined in this study. The calculated elastic modulus and material stiffness are presented in Figs. 8(a) and 8(b), respectively. It can be seen that FR-CPB cured at a warmer curing temperature possesses a higher resistance to non-permanent deformation. The effect of enhanced resistance to the elastic deformation on the mechanical behavior of FR-CPB is twofold. First, the stiffer FR-CPB formed at a warmer curing temperature is able to provide more immediate support when subjected to the static and dynamic loadings from surrounding rock walls and thus contributes to the mechanical stability of underground openings. Secondly, based on the studies on the cemented soil [ 42, 43] and concrete [ 44, 45], a more brittle constitutive behavior is commonly featured in the stiffer cementitious materials, which may cause brittle failure in CPB subjected to finite deformations. Moreover, through a comparison with the control CPB cured at 20°C, it is interesting to find that the addition of fibers has a limited effect on the magnitude of elastic modulus and material stiffness of FR-CPB cured at the same temperature. This can be interpreted by the higher elastic modulus of cement hydration products (over 30 GPa after 7 d [ 46]) relative to that (approximately 3 GPa [ 47, 48]) of PP fibers. Consequently, the elastic response of FR-CPB is dependent mainly on the stiffer binding agent between tailings particles. Therefore, fiber inclusion plays a relatively limited role in the elastic properties of CPB materials.

3.2.2 Compressive and tensile strength of FR-CPB

Figure 9 shows the evolution of compressive strength and tensile strength of FR-CPB cured at different temperatures from early to advanced ages. Compared with FR-CPB cured at 20°C, significant improvement of material strength is obtained from FR-CPB cured at a warmer temperature. Moreover, it is worth noting that strength improvement of FR-CPB cured at a warmer temperature becomes more evident at advanced ages. For example, compared with the FR-CPB cured at 20°C (see Fig. 9(a)), FR-CPB cured at 45°C shows improvement in 7 and 90 d UCS, with 43% (from 543 to 777 kPa) and 165% (from 1135 to 2365 kPa) increase, respectively. A similar improvement is observed in the long term tensile strength as well (see Fig. 9(b)). The significant strength improvement at advanced ages can be mainly explained by the strengthened fiber-matrix interfacial interaction as the progress of cement hydration. This is because a denser and more cohesive CPB matrix can be formed at a warmer curing temperature and thus results in a stronger interfacial friction and bonding force between fibers and tailings particles. Consequently, the desirable effect of fiber bridging can be further strengthened at advanced ages with a warmer curing temperature, which contributes directly to the control of crack propagation in CPB matrix and the improvement of material strengths. Moreover, the strength improvement can also be attributed to the development of matric suction in the porous CPB matrix. Specifically, pore-water consumption by cement hydration causes a continuous transition of CPB from fully to partially saturated states and the formation of air-water (AW) interface within the porous matrix. To maintain the stability of AW interface, the pressure jump (i.e., matric suction) induced by the pore air and pore water is balanced by the combined effect of AW surface tension and capillary force [ 11, 49]. Consequently, the developed matric suction holds the solid particles to a higher extent and thus contributes to a stronger porous matrix. As shown in Fig. 10, the matric suction gradually increases from early to advanced ages and the development of matric suction becomes more pronounced as curing temperature increases. Therefore, the contribution of matric suction to the improvement of material strength is dependent on the curing temperature as well. Furthermore, compared with the improvement of material strength induced by the warmer curing temperature, FR-CPB and control CPB cured at the same temperature (20°C) show relatively less variation in strengths with curing time. Therefore, due to the temperature dependence of cement hydration and its effect on the fiber-CPB matrix interfacial interaction, the extent of fiber reinforcement is dependent on the curing temperature.

3.2.3 Material brittleness of FR-CPB

Based on the obtained constitutive behavior (see Figs. 3 and 6), the enhanced softening behavior is featured at the post-failure stage of FR-CPB cured at a warmer temperature, especially at advanced ages. The greater loss in material strength associated with the strengthened softening behavior illustrates the development of material brittleness. Because the material brittleness controls the tolerance capacity of plastic deformation, it is important to quantitatively evaluate the curing temperature sensitivity of material brittleness of FR-CPB. However, there are no reliable direct measurement methods for the determination of material brittleness [ 50]. Correspondingly, a series of indirect determination approaches of material brittleness was proposed based on stain at failure [ 51, 52], elastic modulus [ 53], friction angle [ 54], and material strengths [ 54, 55]. A previous study on cementitious materials [ 56] has found that the difference between compressive strength and tensile strength can be used to characterize the material brittleness. Therefore, the brittleness index ( B _I) defined by compressive strength ( σ _c) and tensile strength ( σ _t) [ 54] was adopted in this study:

(1) B_{\mathrm{I}} = \frac{{\sigma }_{\mathrm{c}}-{\sigma }_{\mathrm{t}}}{{\sigma }_{\mathrm{c}}+{\sigma }_{\mathrm{t}}} .

Figure 11 shows the evolution of the brittleness index of FR-CPB cured at different temperatures. Compared with control CPB, FR-CPB cured at the same temperature (20°C) possesses a smaller B_I. This is because fibers can absorb and dissipate the strain energy and thus prevent crack propagation in CPB matrix. As a result, a larger permanent deformation can be tolerated by the FR-CPB. Therefore, fiber reinforcement can be used as an effective mitigation technique of brittle failure in CPB design. However, it can also be observed that the warmer curing temperature can significantly increase the material brittleness. This is partly because of the higher elastic modulus (see Fig. 8(a)) and material stiffness (see Fig. 8(b)) formed at warmer curing temperatures. Correspondingly, a relatively small deformation may cause greater changes in the resistance stress and force at the pre-failure stage. As a result, the strain associated with peak stress (see Figs. 3(a) and 6(a)) and displacement linked to the peak load (see Figs. 3(b) and 6(b)) are reduced with the increased curing temperature. Moreover, a larger cohesion can be formed at warmer curing temperatures. Since cohesion cannot be mobilized along crack surfaces, the loss of higher cohesion after peak stress and peak force not only strengthens the softening behavior, but also reduces the material tolerance of inelastic deformation. In consequence, a more brittle response can be observed from FR-CPB cured at warmer temperatures, which may cause an adverse effect on the mechanical stability of FR-CPB mass subjected to finite deformations.

3.2.4 Shear strength parameters of FR-CPB

As a type of cementitious material, cohesion ( c) and internal friction angle ( ϕ) play critical roles in mechanical behavior and material strength. According to the Mohr−Coulomb (M−C) failure theory, c and ϕ can be respectively determined by the intercept of the linear envelope of shear failure with shear stress axis and its slope angle. Therefore, the stress states at compressive and tensile failure can be utilized to draw the Mohr’s circles and thus determine c and ϕ (see Fig. 12). Specifically, at the compressive failure, the major principal stress is represented by the UCS ( σ_c = UCS), and the minor principal stress is zero. For the STS tests on the circular specimens, it has been derived that the magnitude of compressive stress ( σ_t-r) in radial loading direction is three times the tensile stress ( σ_t) in the transverse horizontal direction (i.e., σ_t-r = −3 σ_t) [ 57, 58]. Therefore, the M−C failure criterion can be explicitly expressed by the principal stresses at failure from UCS and STS tests, respectively:

(2) \frac{{\sigma }_{\mathrm{c}}}{2} = \frac{{\sigma }_{\mathrm{c}}}{2} \sin \varphi + c \cos \varphi ,

(3) 2 {\sigma }_{\mathrm{t}} = {\sigma }_{\mathrm{t}} \sin \varphi + c \cos \varphi .

From Eqs. (2) and (3), the cohesion and internal friction angle can be derived as follows:

(4) \varphi = {\sin }^{-1} \left(\frac{{\sigma }_{\mathrm{c}}-4{\sigma }_{\mathrm{t}}}{{\sigma }_{\mathrm{c}}-2{\sigma }_{\mathrm{t}}}\right) ,

(5) c = \frac{{\sigma }_{\mathrm{c}}{\sigma }_{\mathrm{t}}}{2\sqrt{{\sigma }_{\mathrm{t}}\left({\sigma }_{\mathrm{c}}-3{\sigma }_{\mathrm{t}}\right)}} .

Based on Eqs. (4) and (5), the calculated c and ϕ are presented in Fig. 13. From this figure, it can be found that c and ϕ of FR-CPB show increasing trends with curing temperature. The evolution of c and ϕ is intimately related to cement hydration. Specifically, the warmer curing temperature increases the cement hydration rate and thus contributes directly to the formation of higher cohesion. Meanwhile, the capillary water is consumed by cement hydration to a greater extent under warmer curing temperatures (see Fig. 14), which further weakens the lubricant effect of pore water and strengthens the frictional resistance between tailings particles under shear stress. Consequently, a higher internal friction angle is obtained from CPB cured at a warmer temperature. Moreover, compared with control CPB, higher c and ϕ are obtained from FR-CPB cured at the same temperature (20°C). This is because the dowel action of longitudinal fiber across the shear cracks can transfer the shear stress to reinforcements [ 59, 60] and provide an increase into the shear strength. As a result, the shear strength parameters including c and ϕ increase when the fibers are introduced to the CPB matrix.

3.3 Correlation between the compressive and tensile strength of FR-CPB

As discussed in the introduction, the tensile and compressive stresses widely exist in CPB mass under complex field loading conditions. Therefore, the determination of compressive strength and tensile strength is needed by the mechanical stability assessment of FR-CPB mass. To simplify the analysis, it is necessary to establish the correlation between compressive strength and tensile strength. Therefore, the following predictive model is proposed based on the regression analysis of the measured data in this study.

(6) {\sigma }_{\mathrm{t}} = A {\sigma }_{\mathrm{c}}^B ,

where A and B are fitting parameters. A = 0.627 and B = 0.766 were obtained through regression analysis. Figure 15 presents the comparison of measured data and predicted results through Eq. (6). From Fig. 15(a), it can be seen that the tensile strength displays a strong correlation with the compressive strength. The ratio between compressive strength and tensile strength gradually increases from approximately 6 to 10 as curing time elapses. The close link between material strengths can be further confirmed by the very high coefficient of determination ( R² = 0.98) obtained from measured tensile strength and predicted results through Eq. (6) (see Fig. 15(b)). Therefore, the proposed model can be used to estimate the tensile strength of FR-CPB when UCS values are available. It should be noted since there is no published work on the correlation of compressive and tensile strengths of FR-CPB, only the measured data from this study were used to validate the proposed model. Therefore, further studies are recommended to improve the predictability of the developed model.

4 Conclusions

In this study, the time- and temperature-dependence of geomechanical behavior of FR-CPB. The following findings can be drawn based on the experimental and analytical results.

1) Pre- and post-failure behavior of FR-CPB subjected to compressive and tensile stresses are sensitive to the curing time and temperatures. Hardening and softening behavior becomes more obvious as the curing temperature increases from early to advanced ages. Moreover, the pseudo hardening behavior is commonly featured in the tensile behavior of FR-CPB and shows strong temperature sensitivity, especially during the early ages.

2) The elastic modulus and material stiffness can be improved to a greater extent when FR-CPB is cured at a warmer temperature. The stiffer FR-CPB formed at warmer curing temperature indicates the backfill mass is able to offer more immediate secondary support to the surrounding walls and thus contribute to the stope stability.

3) The compressive strength and tensile strength become more sensitive to the curing temperature at advanced ages. The significant improvement of the material strength of advanced-age FR-CPB implies that warmer curing temperature is able to strengthen the fiber-matrix interfacial interaction and thus the bridging effect in the CPB matrix. Therefore, with the development of cementation between tailings particles, fiber reinforcement can significantly improve the long-term material strengths of CPB cured at a warmer temperature.

4) Due to the reduced strain corresponding to peak stress and strengthened softening behavior at the post-failure stage, the material brittleness is enhanced in FR-CPB cured at warmer curing temperatures. The increased brittleness may cause an adverse effect on the mechanical stability of FR-CPB mass under finite deformations induced by surrounding rock contraction.

5) The cohesion and internal friction angle show increasing trends with curing temperature, which can be attributed to the combined effect of cement hydration and dowel action of fiber reinforcement across shear cracks.

6) A predictive model was proposed to capture the strong correlation between compressive strength and tensile strength of FR-CPB, which can be used to predict the material strengths when limited data are available.

References

[1] Lu G, Fall M, Cui L. A multiphysics-viscoplastic cap model for simulating blast response of cemented tailings backfill. Journal of Rock Mechanics and Geotechnical Engineering, 2017, 9( 3): 551– 564

[2] Chen Q S, Sun S Y, Liu Y K, Qi C C, Zhou H B, Zhang Q L. Experimental and numerical study on immobilization and leaching characteristics of fluoride from phosphogypsum based cemented paste backfill. International Journal of Minerals, Metallurgy and Materials, 2021 (in press)

[3] Qian Q, Lin P. Safety risk management of underground engineering in China: Progress, challenges and strategies. Journal of Rock Mechanics and Geotechnical Engineering, 2016, 8( 4): 423– 442

[4] Pourmalek A, Shariatipour S M. Dependence on temperature and salinity gradients and the injection rate of CO ₂ storage in saline aquifers with an angular unconformity. Journal of Porous Media, 2019, 22( 8): 1065– 1078

[5] 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

[6] Bazhuni M F, Kamali M, Ghahremaninezhad A. An investigation into the properties of ternary and binary cement pastes containing glass powder. Frontiers of Structural and Civil Engineering, 2019, 13( 3): 741– 750

[7] Walske M L, McWilliam H, Doherty J, Fourie A. Influence of curing temperature and stress conditions on mechanical properties of cementing paste backfill. Canadian Geotechnical Journal, 2015, 53( 1): 148– 161

[8] Fall M, Célestin J, Pokharel M, Touré M. A contribution to understanding the effects of curing temperature on the mechanical properties of mine cemented tailings backfill. Engineering Geology, 2010, 114( 3–4): 397– 413

[9] 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

[10] Chen X, Shi X, Zhou J, Yu Z. Influence of polypropylene fiber reinforcement on tensile behavior and failure mode of tailings cemented paste backfill. IEEE Access, 2019, 7 : 69015– 69026

[11] 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–

[12] Kumar D, Singh U K, Singh G S P. Laboratory characterization of cemented rock fill for underhand cut and fill method of mining. Journal of the Institution of Engineers (India): Series D, 2016, 97( 2): 193– 203

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

[14] 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–

[15] Cao S, Zheng D, Yilmaz E, Yin Z, Xue G, Yang F. Strength development and microstructure characteristics of artificial concrete pillar considering fiber type and content effects. Construction & Building Materials, 2020, 256 : 119408–

[16] Xu W, Li Q, Zhang Y. Influence of temperature on compressive strength, microstructure properties and failure pattern of fiber-reinforced cemented tailings backfill. Construction & Building Materials, 2019, 222 : 776– 785

[17] Chen X, Shi X, Zhou J, Chen Q, Li E, Du X. Compressive behavior and microstructural properties of tailings polypropylene fibre-reinforced cemented paste backfill. Construction & Building Materials, 2018, 190 : 211– 221

[18] Cui L, Fall M. Multiphysics modeling and simulation of strength development and distribution in cemented tailings backfill structures. International Journal of Concrete Structures and Materials, 2018, 12( 1): 1– 22

[19] Pokharel M, Fall M. Combined influence of sulphate and temperature on the saturated hydraulic conductivity of hardened cemented paste backfill. Cement and Concrete Composites, 2013, 38 : 21– 28

[20] Wang Y, Cao Y, Cui L, Si Z, Wang H. Effect of external sulfate attack on the mechanical behavior of cemented paste backfill. Construction & Building Materials, 2020, 263 : 120968–

[21] Tariq A, Yanful E K. A review of binders used in cemented paste tailings for underground and surface disposal practices. Journal of Environmental Management, 2013, 131 : 138– 149

[22] 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

[23] Wu A, Wang Y, Wang H, Yin S, Miao X. Coupled effects of cement type and water quality on the properties of cemented paste backfill. International Journal of Mineral Processing, 2015, 143 : 65– 71

[24] Cao S, Xue G, Yilmaz E. Flexural behavior of fiber reinforced cemented tailings backfill under three-point bending. IEEE Access, 2019, 7 : 139317– 139328

[25] Cao S, Yilmaz E, Song W. Fiber type effect on strength, toughness and microstructure of early age cemented tailings backfill. Construction & Building Materials, 2019, 223 : 44– 54

[26] Xu W, Chen W, Tian M, Guo L. Effect of temperature on time-dependent rheological and compressive strength of fresh cemented paste backfill containing flocculants. Construction & Building Materials, 2021, 267 : 121038–

[27] Xu W, Zhang Y, Zuo X, Hong M. Time-dependent rheological and mechanical properties of silica fume modified cemented tailings backfill in low temperature environment. Cement and Concrete Composites, 2020, 114 : 103804–

[28] ASTM C192/C192M–18. Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory. West Conshohocken, PA: ASTM International, 2018

[29] Chen Q, Zhang Q, Qi C, Fourie A, Xiao C. Recycling phosphogypsum and construction demolition waste for cemented paste backfill and its environmental impact. Journal of Cleaner Production, 2018, 186 : 418– 429

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

[31] ASTM C39/C39M–18. Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. West Conshohocken, PA: ASTM International, 2018

[32] ASTM D3967–16. Standard Test Method for Splitting Tensile Strength of Intact Rock Core Specimens. West Conshohocken, PA: ASTM International, 2016

[33] Sun B, Wu H, Song W, Li Z, Yu J. Hydration, microstructure and autogenous shrinkage behaviors of cement mortars by addition of superabsorbent polymers. Frontiers of Structural and Civil Engineering, 2020, 14( 5): 1274– 1284

[34] Ghirian A, Fall M. Coupled behavior of cemented paste backfill at early ages. Geotechnical and Geological Engineering, 2015, 33( 5): 1141– 1166

[35] Haruna S, Fall M. Strength development of cemented tailings materials containing polycarboxylate ether-based superplasticizer: Experimental results on the effect of time and temperature. Canadian Journal of Civil Engineering, 2021, 48( 4): 429– 442

[36] Fall M, Belem T, Samb S, Benzaazoua M. Experimental characterization of the stress–strain behaviour of cemented paste backfill in compression. Journal of Materials Science, 2007, 42( 11): 3914– 3922

[37] Martin B E, Chen W, Song B, Akers S A. Moisture effects on the high strain-rate behavior of sand. Mechanics of Materials, 2009, 41( 6): 786– 798

[38] Boughanem S, Jesson D, Mulheron M, Smith P, Eddie C, Psomas S, Rimes M. Tensile characterisation of thick sections of Engineered Cement Composite (ECC) materials. Journal of Materials Science, 2015, 50( 2): 882– 897

[39] Libos I L S, Cui L. Mechanical properties and behavior of early-age fiber-reinforced cemented paste backfill. In: Proceedings of the 5th International Conference on Civil Structural and Transportation Engineering, Virtual Conference. Avestia, 2020, 1–6

[40] Cui L, Fall M. Modeling of self-desiccation in a cemented backfill structure. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42( 3): 558– 583

[41] Cui L, Fall M. Numerical simulation of consolidation behavior of large hydrating fill mass. International Journal of Concrete Structures and Materials, 2020, 14( 23): 1– 16

[42] Wang H S, Tang C S, Gu K, Shi B, Inyang H I. Mechanical behavior of fiber-reinforced, chemically stabilized dredged sludge. Bulletin of Engineering Geology and the Environment, 2020, 79( 2): 629– 643

[43] Liu L, Liu H, Stuedlein A W, Evans T M, Xiao Y. Strength, stiffness, and microstructure characteristics of biocemented calcareous sand. Canadian Geotechnical Journal, 2019, 56( 10): 1502– 1513

[44] Gafoor A H M A, Dinkler D. A macroscopic gradient-enhanced damage model for deformation behavior of concrete under cyclic loadings. Archive of Applied Mechanics, 2020, 90( 5): 1179– 1199

[45] Bekele A, Ryden N, Gudmarsson A, Birgisson B. Effect of cyclic low temperature conditioning on stiffness modulus of asphalt concrete based on non-contact resonance testing method. Construction & Building Materials, 2019, 225 : 502– 509

[46] Kim J J, Rahman M K, Taha M M R. Examining microstructural composition of hardened cement paste cured under high temperature and pressure using nanoindentation and 29 Si MAS NMR. Applied Nanoscience, 2012, 2( 4): 445– 456

[47] Kim Y J, Hu J, Lee S J, You B H. Mechanical properties of fiber reinforced lightweight concrete containing surfactant. Advances in Civil Engineering, 2010, 2010 : 1– 8

[48] Bhaskar P, Mohamed R H. Analytical estimation of elastic properties of polypropylene fiber matrix composite by finite element analysis. Advances in Materials Physics and Chemistry, 2012, 2012 : 23– 30

[49] Ravichandran N, Krishnapillai S H. Effect of deformation-induced suction in the behavior of unsaturated fine-grained soils using simplified finite-element model. International Journal of Geomechanics, 2013, 13( 5): 483– 495

[50] Zhou W, Wang H, Wang D, Du Y, Zhang K, Qiao Y. An experimental investigation on the influence of coal brittleness on dust generation. Powder Technology, 2020, 364 : 457– 466

[51] Coates D, Parsons R. Experimental criteria for classification of rock substances. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1966, 3( 3): 181– 189

[52] Hajiabdolmajid V, Kaiser P. Brittleness of rock and stability assessment in hard rock tunneling. Tunnelling and Underground Space Technology, 2003, 18( 1): 35– 48

[53] Rybacki E, Meier T, Dresen G. What controls the mechanical properties of shale rocks?—Part II: Brittleness. Journal of Petroleum Science Engineering, 2016, 144 : 39– 58

[54] Hucka V, Das B. Brittleness determination of rocks by different methods. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1974, 11( 10): 389– 392

[55] Altindag R. The evaluation of rock brittleness concept on rotary blast hold drills. Journal of the Southern African Institute of Mining and Metallurgy, 2002, 102( 1): 61– 66

[56] Ghadakpour M, Choobbasti A J, Kutanaei S S. Investigation of the Kenaf fiber hybrid length on the properties of the cement-treated sandy soil. Transportation Geotechnics, 2020, 22 : 100301–

[57] Piratheepan J, Gnanendran C, Arulrajah A. Determination of c and φ from IDT and unconfined compression testing and numerical analysis. Journal of Materials in Civil Engineering, 2012, 24( 9): 1153– 1164

[58] Sivakugan N, Das B, Lovisa J, Patra C. Determination of c and φ of rocks from indirect tensile strength and uniaxial compression tests. International Journal of Geotechnical Engineering, 2014, 8( 1): 59– 65

[59] Soetens T, Matthys S. Shear-stress transfer across a crack in steel fibre-reinforced concrete. Cement and Concrete Composites, 2017, 82 : 1– 13

[60] Zanotti C, Randl N. Are concrete-concrete bond tests comparable?. Cement and Concrete Composites, 2019, 99 : 80– 88

RIGHTS & PERMISSIONS

Higher Education Press 2021.