1 Introduction

The underground mined-out voids (stopes) must be backfilled to provide regional support for the surrounding rock mass and thereby prevent excessive deformations and development of stress concentrations which could lead to dangerous rockbursts within the host rock. Backfilling using mine tailings (fine-grained materials left after ore processing) has the added benefit of reducing the need for surface disposal of mine tailings and hence its adverse environmental impacts. The type of backfill studied in this work is called Cemented Paste Backfill (CPB), which is simply a mixture of tailings, binders, and mine process water. Non-plastic mine tailings are de-watered to a solid content between 75 to 85% so that they achieve a paste consistency and have a measurable slump when tested using the standard concrete materials 12″ slump cone. Portland cement and other binders are added at typical concentrations of 3–8% by weight so that the cured CPB stabilizes the host rock surrounding underground mining excavations. Key advantages of CPB over other backfill types are relatively high delivery rates and the ability to tight-fill the mined-out voids. CPB’s characteristics are mainly influenced by the type of binder, mine tailings grain size distribution, mine tailings and process water chemical properties, binder to mine tailings ratio, and water content (Simon 2004; Simms and Grabinsky 2009; Abdelaal 2011; Fahey et al. 2011; Yilmaz et al. 2011; Grabinsky et al. 2013; Walske 2014; Thompson et al. 2012; Jafari 2020; and Jiang et al. 2020).

Fast and continuous backfilling reduces the overall mining cycle time, leading to better mining efficiency and profitability. However, it may also require building substantial and expensive barricades in the absence of accurate estimates of the imposed backfill stresses. To mitigate these stresses, usually a 6 to 10 m high backfill "plug" is placed first and allowed to cure and to undergo self-weight consolidation for between 12 to 72 h. It is generally hoped the backfill plug will achieve an Unconfined Compressive Strength (UCS) between 100 to 150 kPa before filling the remaining void with the "main" backfill (Fig. 1). Understanding how fast the target UCS can be achieved is, therefore, an essential element of backfill design.

Fig. 1
figure 1

Schematic diagram of a typical stope

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Interactions between the rates of backfilling (total stress increments), binder hydration (which increases stiffness and reduces permeability), and consolidation (pore water pressure reduction and effective stress gains) affect the in-situ behavior and strength of CPB. It is crucial to understand these interactions in order to estimate in-situ strength developments and deformations of CPB with time. It has been shown that the application of effective stresses at early cure times leads to void ratio reduction and potentially significant increases in CPB strength (Fahey et al. 2011; Yilmaz et al. 2014). However, it is unclear if effective stresses can develop early enough in backfill practice to achieve similar strength gains at mining operations.

Cayouette (2003) cored cured backfill and showed that the in-situ UCS almost doubled over a 30 m fill height. It was assumed this was a result of self-weight consolidation, but unfortunately, the samples' bulk properties were not determined to support this hypothesis. Alcott et al. (2019) also cored cured backfill and reported a reduction in void ratio with depth; however, this did not strongly correlate with the samples' UCS values suggesting that some sample disturbance may have occurred. It is also important to note that Alcott et al. (2019) measured stresses during backfilling and found no effective stresses in the first 11 h within the plug, followed by increasing vertical and horizontal effective stresses at rates of 1 kPa/hr and 0.5 kPa/hr, respectively. The hydration occurring during this prolonged delay to the development of effective stress could have significantly affected the backfill's engineering properties; however, no other information was reported to support this hypothesis. Yumlu and Guresci (2007) monitored stress developments within three stopes at the Cayeli mine in Turkey. Initial states of zero effective stress lasted between 6 to 20 h, with subsequent effective stresses developing at rates of 0.66 kPa/hr to 5.5 kPa/hr.

Figure 2 shows the pore water pressure and total stresses that were measured at two different locations near the barricade within a stope at Cayeli mine in Turkey (Thompson et al. 2012). As shown in Fig. 2, effective stresses (which is simply the subtraction of pore water pressure from total pressure) do not develop until about 19 h. Hence, CPB cures under a state of zero effective stress initially. After that, the effective stresses develop at a rate of 2 to 3 kPa/hr until 2.5 to 4 days. At Williams mine, effective stresses developed at a rate of about 5 kPa/hr after the initial state of zero effective stress lasted about 6 h, as shown in Fig. 3 (Thompson et al. 2012). Duration of curing under zero effective stress, curing under a constant rate of effective stress development and final level of effective stress can affect the void ratio changes within CPB during deposition and, subsequently, its UCS. Fahey et al. (2011) performed UCS tests on CPB samples that were subjected to 100 kPa vertical stress at different curing times. It was concluded that applying earlier vertical stress leads to higher UCS. A similar trend was observed by Yilmaz et al. (2014). Fahey et al. (2011) also applied the vertical stress at different rates; however, it is not clear if the applied stresses were continuous and what the state of pore water pressure was within the samples before applying the next loading step.

Fig. 2
figure 2

Total earth pressure and pore water pressure variations with time within a test stope at Cayeli mine: a near the barricade b at the middle of the bottom of the stope (after Thompson et al. (2012))

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Fig. 3
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Total earth pressure and pore water pressure variations with time in two locations of a test stope at Williams mine (after Thompson et al. (2012))

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In this study, a series of experiments have been performed to understand the coupling between loading and cement hydration rates on CPB's behavior and bulk properties by simulating the in-situ loading conditions as accurately as possible within the limitations of available laboratory technologies. Hence, some other in-situ factors and complexities such as stope’s geometry or CPB-Rock interface interactions are not studied and are subjects of future studies. CPB samples with binder contents 3.0%, 5.3%, and 7.5% are cured under zero effective stress (i.e. delay times) for 4, 12, 24, and 48 h prior to being subjected to vertical stresses. Samples of CPB are subjected to loading rates that are typical of in-situ backfilling rates. These loading rates represent total stress backfilling rates of 0.25, 0.50, and 1.00 m/hr of a CPB with a unit weight of 20 kN/m3. Also, the void ratios obtained from these small-scale consolidation tests are compared with the ones measured from in-situ samples to provide insight into a method to prepare more representative CPB samples for strength testing.

2 Background

Only a limited number of studies have been performed to understand the one-dimensional consolidation behavior and properties of CPB using conventional test methods (Le Roux 2004; Jamali 2012; Yilmaz et al. 2015; Jafari et al. 2020a). Jamali (2012) showed that CPB's primary consolidation occurs at a much faster rate than natural soils like clays. This higher rate of consolidation means that if the sample is kept under a constant load for durations suggested by ASTM D2435 (Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading), significant secondary consolidation (based on Terzaghi's (1943) consolidation theory) could occur before the application of the next loading step. In addition to the accumulation of secondary consolidation deformations and structure changes, cement hydration still goes on during loading, which changes the stiffness and also, affects the deformations. Therefore, all the previous studies tried to minimize the loading durations. Jamali (2012) limited the duration of each loading step to \(20\) minutes, while Yilmaz et al. (2015) monitored pore water pressures and limited the total test duration to \(10\) hours. Electrical conductivity measurements (Simon 2004; Jamali 2012; Shahsavari 2020) show that a significant amount of hydration and change in properties can occur within the first 10 h. Therefore, applying a representative loading regime and test duration is essential when doing such tests on CPB.

Among the previous studies, only Le Roux (2004), Fahey et al. (2011), and Jamali (2012) tried to simulate the in-situ response of CPB by applying loading rates that were similar to those of in-situ backfilling rates. Le Roux (2004) applied stress rates equivalent to 1 m of backfill material every 24, 48, and 144 min to simulate backfilling rates of 2.5, 1.25, and 0.4 m/hr, respectively. All the experiments were performed on fresh CPB samples (i.e., load application starting within about 30 min of mixing). Jamali (2012) simulated backfilling rates of 0.25 and 1.25 m/hr on fresh CPB samples of the same mine tailings used in this study. Jamali's (2012) CPB samples had 3.0% and 7.0% cement content, and comparing Le Roux (2004) 's loading rate Jamali (2012) left each load increment to be applied to the sample for \(1\) hour. In contrast, the field loading regime is nearly continuous, and so those laboratory "backfilling rates" only represent the average rates based on pumped CPB volume and stope geometry. Therefore, none of the previous studies simulated a continuous backfilling scenario and instead had a discrete loading increment. The discrete loading would lead to either too much deformation and packing of the pore structure before the formation of cement bonds, or too much progress in hydration before the application of the next loading increment. In the current study, loading has been applied as a continuous function of time. Small load increments are applied in a short time period (i.e. \(1\) minute) to simulate continuous backfilling. This allows for a better understanding of the coupling between deformations and cement hydration as CPB undergoes consolidation.

All the previous studies were performed on fresh CPB samples. Those experiments only simulated the accumulation of CPB on a freshly placed layer of CPB. There is a lack of data on the behavior of CPB that is being cured for some time under zero effective stresses and then exposed to a time-dependent loading regime from backfilling the rest of the stope (as has been presented in Figs. 2 and 3). In this study, the coupled effect of backfilling rate and cement hydration on the behavior of cured plug CPB samples is also studied. CPB samples were cured for a certain amount of time under zero effective stress condition to simulate the delay time before they were subjected to time-dependent loading (similar to in-situ conditions). These experiments are intended to help make better decisions about the plug's curing time and cement content in order to reduce the stope cycle time. In addition, this study helps improve the laboratory sample preparation techniques for strength testing through better estimation of in-situ void ratios under different loading and curing regimes.

3 Experimental Program

CPB samples were prepared with cement contents of 3.0%, 5.3%, and 7.5% to cover the commonly used binder contents at the studied mine (and many other mines). Experiments have been performed on samples that were "fresh" and those cured for 12, 24, and 48 h initially under no external loads to simulate the delay time in loading. The fresh samples were cured for 3 to 4 h. These curing times for fresh samples represent the approximate initiation of the acceleration phase of cement hydration based on electrical conductivity measurements, which correlate to the "initial set" (Simon 2004; Shahsavari 2020). In concrete materials, the initial set is regarded as the time when hydration reactions become significant, and the concrete starts to lose its plasticity, making it more difficult to place and finish.

All the experiments were performed to simulate the backfilling of a 20 m high stope with backfill having unit weight 20 kN/m3. The typical backfilling rates of 0.25, 0.5, and 1.0 m/hr were used in this study. Considering the unit weight, these backfilling rates are equivalent to loading rates of 5, 10, and 20 kPa/hr, respectively. The automatic load control system of the consolidation testing equipment used in this study allowed for the application of virtually continuous small load increments (i.e., load adjustments every \(1\) minute). The loading rates of 5, 10, and 20 kPa/hr were then applied at increments of 0.0833, 0.0167, and 0.333 kPa per minute. These small load increments better simulate the actual continuous backfilling.

4 Materials, Mix Design, and Sample Preparation Method

Mine tailings used in this study were obtained from Williams mine in northern Ontario, Canada. The grain size distribution is shown in Fig. 4 as determined using sieve analysis (ASTM D6913-17) and hydrometer testing (ASTM D7928-17). X-Ray Fluorescence (XRF) tests showed that the Silicates were the main mineral constituent of the tailings, and also, a low concentration of sulphur-bearing minerals (particularly pyrite and pyrrhotite) was found in the tailings. Type 10 Portland Cement (PC, Canadian Standard Association, from Lafarge, Canada) was used in CPB mix design to reflect the mine's current practice.

Fig. 4
figure 4

The grain size distribution of Williams mine tailings

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CPB mixes were prepared at cement contents of 3.0%, 5.3%, and 7.5% by weight of dry tailings. All the samples were prepared at a gravimetric water content of 38% (mass water to mass tailings + cement) as used by the studied mine. First, mine tailings were mixed with water in large buckets to achieve a water content below the target value. Then the required amount of water and cement was calculated based on wet tailings water content and target water and cement contents. Mine tailings were then mixed with cement and water. The mixing was performed using a hand mixer and took 15 min. The water content of the prepared CPB was then measured to ensure that the target value was achieved.

After the mixing step, the CPB mix was poured into stainless-steel consolidation moulds in 3 layers. Each layer was rodded 20 times to avoid having entrapped air voids within the sample. A schematic diagram of the moulds used in this study is shown in Fig. 5. These moulds were designed by Jafari et al. (2020c) to prepare samples at maximum attainable void ratios that are representative of field conditions. O-rings were used at the top and bottom of the mould, where it was attached to the bottom and top caps to prevent water loss from the sample. These moulds produced cured 19 high samples with a diameter of 50 mm. As shown in Fig. 5, these moulds have a top cap that penetrates into the sample to provide sealing during curing.

Fig. 5
figure 5

Prepared samples and schematic diagram of the consolidation samples’ mould for consolidation testing (after Jafari et al. (2020c))

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Samples within the sealed moulds were then placed in containers filled with water to be cured at room temperature of 22 ± 1°C. To avoid the oxidization of samples during curing as noted by others (Benzaazoua et al. 2004; Kesimal et al. 2005; Klein and Simon 2006; Ouellet et al. 2007; Jafari et al. 2020b), all samples were submerged in the mine process water. Based on the testing program, the fresh samples of CPB mixture with 3.0%, 5.3%, and 7.5% were left to cure for 4, 3.5, and 3 h, respectively and the rest of the samples were left to cure for 12, 24, and 48 h. The initial void ratios of samples with different cement contents and curing times at the beginning of each test (e0) are shown in Table 1.

Table 1 Initial void ratios of CPB samples
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5 Testing Set-Up

This study used a fully automatic one-dimensional consolidation apparatus manufactured by Wille Geotechnik. The testing machine is an electromechanical, microprocessor-controlled apparatus that enables fully automatic loading with adjustable load increments. The microprocessor-controlled system is advantageous in these tests where time-dependent loads are applied continuously and do not follow the conventional loading paths that are specified in ASTM D2435 (Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading). The device is equipped with a Linear Variable Displacement Transducer (LVDT) with resolution 0.001 mm and range 25 mm to record vertical deformations. An "S"-Beam load cell with capacity 10 kN was used to measure the applied vertical load.

6 Results and Discussion

Variations of void ratio with stress for samples with different cement contents and subjected to a variety of stress rates are shown and discussed in this section. Cement hydration leads to a change in hydraulic conductivity and stiffness of CPB with time. These changes affect the behavior and deformations of CPB. Since loading is also time-dependent in these experiments, the coupling between the loading and cement hydration rates must also be considered in data interpretations.

Different hydration stages can be identified by monitoring the evolution of electrical conductivity (EC) with curing time (Simon 2004). Figure 6 shows the correlation of EC with six stages of hydration, including: 1. Initial hydrolysis of dry cement particles; 2. Induction period; 3. Rapid dissolution of Portland cement (PC) particles; 4. Acceleration period; 5. Steady-state period; and 6. Deceleration period. Simon (2004) found that the acceleration period (stage 4) correlated with CPB's initial set, as previously discussed, and that after the onset of the steady-state period (stage 5), the "final set" was achieved. In concrete materials, the final set is regarded as the time when the concrete has lost its ductility, making it no longer possible to place within formwork and very difficult to finish without forming surface cracks.

Fig. 6
figure 6

Correlation of various stages of cement hydration with electrical conductivity

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A series of experiments to monitor the evolution of electrical conductivity of the same CPB samples were also performed. Figure 7 shows the variations of electrical conductivity with curing time for CPB samples with 3.0%, 5.3%, and 7.5% cement contents. The time-dependent stress paths are also shown in this figure. Note that the "fresh" samples are loaded starting at their initial sets, and at the fastest loading rate the samples may not have achieved the final set before the test ends at 400 kPa vertical stress. In contrast, for the longest delay time (48 h) prior to loading, the samples have likely achieved final sets before loading starts. The range of delay times and loading rates used in this study, therefore, encompasses the most significant range of hydration processes that would take place during CPB plug placement within a backfilled stope. Additional interpretations based on this model will be made subsequently.

Fig. 7
figure 7

Variation of electrical conductivity and stress with time

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6.1 Pore Water Pressure State

Total stress and deformations were measured in these experiments. However, the deformations are dependent on the effective stress values, and the knowledge of effective stress within the samples is essential to interpret their stress–strain response. Terzaghi's (1943) consolidation theory is used to estimate pore water pressures. Based on Terzaghi's (1943) consolidation theory, soil samples achieve 99% degree of consolidation (i.e. drainage of excess pore water pressure) if the dimensionless time factor (\({T}_{v})\) reaches a value of 1.4. \({T}_{v}\) is a function of the coefficient of consolidation (\({C}_{v}\)), as shown in Eq. 1.

$$T_{v} = \frac{{C_{v} .t}}{{H_{dr}^{2} }}$$
(1)

where \(t\) and \({H}_{dr}\) are time and drainage path length, respectively. The minimum required \({C}_{v}\) for the dissipation of 99% of excess pore water pressure during each load increment can be calculated using Eq. 1 and setting \({T}_{v}\) and \(t\) to 1.4 and 1 min, respectively. The minimum \({C}_{v}\) was calculated to be 2.1 × 10–6 m2/s for an average sample height of 19 mm. \({C}_{v}\) is related to constrained modulus (M) and saturated hydraulic conductivity (\({k}_{sat}\)) through Eq. 2.

$$C_{v} = \frac{{k_{sat} .M}}{{\gamma_{w} }}$$
(2)

where M and \({\gamma }_{w}\) are CPB's stiffness and water unit weight, respectively.

In CPB, both M and \({k}_{sat}\) are dependent on cement content and curing time. M can only be calculated if the value of effective stress is known, and that is not possible with the experimental set-up used in this study. Therefore, the minimum required M values at different curing times can be calculated using Eq. 2 if \({k}_{sat}\) values at the respective curing times are known.

Shahsavari (2020) measured the hydraulic conductivity of similar CPB samples at different curing times and at maximum attainable void ratios. He suggested Eq. 3 to estimate the hydraulic conductivity of CPB samples made from Williams mine tailings.

$$\begin{gathered} k_{sat} = a_{0} + a_{1} .\ln \left( t \right) + a_{2} .C_{c} .{\text{ln }}\left( {\text{t}} \right) + a_{3} .C_{c } ; t \ge 3 hours \hfill \\ a_{0} = 2.402 \times 10^{ - 4} \hfill \\ a_{1} = - 3.21 \times 10^{ - 5} \hfill \\ a_{2} = 1.71 \times 10^{ - 6} \hfill \\ a_{3} = - 1.80 \times 10^{ - 5} \hfill \\ \end{gathered}$$
(3)

where t and \({C}_{c}\) are curing time (in hours) and cement content (in percent of total solid weight), respectively. The minimum required M values for the dissipation of 99% of excess pore water pressure in 1 min at different curing times and within samples with different binder contents are calculated by combining Eqs. 1–3. The minimum required constrained modulus values are shown in Fig. 8.

Fig. 8
figure 8

Minimum required constrained modulus for dissipation of excess pore water pressure in \(1\) minute and measured modulus values

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Jamali (2012) performed consolidation tests on similar CPB samples at 3% and 7% binder contents and measured the constrained modulus of samples at different curing times. These measured M values are shown in Fig. 8. As shown in this figure, the constrained moduli of samples with different binder contents are much higher (by a factor 10 to 30) than the required minimum M values for the dissipation of 99% of pore water pressure at all curing times. Therefore, at each load increment, all the excess pore water pressures are dissipated, and effective stresses are fully developed within the samples before the application of the next load increment.

6.2 One-Dimensional Consolidation Behavior and Secant Stiffness Variations

Both load and material properties (i.e. stiffness, strength, and hydraulic conductivity) are functions of time in these experiments. Hence, the stress–strain response interpretations are complicated due to the various interactions. To facilitate the interpretation of the results, general trends in the one-dimensional behavior of CPB with variations in cement content, initial curing time (i.e. delay time), and loading rates are shown and discussed briefly before the detailed analysis of the tests' results.

Table 1 shows the initial void ratios for all samples, ranging from 1.020 to 1.036. For comparative analysis between the test results, it is convenient to normalize each test's void ratios with respect to that test's starting void ratio, as was done by Le Roux (2004) for a virtually identical CPB from an adjacent mine in the same orebody, and by Crowder (2004) for a similar non-plastic paste (but uncemented). This normalization is deemed to be reasonable because the deviation of initial void ratios (1.036−1.020 = 0.016 =  ± 0.008) is less than 1% of the average (1.028). Figures 9, 10 and 11 show the variation of normalized void ratio with effective vertical stress and delay time for samples with different cement contents. A visual inspection of the results indicates, as expected, the initial compliance (i.e., tangent to the e/eo vs \({\sigma }_{v}^{^{\prime}}\) curve at the start of loading) decreases with increasing delay time and with decreasing loading rate. The rational interpretation for this is that increasing hydration time permits stronger and stiffer cement bonds to develop, and so any delay before load application and/or slower loading rate results in an initially stiffer response. However, the effects on the final void ratio (at 400 kPa load application) are less clear, and a consistent trend is not immediately evident from these Figures.

Fig. 9
figure 9

Void ratio variations with vertical stress and stress rate of CPB samples with 3.0% binder content: a fresh, b 12 h delay time, c 24 h delay time, and d 48 h delay time samples

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Fig. 10
figure 10

Void ratio variations with vertical stress and stress rate of CPB samples with 5.3% binder content: a fresh, b 12 h delay time, c 24 h delay time, and d 48 h delay time samples

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Fig. 11
figure 11

Void ratio variations with vertical stress and stress rate of CPB samples with 7.5% binder content: a fresh, b 12 h delay time, c 24 h delay time, and d 48 h delay time samples

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To better understand the impact of delay time versus loading rate, the results are reinterpreted and presented as a series of stress-time histories with each load path terminated at a common strain level: 2.5% strain (e/e0 = 0.95) for all three cement contents; and also at 5% strain (e/e0 = 0.90) for the softer 3.0% cement content CPB. By choosing a common strain level, it is then possible to determine the impact of load path on the sample's stiffness for the corresponding strain level and assess which load paths may have damaged early hydration products and the degree to which this reduces sample stiffness. Since stiffness generally correlates to strength (usually correlated to Unconfined Compressive Strength), softer materials may imply weaker materials as well, although strengths are not determined directly in this study.

Figure 12 shows the effective stress levels required to achieve 2.5% and 5.0% strain within samples with 3.0% cement content and 2.5% within samples with 5.3% and 7.5% cement contents for various stress paths (i.e. delay times of 3 to 4 (i.e. fresh), 12, 24, and 48 h; and loading rates of 5, 10, and 20 kPa/hr). For the 2.5% and 5.0% strain levels, the data points correspond to secant moduli values 40 and 20 times the effective stress levels. However, for the sake of simplicity, the subsequent discussion will refer to the stress levels as indicators of "stiffness" rather than calculating the stiffness explicitly.

Fig. 12
figure 12

Stress levels required to achieve e/e0 of 0.90 or 0.95 within CPB with a 3.0%, b 5.3%, and c 7.5% cement contents

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Using the maturity function concept (Rastrup 1956), a bounding curve has been fitted to the data points in the form of Eq. 4.

$$\sigma_{v}^{,} \left( t \right) = a + b. e^{{\left( {{\raise0.7ex\hbox{${ - c}$} \!\mathord{\left/ {\vphantom {{ - c} {\sqrt {t - 4} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sqrt {t - 4} }$}}} \right)}}$$
(4)

where effective vertical stress (\({\sigma }_{v}^{,}\)) and time (t) are in kPa and hours, respectively. The constant a, b, and c are defined based on trial and error so that the curve fits the data point visually. It must be noted due to the nature of the tests and material in addition to the number of variables, fitting a curve by minimizing the sum of squared residuals was not practical. The fitted curve is only used to facilitate the data interpretation rather than being used as a function to predict stress values at a specific total curing time.

For the 3.0% binder CPB, the constants a, b, and c in Eq. 4 are 15 kPa, 650 kPa, and 8 s1/2, respectively, for the stress levels to achieve 2.5% vertical strain. All three loading rates fit this bounding curve reasonably well when the delay time is only 4 h. However, for subsequent delay times the fastest loading rate (20 kPa/hr) curve lies beneath the medium loading rate (10 kPa/hr) curve, which in turn lies beneath the slowest loading rate (5 kPa/hr) curve. Thus, the stiffness has been compromised by faster loading rates after delay times. For example, at roughly 65 h, about 260 kPa is required to produce 2.5% strain if the slowest loading rate starting at 12 h is used, whereas about 190 kPa is required for the same level if the medium loading rate starting at 48 h is used, and about 135 kPa is required if the fastest loading rate starting at 48 h is used. All three load paths have approximately the same total cure time; however, the slowest load path has virtually twice the stiffness as the fastest load path. Therefore, for the 3.0% binder CPB, delays in the start of load (up to 48 h) imply subsequent damage to the hydration products and loss of stiffness, such that lower stress levels are required to achieve the same 2.5% strain level.

Figure 12a also shows the required stress levels to achieve 5.0% axial strain within 3.0% binder content CPB samples. Equation 4 is fitted to these data points with the constant a, b, and c having values of 15 kPa, 1300 kPa, and 9.5 s1/2, respectively. No drop in the requires stress level to reach 5.0% axial strain is observed in samples that are loaded under 5 kPa/hr and 10 kPa/hr, indicating that the combined effects of curing, damage, and consolidation have led to an overall stiffness gain. However, at this strain level, the effects of damage due to faster loading rate are evident at about 65 h where the sample with the initial delay of 48 h and loaded under 20 kPa/hr requires 320 kPa to achieve 5.0% vertical strain, whereas the one that is loaded under 10 kPa/hr requires 400 kPa at the same curing time. Portions of the fastest loading rate curve are above the medium loading rate initially, indicating some stiffness gain due to faster loading (hence higher stress level) at about 20 h. A similar effect is observed between the slow and medium loading rate curves at about 80 h.

The bounding curve (i.e. Equation 4) that is fitted to the 5.3% binder CPB with the stress levels required to reach 2.5% axial strain are shown in Fig. 12b. The constant a, b, and c have values of 20 kPa, 900 kPa, and 10 s1/2, respectively, for the 5.3% binder CPB. At this binder content, the effects of loading path are less important for the slow and medium loading rates (i.e. 5 kPa/hr and 10 kPa/hr). A portion of the medium loading rate curve is above the slow loading rate curve at approximately 47 h indicating some stiffness gains due to a faster loading rate. However, the differences are negligible and most of the data points follow the fitted curve even though it is obtained by trial and error. Some damage effects are observed at about 57 h, where the fast loading rate curve falls below the fitted curve.

For the 7.5% binder CPB a similar bounding curve is fitted with constants a, b, and c have the values 60 kPa, 1300 kPa, and 13 s1/2, respectively. Figure 12c shows the stress levels required to reach 2.5% axial strain under different stress paths for the 7.5% binder CPB. In this case, the effect of load path is less clear, and certainly less important than for the 3.0% and 5.3% binder CPBs. A portion of the fastest loading rate does lie underneath the medium loading rate curve, although the data for 48 h delay and 20 kPa/hr was corrupt in the data collection and so is not represented on the plot to determine if the trend would continue or not. For later times (> ~ 48 h), a portion of the medium loading rate curve lies above the slowest loading rate curve (implying in this case higher stiffness for the faster load paths); however, the differences do not appear to be significant compared to the overall trend exhibited by the bounding curve. The general conclusion for the 7.5% binder case, therefore, is that the different load paths (delay time and loading rates) do not significantly affect stiffness development in the first several days of hydration.

Although the maturity functions were fitted by trial and error, it is interesting that extrapolating the stress levels to 28 days results in \({\sigma }_{v}^{,}\)= 846 kPa for the 7.5% case and \({\sigma }_{v}^{,}\) = 492 kPa for the 3.0% case. The corresponding constrained moduli are about 33,840 kPa and 19,680 kPa, respectively, and the 1-D compliances are 6 × 10–5 kPa−1 and 10–4 kPa−1. Although these are secant values (not tangent), those values are consistent with the trends previously observed by Jamali (2012) in conventional oedometer tests on similar materials. A more detailed analysis of the couplings between cement hydration, deformations, and strength gains are explored in the next section by comparing the tangent moduli, UCS, and void ratios at specific curing times.

6.3 Interactions Between Cement Hydration, Deformations, and Strength

CPB's strength and stiffness increase with an increase in cement content and/or curing time. Unconfined Compressive Strength can be used as a measure of strength, while stiffness (or compliance) can be obtained from stress–strain curves (i.e. Figures 9, 10 and 11). A series of experiments were performed by Jafari (2020) to measure the UCS of similar CPB samples cured under zero effective stress. The measured UCS values only represent the effect of cement hydration on strength gains (the details of the experiments can be found in Jafari (2020)). Figure 13 shows the evolution of UCS with curing time for CPB samples with 3.0%, 5.3%, and 7.5% cement contents up to 28 days. To cover the data gap for the different curing times (e.g. at 12 h and 48 h), the maturity function (Rastrup 1956) in the form of Eq. 5 as suggested by Helinski et al. (2007) was fitted to the UCS data.

$$UCS \left( t \right) = UCS_{0} + \Delta UCS.e^{{\left( {{\raise0.7ex\hbox{${ - d}$} \!\mathord{\left/ {\vphantom {{ - d} {\sqrt {t - t_{0} } }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sqrt {t - t_{0} } }$}}} \right)}}$$
(5)

where \({UCS}_{0}\) and \(t\) are the initial UCS measured at the initial time (\({t}_{0}\) in hours) and curing time in hours, respectively. \(\Delta UCS\) in Eq. 5 is the difference between the UCS of the 28 days old and fresh CPB. \({t}_{0}\) is the time at which the acceleration period of the hydration process initiated and corresponded to the first peak of electrical conductivity values. \({t}_{0}\) values of 4, 3.5, and 3 h for samples at binder contents of 3.0%, 5.3%, and 7.5%, respectively, were used in Eq. 5. \(d\) is a constant value and was calculated to be 5.76, 5.26, and 5.01 hour1/2 for samples with 3.0%, 5.3%, and 7.5% binder contents, respectively, using the least-squares method.

Fig. 13
figure 13

Evolution of UCS with curing time and cement content: experimental data (symbols) and best-fitted curves Eq. 5 (solid lines)

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Due to the porous nature of CPB, an increase in effective stress can cause a decrease in porosity and hence an increase in stiffness and strength. At early curing times, when significant hydration has not taken place, stiffness is more dependent on porosity changes. Thus, higher UCS values are expected compared to the ones shown in Fig. 13 at early curing times. Fahey et al. (2011) demonstrate this by subjecting CPB samples to 100 kPa vertical stress at different curing times. The effect of load application on UCS became less evident with an increase in the delay time prior to load application. Fahey et al. (2011) concluded that higher UCS can be achieved if the load is applied as early as possible during curing. However, during the deposition of CPB within the stope, the load is applied gradually and at a specific rate, which results in a specific rate of effective stress developments depending on in-situ conditions (i.e. CPB's consolidation characteristics and access to drainage). Fahey et al. (2011) only measured the total stress and hence, it is not clear what the value of effective stress or its applying rate was within the samples. As shown in Fig. 12, the rate at which effective vertical stresses develop can affect the stiffness (and therefore strength) of CPB at specific curing times and levels of deformation. The 3.0% binder content CPB experienced the most damage with an increase in loading rate while the 7.5% binder CPB experienced the least amount of damage. Therefore, the in-situ effective stress development rates and final values must be considered in the preparation of samples to measure the UCS in the lab and use those values for design purposes.

Figure 14 shows the variations in normalized void ratio with effective stress rate and initial curing time for samples with 3.0%, 5.3%, and 7.5% cement contents at 25, 100, and 400 kPa effective stress levels. If the effective stress development rate within the backfilled CPB is known, then the void ratio can be estimated at different stress levels. This estimated void ratio can be used to prepare samples for UCS measurements that are more representative of the in-situ condition. For instance, for the 3.0% binder CPB and with a delay time of 4 h, normalized void ratios of 0.90, 0.86, and 0.85 are reached. These void ratios are much lower than the initial void ratio of the 3.0% binder CPB (as shown Table) that is used to prepare the UCS testing sample. Therefore, it is expected that for this loading scenario, the in-situ UCS differs from the laboratory-measured value (i.e. Fig. 13). As shown in Fig. 14, the difference between the void ratio at different stress levels and the initial void ratio decreases as the delay time and cement content increase and the stress rate decreases.

Fig. 14
figure 14

Normalized void ratio at 25, 100, and 400 kPa stress levels for samples with a 3.0%, b 5.3%, and c 7.5% cement content

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The tangent constrained moduli of samples with 3.0% and 7.5% binder content at total curing times of 24 and 72 h are calculated and compared with the values measured by Jamali (2012) by testing similar CPB under conventional loading (Fig. 15). Compared to the conventionally measured moduli values, samples that were cured under effective stress, regardless of the applied effective stress rate, yielded higher moduli values at both binder contents and curing times. As shown in Fig. 15, at 3.0% binder content, the average constrained moduli at 24 and 72 h were 60% and 40% higher than the ones measured by Jamali (2012), respectively. The average constrained moduli for the 7.5% binder content CPB at 24 and 72 h were 52% and 21% higher than the previously measured values, respectively. Both the magnitude and rate of effective stresses have affected the tangent moduli at a specific total curing time. This observation has the important practical implication that not considering the effects of in-situ effective stresses in laboratory sample preparations can result in lower stiffness values.

Fig. 15
figure 15

Tangent moduli comparison

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6.4 Void Ratio Comparisons with In-Situ Samples

The experiments in this study were aimed to represent the backfilling process as closely as possible to the in-situ conditions. Comparing the void ratios obtained from these experiments with the ones measured from samples taken from the in-situ CPB can provide a better understanding of the effect of in-situ effective stress developments on the bulk properties of CPB.

Grabinsky et al. (2013) performed in-situ monitoring of pore water pressure and total stresses within an Alimak test stope at the Williams mine. The test stope was 5 m by 30 m in plan and 149 m high. Backfilling was performed in multiple stages with an 8 m high plug. The plug and main pour were backfilled at rates of 0.36 and 1.33 m/hr, respectively. The CPB was made of the same tailings used in this study with 3.0% binder content. The binder consisted of 50% fly ash and 50% type 10 Portland Cement.

The in-situ backfilling was performed in several stages. Hence, none of the experiments performed in this study could completely represent the in-situ conditions. However, comparing the average void ratio measured from the in-situ samples with the ones obtained in this study can show how close the element tests are to actual filling conditions. As shown in Fig. 3b, the effective stresses started to develop after about \(6\) hours of curing and at a rate of about 5 kPa/hr up to 18 h and at a rate of about 0.65 kPa/hr until the end of backfilling. The oedometer test with 3.0% binder content and initial curing time of 4 h subjected to 5 kPa/hr stress rate is the closest to the in-situ backfilling condition. It must be noted that the addition of fly ash to the binder would delay the hydration process. Therefore, the in-situ CPB might have experienced more deformations during backfilling due to lower stiffness gains in a given time frame compared to the CPB with a binder consisting of 100% Portland cement.

After the CPB cured, the barricade was removed and samples were obtained to measure the void ratios at different locations within the stope. The measured void ratios showed an average value of 1.02, with a standard deviation of 0.09. The scatter in the in-situ void ratios is due to varying amounts of entrained air, presumably resulting from splashing around during deposition. In addition, the variation in water content for field samples was consistent with variations in plant mixing water contents which can also result in variations in void ratio.

The test here on a CPB sample with 3.0% cement content and loaded at the stress rate of 5 kPa/hr yielded a void ratio of 1.00 at the effective stress level of 75 kPa, which is comparable to the in-situ effective vertical stress at the end of backfilling. Since the void ratio obtained from the consolidation test is very close to the average value obtained in the field, it is concluded that curing under effective stress paths comparable to the ones expected to occur in the field would result in CPB samples with similar bulk properties.

The major challenge in predicting in-situ void ratios is the uncertainty associated with the effective stresses developed during backfilling. The delay time until the development of effective stresses (i.e. the initial curing time under zero effective stress) is dependent on the in-situ drainage conditions, arching, and CPB's characteristics. For instance, as shown in Fig. 2, at Cayeli mine, CPB was cured under essentially zero effective stresses for 19 h. On the other hand, at Williams mine, the effective stresses started to develop at around 6 h. Therefore, a better understanding and estimation of effective stress development within CPB is required before the laboratory techniques shown here can be used to estimate the in-situ void ratios.

7 Conclusions

In the current study, a series of experiments were performed to better understand the behavior of cemented paste backfill during one-dimensional deposition. The experiments were intended to simulate the backfilling process using element tests within a controlled testing set-up and environment. Samples were subjected to time-dependent effective stresses at rates of 5, 10, and 20 kPa/hr that simulated typical backfilling rates. The effect of delay time before the development of effective stresses on deformation variations was simulated by curing samples under zero effective stress up to 12, 24, and 48 h prior to loading.

It was shown that at a specific cement content CPB's secant stiffness can be affected by the delay time, effective stresses development rate, level of deformations, and total curing time. As the cement content increased, the influence of effective stress development rates on the stiffness variation was reduced up to the stress levels used in this study. At 3.0% cement content, as the effective stresses were applied at a faster rate, more damage within samples was observed. For instance, a 100% increase in secant stiffness at 2.5% axial strain level was observed in samples loaded at 5 kPa/hr with 12 h delay time compared to the ones loaded at 20 kPa/hr with a delay time of 48 h despite both having the same curing time of 65 h. The tests results also showed that the tangent constrained modulus is also affected by these stress path complexities. At 3.0% binder content, the average constrained moduli between all tests at 24 and 72 h were 60% and 40% higher than the ones measured by conventional consolidation tests on similar CPB. Both the magnitude and rate of effective stresses have affected the tangent moduli at a specific total curing time. As part of future work, it is planned to measure the UCS of samples cured under the stress paths mentioned in this study. Those UCS values would facilitate better understanding of strength dependency on effective stress changes regime including the application rate and onset delay time.

The test results indicate that sample preparation techniques must be improved to prepare samples that are subject to the effective stress paths comparable to the ones expected to occur in the field. The parameters that can affect the in-situ effective stress path depend on CPB's in-situ hydromechanical properties, backfilling rate, and drainage conditions. A series of graphs were presented to estimate the in-situ void ratios based on the effective stress development rate, cement content, and initial curing time. These void ratios can be used to prepare more representative CPB samples for strength and hydraulic testing.

To better understand the effects of complexities associated with the changes in drainage paths, arching, and self-weight consolidation, the void ratios obtained from these element tests were compared with the ones obtained from in-situ measurements. Despite the scatter observed in the in-situ void ratios of similar CPB, the average in-situ void ratio was similar to the ones obtained from these element tests that used comparable effective stress paths. In particular, the delayed onset of effective stress and the relatively slow rate of subsequent effective stress development means the backfill plug undergoes very little self-weight consolidation, and therefore such consolidation effects cannot be expected to increase plug strength significantly. This observation also shows that to obtain samples comparable to the in-situ CPB, they must be cured under the same effective stress regime that develops within a stope. The in-situ effective stress regime includes the initial curing under zero effective stress and subsequent rate of effective stress development until reaching a specific final effective stress value. Cement hydration results in changes in temperature and on the other hand, hydration rate is also impacted by the environment temperature. Hence, the effect of temperature is required to be studied by controlling samples' temperature while being cured under a continuous increase in effective stresses to better simulate the in-situ curing conditions. Samples prepared by controlling temperature, effective stress application rate, and initial curing under zero effective stress duration shall be then used for strength testing to better estimate the expected in-situ strength of CPB.