Numerical Simulation of Consolidation Behavior of Large Hydrating Fill Mass

Due to the strongly coupled THMC processes that occur in fill mass, the consolidation behavior of CPB in a slurry state is a very complex process compared to that of conventional geomaterials, such as natural soils. A multiphysics model for the consolidation behavior of CPB must satisfy the principle of pore space continuity (Cui and Fall 2016a), which requires that the pore space changes associated with the CPB skeleton and solid phase must be consistent with the volume changes in the pore water and pore air. Hence, based on the principle of pore space continuity, a consolidation equation based on multiphysics can be derived as follows and is elaborated in detail in Cui and Fall (2015a, 2016a):where \(S\) is the degree of saturation; \(P_{w}\) and \(P_{a}\) denote the PWP and pore-air pressure, respectively; \(\upsilon\) and \(E\) denote the Poisson’s ratio and elastic modulus, respectively; \(\alpha_{Biot}\) is the Biot’s coefficient; \(\xi\) is the degree of binder hydration; \(\sigma\) is a total stress tensor; \(S_{e}\) is the effective degree of saturation; \(\theta_{r}\) is the residual water content; \(n\) refers to the CPB porosity; \(v_{w}\), \(v_{ch - w}\), \(v_{ab - w}\), \(v_{tailings}\) and \(v_{c}\) denote the specific volume of the capillary water, chemically consumed water, physically adsorbed water, tailings and cement respectively; \(R_{n - w/hc}\) means the mass ratio of the chemically consumed water and hydrated cement; \({w \mathord{\left/ {\vphantom {w c}} \right. \kern-0pt} c}\) is the water to cement ratio; \(C_{m}\) is the binder content; \(t\) refers to the elapsed time; \(\lambda_{p}\) denotes a non-negative plastic multiplier; \(Q_{CTB}\) is a plastic potential function; \(I_{1}\) represents the first stress invariant; and \(\alpha_{Ts}\) refers to a coefficient of the thermal expansion of the solid phase in the CPB. The determination of the model parameters mentioned above is given in Cui and Fall (2015a, 2016a).

As demonstrated in the consolidation model (i.e., Eq. (1)), the chemical process is incorporated into the volume changes in CPB through the variable \(\xi\), namely, the degree of binder hydration. To characterize the progress of the hydration reaction in CPB, the following exponential equation proposed by Schindler and Folliard (2003) is adopted:withwhere \(\tau\) and \(\beta\) respectively represent the time parameter (hours), and hydration shape parameter, \(T_{r}\) refers to the reference temperature (K), \(R\) is the ideal gas constant (8.314 J/mol/K), \(E_{a}\) refers to the apparent activation energy (J/mol), and \(X_{slag}\) and \(X_{FA}\) denote the weight proportion of the blast furnace slag and fly ash relative to the total binder mass, respectively. In accordance with the definition of the degree of binder hydration (i.e., Eq. (2)), the influence of temperature, mixture recipe and elapsed time are incorporated to determine the progression of the hydration reaction.

To incorporate the effect of the interface behavior between the CPB/rock mass into the analysis of the consolidation process, an evolutive elastoplastic interface model developed by Cui and Fall (2017) is adopted to assess the interface shear stress in the present study. In this model, the changes of the yield surface in the stress space is characterized by a modified Drucker-Prager (D-P) yield function \(F_{intf}\), and the changes in the direction of the plastic displacement is determined with a non-associative plastic flow rule (i.e., the plastic potential function \(Q_{{_{intf} }}\) differs from the yield function \(F_{intf}\)).where \(J_{2}\) is a second deviatoric stress invariant, \(\Delta_{\kappa }\) is the effective plastic displacement, \(\alpha_{intf}\) and \(C_{intf}\) are the yield function parameters, and \(\psi_{intf}\) denotes the interface dilation angle which will change with binder hydration and normal stress level acting on the interface. Details on how the interface model coefficients are determined can be found in Cui and Fall 2017).

To study the consolidation behavior of CPB, a series of pressure cell tests were conducted by using a THMC pressure cell apparatus (see Fig. 1). This pressure cell apparatus was originally developed by Ghirian and Fall (2013), which is mainly composed of an air pressure system, a Perspex cylinder [10 cm (diameter) × 30 cm (height)], an air-pressure driven piston and two plates with three tie rods to hold the THMC cell. The adopted air pressure system can apply up to 600 kPa of air pressure onto the CPB sample to simulate the increase of self-weight stress in a stope during backfilling operations. To collect the data, a linear variable displacement transformer (LVDT) was mounted onto the top of the cell to record the vertical settlement, and a suction meter (model: MPS-2) and a temperature sensor (model: 5TE) were installed inside the THMC cell. Artificial silica tailings (medium size tailings; contain 45% of particles with size ≤ 20 μm), Portland cement Type 1 (4.5 wt%) and tap water (w/c = 7.6) were used to prepare the CPB samples. After placement, the pressure cell was covered with a thermal insulation blanket to slow down the heat transfer between the CPB sample and the surrounding environment. In terms of the application of air pressure, the applied pressure was gradually increased to 150 kPa in the first 12 h. Then, the pressure was increased every 24 h until 600 kPa (an average filling rate equal to 0.131 m/h was used in this study). Moreover, two different initial temperatures of the CPB (5 °C and 25 °C) were used to investigate their effects on the consolidation process.

A 2D axisymmetric model was used to simulate the pressure cell test. The geometry model and mesh are presented in Fig. 2.

A comparison of the simulation results and monitored data from the vertical settlement is plotted in Fig. 3. It can be clearly seen that the simulated results are in good agreement with the recorded data in terms of both changes in trend and magnitude. Moreover, the results show that (1) the vertical displacement increases with applied air pressure, which confirms that the developed model is able to capture the effect of backfilling operations on the self-weight stress, and thus its effects on the consolidation behavior of CPB; (2) the initial temperature of the CPB has a significant effect on its vertical settlement. As shown in Fig. 3, the vertical settlement of the CPB with an initial temperature of 25 °C (can represent the initial temperature of CPB in summer season) increases by approximately 8% compared to that of the CPB with an initial temperature of 5 °C (can represent the initial temperature of CPB in a cold mining region) at 7 days; (3) during each curing age, the air pressure applied is constant but the vertical settlement continues to increase, which indicates that chemical shrinkage contributes to the volume changes in the CPB.

Apart from the settlement, the changes in the PWP (Fig. 4a), and temperature (Fig. 4b) can also be accurately captured by using the developed model. From these two figures, it is evident that (1) the major changes in the PWP and temperature occur at the very early ages, which coincides with changes in the vertical settlement (see Fig. 3). This is because the binder hydration takes place rapidly at the very early ages. As a result, a relatively large volume of pore water is consumed, which in turn results in a significant change in the PWP. Meanwhile, the rapid binder hydration releases a large amount of heat and thus affects the temperature in the CPB at the early ages; (2) similar to the obtained results from the vertical settlement, the initial temperature of the CPB can also impose a significant impact on the changes in the PWP and temperature. The good agreement between the numerical simulations and results from the laboratory tests further confirms that the developed model can reliably simulate the consolidation behavior of CPB.

To study the field behaviors of CPB, a series of field monitoring programs have been carried out (e.g., Thompson et al. 2009; Helinski et al. 2010; Li et al. 2014). Although the reported field data are limited to total stress (e.g., Hassani et al. 2001a, b), PWP (e.g., Shahsavari and Grabinsky 2015) and temperature (e.g., Williams et al. 2001) in the CPB, the obtained results can still provide useful information on the field behaviors of CPB, including the consolidation process.

In the present study, the predicted results are compared with the measured data from a field monitoring program conducted by Belem et al. (2004) at the Doyon Gold (DG) Mine (Canada). The investigated stope has a height of 29 m and a width of 11 m with a dip of 90° and an azimuth of 90°. A backfilling operation that consists of two stages was adopted, which includes a plug layer (cement content: 7% and solid content: 70%). After 3-days of curing, the residual stope was filled with CPB with a cement content of 3% and a solid content of 70%. An earth pressure cell (TPC series) was used to record the changes in the total pressure at the stope base (elevated 0.6 m). Water drainage was not allowed on this stope. The corresponding mesh and stope geometry are shown in Fig. 5.

A comparison of the predicted results and monitored total stress values is presented in Fig. 6. Based on the obtained results, it can be found that (1) as expected, the filling processes have significant impacts on the changes in total stress, especially during the plug placement stage; (2) during the curing of the plug layer (from the 2nd to the 5th day), there is a slight reduction in total stress which gradually took place and can be attributed to the transfer of stress from the fill mass to the rock walls (arching effect) with the development of consolidation of the CPB mass; and (3) after the residual filling commenced (from the 5th day), the total stress shows a relatively limited increase compared with that observed during the plug-fill, which further contributes to the discrepancy between the total stress and self-weight stress. From Fig. 6, it can be seen that the predicted results are in good agreement with the monitored data. Hence, the developed model is able to reliably assess the changes in total stress in CPB under undrained conditions.

To investigate the field behavior of CPB under drained conditions, in situ measurements were conducted by Helinski et al. (2010) in the Kanowna Belle mine. In this monitoring program, a piezometer was installed at the center of the stope base to monitor the changes in the PWP in the CPB. The backfilling strategy was to carry out filling in two stages. Pore-water drainage through the retaining structure (i.e., the barricade) was allowed. More details on the CPB design are provided in Helinski et al. (2010). The geometry model and mesh are presented in Fig. 7.

As can be seen in Fig. 8, the changes in the PWP are captured well by the developed model. Specifically, during the first stage of filling, the PWP gradually increases with filling. After 1.4 days (the commencement of the curing of the plug layer), dissipation of the PWP is observed in the CPB, which is attributed to the water drainage through the barricade and binder hydration induced water consumption (i.e., the self-desiccation process). The dissipation of the PWP can directly contribute to reductions in pore space and thus to the consolidation process of CPB. In addition, from Fig. 8, it can be observed that the effect of the residual filling on PWP is minimal, and a slight increase in the PWP appears during the middle of the second and third days. Then, the PWP decreases regardless of the backfilling that followed, which can further contribute to the volume changes in the fill mass. Therefore, the good agreement between the predicted results and field data further validates the predictive ability of the developed model for CPB behavior under drained conditions.

With curing time, binder hydration induced chemical shrinkage, water drainage through the barricade and/or fractured rock mass, and self-weight induced volume changes will contribute to the consolidation process in CPB. Moreover, due to the temperature dependence of binder hydration (Cui and Fall 2015a; Schindler and Folliard 2003), the heat generated by hydration reactions, and heat transfer between the CPB and surrounding rock can affect the chemical reaction rate and thus the consolidation process. Therefore, the effect of curing time on the consolidation behavior of CPB needs to be examined. Figure 11 presents the changes in the average degree of consolidation (i.e., the ratio of the vertical settlement at any time and the final settlement) for three different heights of the CPB. From this figure, the following characteristics that depict the changes in the consolidation process in the CPB are found:

To further illustrate the spatial distribution and development of the consolidation process in CPB, void ratio changes in the control stope are investigated and presented in Fig. 12. It can be observed that the development of consolidation of CPB is relatively uniform at a given height at the early ages (see Figs. 12a, b). With time, the non-uniform distribution of the void ratio becomes apparent, especially in the vicinity of the rock walls (see Fig. 12c). The non-uniform change in the void ratio is mainly attributed to the arching effect (Yilmaz et al. 2018). In addition, Fig. 12 shows that a major change in the void ratio takes place around the layer interface when the filling takes place in stages (i.e., 7 m from the stope base). This is due to (1) the distinct interface properties and inconsistent rate of consolidation near the layer interface (Cui and Fall 2016a), and (2) the difference in the refinement of the capillary pore space around the layer interface when filling takes place in stages. More specifically, the interface adhesion and friction angle will be gradually increased during the 1-day of curing. Therefore, the first layer (i.e., the plug layer) is able to form higher shearing resistance along the backfill/rock-wall interface compared to the second CPB layer. Moreover, the precipitation of hydration products also plays an important role in the reduction of the void ratio. Compared with the fresh residual CPB layer, more hydration products can form in the pore space of the plug layer, which can contribute to the changes in the void ratio near the layer interface. In addition, compared to the plug layer, binder hydration occurs more quickly in relatively fresh CPB (i.e., second layer), which causes significant chemical shrinkage and thus contributes more to the development of consolidation of the CPB along the layer interface. Consequently, the variations in the void ratio near the interface of the different backfill layers gradually become more pronounced with time. Similar results have been found in previous studies on CPB (e.g., El Mkadmi et al. 2013; Li and Aubertin 2009).

Due to the different ore bodies and adopted stoping methods, the resultant stopes may differ in terms of size and inclination angle (Cui and Fall 2016a; Dirige et al. 2009). To investigate the effect of the stope geometry, three stopes with different height-to-width (H/W) ratios, including 1:1 (15 m × 15 m), 2:1 (30 m × 15 m) and 4:1 (45 m × 15 m) are chosen for further investigation in this study. The changes in the average degree of consolidation at a monitored point of 7 m from the stope floor with different H/W ratios are plotted in Fig. 13. It can be seen that the changes in the H/L ratio have significant impacts on the consolidation behavior of CPB, especially in the post-filling stage. Specifically, during the filling stage, the consolidation curves for the different H/L ratios follow a similar trend of change, namely, an increase in the self-weight stress with filling can significantly affect the consolidation behavior of CPB. However, after the filling takes place, there is an apparent discrepancy in the consolidation behavior of the CPB stopes with different H/L ratios, and a lower rate of consolidation is obtained in the stope with a high H/L ratio. This is because the CPB placed at a greater height exerts more overburden stress onto the monitored point. As a result, there are more volume changes in the CPB with a higher H/L ratio (re: Fig. 14) during the filling process (void ratio decreases with higher H during the filling process due to more overburden stress), which can further increase CPB stiffness (Cui and Fall 2016a, b). Consequently, after placement, the stiffer CPB placed at a greater height can significantly reduce the rate of consolidation. Hence, CPB demonstrates distinct post-filling consolidation behavior in stopes with different H/L ratios.

Apart from the H/W ratio, the stope inclination angle is another key factor that affects the resultant backfill geometry. To investigate the effect of the stope inclination on the consolidation behavior, two dip angles of 90° and 50° are selected for further examination in this study. To isolate the effect of self-weight, the backfill height (i.e., 30 m) and backfilling strategy (i.e., filling that takes place in two stages with 1-day plug) are set to be same for these two cases. The modeling results are presented in Fig. 15, and indicate that during the curing of the plug layer and in the early onset of the second stage of filling, the development of consolidation for these two cases follows a similar trend of change. However, the differences in the degree of consolidation between these two stopes become progressively more evident after approximately 2.75 days. In particular, a lower degree of consolidation is observed in the inclined stope due to the effect of the inclination angle on the stress distribution in CPB. Previous studies on CPB (Cui and Fall 2016a, c, 2017) found that under the gravity effect, more overburden stress is transferred to the footwall (i.e., lower rock wall). As a result, non-symmetrical distribution of stress and volume changes emerge in the inclined stope, and become more pronounced with reductions in the inclination angle (see Fig. 16). Moreover, the inclined stope can further contribute to the arching effect (Cui and Fall 2016a; Suazo and Fourie 2015). As a result, vertical stress acting on the monitored point is reduced with the enhanced arching effect in the inclined stope. Therefore, there are smaller volume changes in the inclined CPB, which is clearly shown in Fig. 16 as well.

Ore extraction operations (e.g., the use of explosives) cause the roughness of rock walls. However, the roughness of rock walls can affect the rock mass/CPB interface behavior or properties (i.e., friction angle and adhesion) and thus influence the consolidation process of CPB. To quantitatively characterize the roughness of a rock wall, the roughness index R_L (i.e., the ratio of the actual and projected lengths along the rock wall in the shearing direction) is used in this study. Three different R_L including 1 (smooth rock wall), 1.5 and 2 are selected to investigate the effect of rock wall roughness on the consolidation behavior of CPB. The modeling results are presented in Fig. 17. It is evident that the rock wall roughness has significant impacts on the consolidation behavior of the CPB. The changes in the consolidation curves which start from the second stage of filling becomes more apparent with each layer. As demonstrated in Fig. 17, with increases in the rock wall roughness, there is a greater degree of consolidation of the CPB during filling, namely, the volume changes in a stope with more rough rock walls are reduced after the completion of the stope filling process (post filling stage). This can be attributed to the increased arching effect with a CPB/rock mass interface that has more surface roughness (Cui and Fall 2017). As a result, the resultant vertical stress acting on the monitored point decreases with an increased arching effect, and thus the associated volume changes are reduced in the stope with a more rough rock wall during the post filling stage. However, it should be underlined that arching effect is only significant in narrow stopes. Several field (e.g., Thompson et al. 2009; Li et al. 2014) and modeling studies (e.g., Cui and Fall 2017) have shown that the vertical stress in narrow backfilled stope is significantly less than the overburden stress because of the arching effect, which is primarily due to the consolidation process of the CPB, and the improvement of CPB/rockmass interface characteristics with binder hydration (Cui and Fall 2017). The consolidation of the CPB leads to the development of settlement and effective (horizontal) stresses, thus allowing shear stresses to develop at the CPB-rock interface (Fahey et al. 2009).

The mix recipe plays a key role in the stability of CPB structures (Cui and Fall 2015a, c). In fact, cement consumption can account for up to 75% of the production costs of CPB (Fall et al. 2008; Grice 1998). In other words, a cost-effective design of CPB structures largely depends on the cement content. Due to the significance of the cement content in CPB design, three different binder contents, including 3 wt% (43.9 kg/m³), 4.5 wt% (60.4 kg/m³) and 7 wt% (82.2 kg/m³) are examined to study their impacts on the consolidation behavior of CPB. The effect of cement content on the changes in the void ratio of the CPB is plotted in Fig. 18. It can be seen that the discrepancy in the consolidation behavior in CPB with different cement contents appears since the very early ages, and becomes progressively more obvious with filling and the curing that follows. Specifically, CPB with less cement content shows a higher rate of consolidation up to the completion of the filling. After completion of the filling, CPB with more cement content becomes more consolidated. This is because during the filling process, more cement content generates more cement hydration products which can further increase the stiffness of the CPB. As a result, the increase in the overburden stress by the newly placed CTB will cause a lower degree of consolidation when the cement content is higher. However, after the completion of the filling, consolidation induced by chemical shrinkage may be prevalent. As a result, CPB with a higher binder content becomes more consolidated during the post-filling stage. Therefore, this study clearly demonstrates the combined effect of hardening induced by binder hydration, overburden stress and chemical shrinkage on the consolidation behavior of CPB.

Due to the differences in planning and scheduling underground mining, the backfilling rate may vary from one stope to another. The differences in filling rate affect the CPB operation time and thus the mining cycle and mine productivity (Khaldoun et al. 2016; Veenstra et al. 2011). Therefore, it is necessary to study the effect of the filling rate on the consolidation behavior of the CPB. In this study, a range of backfilling rates including 0.5 m/h (i.e., 12 m/day), 1 m/h (i.e., 24 m/day) and 2 m/h (i.e., 48 m/day) are simulated. The simulation results are presented in Fig. 19. It can be observed that the filling rate has a significant effect on the development of CPB consolidation. As the filling rate is reduced, there is an increase in the consolidation at the end of the filling sequence. For example, after the filling operation is carried out; i.e., 1.625 days for 2 m/h, 2.25 days for 1 m/h, and 3.5 days for 0.5 m/h, the average degree of consolidation is 0.57, 0.62 and 0.67 respectively. This is because a reduced rate of filling results in a longer filling time (and thus curing time) for a given CPB height. Consequently, the consolidation process can continue longer, and the precipitation of more hydration products can further refine the pore space. Thus, the CPB becomes more consolidated with a slower rate of filling.

During and after pouring into underground stopes, CPB may be subjected to drained (Thompson et al. 2009, 2012) or undrained (Helinski et al. 2010; Suazo and Fourie 2015; Doherty et al. 2015) conditions. Water seepage through the barricade not only causes the dissipation of PWP, but also contributes to the consolidation of CPB. Hence, CPB placed into a stope in both drained and undrained conditions is investigated in this study. The variation in the void ratio at a monitored point is plotted in Fig. 20. For the implementation of the drainage condition, a mass flux (i.e., a product of water density and Darcy’s velocity) boundary condition is applied on the barricade surface (right vertical side of the drawpoint). The obtained results demonstrate that the differences in the consolidation behavior start from the second stage of filling. As the filling operation progresses, and stops (post filling stage), the difference between the drained and undrained conditions becomes even more evident. As shown in Fig. 20, the major change in the consolidation of the CPB for the undrained condition mainly occurs during the filling stage, namely an increase in the overburden stress due to the filling operation significantly contributes to the volume changes in CPB in the undrained condition. However, the degree of consolidation in the drained condition is only 0.72 after filling is carried out, namely, greater volume changes take place in the CPB in the drained condition after filling is carried out. This is due to water drainage which can further contribute to the densification of the CPB skeleton, and is thus more favorable for the stability of the CPB structure.

The spatial distribution of the void ratio of CPB is presented in Fig. 21. It can be seen that the arching effect in the stope in the drained condition (i.e., Fig. 21b) is more obvious in comparison with that in the undrained condition (i.e., Fig. 21a). This is because more settlement occurs in the former. Correspondingly, there is also relatively more interface displacement. Therefore, a large degree of shear stress will take place on the interface resistance which can further contribute to the arching effect in CPB. Moreover, it is evident in Fig. 21 that there is a pronounced change in the void ratio which occurs around the interface during the filling stages (i.e., 7 m from the stope floor) for the drained condition. This is due to the fact that there is more reduction in the pore space in the drained condition during and after plug placement. As a result, after 1-day of curing, the plug layer becomes stiffer in comparison to that in the undrained condition. Therefore, after subsequent filling, there is a greater difference in the stiffness of the CPB at the interface, which can result in strain concentration in the corresponding regime for the drained condition.