4.1 Volume change of tailings with the presence of WRI
The amount of volumetric compression of the tailings body resulting from settlement of tailings (i.e., equal to the average settlement of the tailings body times the area of the TSF, which was automatically calculated using a Fish function). Simulated results indicated that volume change always increased with time as more tailings were disposed (Fig. 8a). For example, volume change after the placement of the 2nd layer for tailings A without WRI was around 62 m3 and increased to around 132 m3 after the placement of the 10th layer. The changes in the slope of the curves also indicated a slower rate of volume change as tailings height increased (Fig. 8a). Tailings C had the smallest volume change (around only 40 m3) among simulated tailings, which was explained by the smallest settlement of this type of tailings (session 3.2).
The presence of WRI can increase the consolidation rate of tailings, but they also occupy some space in the TSF. In practice, results have shown that most of the simulated tailings were fully consolidated after around 6 months. Using WRI therefore did not have a significant influence on the volume gain, but rather contributed to decrease the space available for tailings deposition. In other words, the volume of tailings that could be deposited in the TSF with the presence of WRI was always smaller than the case without WRI for all types of tailings (Fig. 8a). For example, the volume change of tailings A without WRI after the placement of the 10th layer was around 132 m3/per 5 linear meter, i.e., around 14% more than that of model with WRI (113 m3/ per 5 linear meter) (Fig. 8a). The differences of volume change (DV) between models with and without WRI was estimated as:
$$\frac{\left({V}_{t }{V}_{w}\right) }{{V}_{t }}*100%$$
Where Vt: the volume change of model with tailings only (m3); Vw: the volume change of model with WRI (m3)
DV tended to become relatively constant after the deposition of the first fifth layers (Fig. 8b). For instance, DV of tailings A decreased from 25% after the placement of the 2nd layer to 16% after the filling of the 5th layer, while that of tailings C exhibited a reduction of nearly 17% (Fig. 8b). DV for tailings C and D tended to be greater than those of tailings A and B. For example, DV for gold tailings after the filling of the last layers were around 15%, while that for tailings C were somewhat higher, at around 20% (Fig. 8b). These differences could be explained by the difference in the stiffness evolution during compression of other types of tailings.
The additional height of the TSF required to dispose the same amount of tailings with WRI presence as without WRI can be accordingly estimated. This height can be estimated as the sum of volume occupied by WRI and total differences of volume change of tailings body between models with and without WRI divided by the area of the TSF (Table 2). These heights were around 2.22, 2.17, 2.06 and 2.45 m for tailings A, B, C and D, respectively. In other words, the increase of thickness of the TSF was less than 8% total thickness of tailings (Table 2). This was very meaningful for practitioners to briefly calculate the additional height of TSFs required when applying codisposal technique (at least at the primary design stage).
Table 2
Additional height required because of the presence of WRI in the TSF for various types of tailings

Volume occupied by WRI
(m3)

Total volume loss*
(m3)

TSF area
(m2)

Additional height
(m)

Tailings A

900

143

470

2.22

Tailings B

900

119

470

2.17

Tailings C

900

69

470

2.06

Tailings D

900

251

470

2.45

* Equal total differences of volume change resulting from tailings settlement between models with and without WRI 
Ratio between volume of tailings and WRI disposed in this study was around 15.7. In practice, this ratio could widely change depending on the practical considerations of each mine sites. For example, this could depend on the primary goal of mine waste management of each mine site. Some might prioritize the volume of WRI that can be disposed to eliminate the need for the construction of waste rock piles. Coarse waste rocks might, indeed, contain sulfide minerals that can oxidize and generate acid mine drainage, and the placement of waste rock as inclusions inside the TSF could therefore efficiently contribute to prevent potential AMD generation (Jahanbakhshzadeh et al. 2019; Bussière and Guittonny 2020). The volumes of tailings and waste rock produced by mining activities can also vary widely in practice depending on the ore body characteristic and production technique (Blight 2010). The ratio of tailings and waste rocks volume was thus changed by changing the width of WRI in the model (i.e., from 6 m to 10, 12, 18 and 24 m corresponding to the volume ratio of 15.7, 9.0, 7.3, 4.6 and 3.2, respectively) to estimate the volume loss as a function of the quantity of waste rocks used in the TSF as inclusions. In general, the more volume of WRI placed in the pit, the less space dedicated for tailings that can be stored in the TSF (Fig. 9). For example, the DV values of tailings A for model with WRI width of 24 m was around 30 % which was nearly 2 times higher than that of model with WRI width o 6 m. The same trend was recorded for tailings B and C (Fig. 9). The trend of tailings A and B was somewhat similar to each other, while DV for tailings C seemed to be higher than those of tailings A and B. Accordingly, equations presenting the evolution of DV with the changes in the volume ratio of tailings and WRI were derived as: \(y=49.6{x}^{0.48}\) (R2 = 0.97) for tailings A, \(y=55.6{x}^{0.58}\) for tailings B (R2 = 0.99) and \(y=56.8{x}^{0.39}\) (R2 = 0.980) for uranium tailings. These results can, thus, provide practitioners with a brief estimation (at least for the primary design stage) the potential volume of tailings that might be loss due to the presence of WRI for various volume ratios.
4.2 Effect of the filling rate
TSF depth and deposition rates vary with mine size, production rate and type of operations (surface or underground) (Blight 2010; MEND 2015). Filling rate for TSF at Malartic mine is, for example, around 3 m per year (Boudrias 2018), and between 2 m and 14 m per year at Rabbit Lake mine (MEND 2015). Additional simulations corresponding to 6 and 9 m/year filling rate were therefore carried out for tailings A to evaluate effects of tailings thickness on the evolution of tailings consolidation with the presence of WRI. Filling rate seemed to have a negligible effect on the volume change between the cases with and without WRI, which remained around 14% at the end of the filling process for all models regardless of layer thickness (Fig. 10a).
A ratio Rt90, i.e., the ratio of t90 between models with and without WRI, was introduced to represent the effect of filling rate on the consolidation rate of tailings (Fig. 10b). The effect of WRI on the consolidation rate was increased for greater filling rates, which indicated that the use of WRI would be more beneficial with higher filling rate in practice. Rt90 at 10 m from the WRI after the deposition of the 6th layer was 1.45, 1.70 and 1.83 for the 3m, 6m and 9m thick models respectively (Fig. 10b). The ratio also increased with the number of tailings layers. This ratio was, for example, around 1.46 and 1.54 for the 6m thick model after the placement of the 2nd and 4th layer (Fig. 10b).
Models with 3 m/year but with different filling scheme instead of an instantaneously adding (i.e., layer of 1.5 m per 6 months and layer of 1 m per 4 months, respectively) were performed for tailings A to evaluate the potential effect of the assumption of instantaneous filling scheme on the rate of consolidation of tailings. Simulated results indicated that the effect of instantaneous filling on the rate of consolidation of tailings was insignificant. It took essentially the same amount of time with such filling intervals to dissipate 90% of excess PWP. The same trend was also observed by Boudrias (2018).