Consolidation process of uncemented backfill slurry in a mine stope considering hydro-geotechnical properties of rockmass in adjacent stopes

doi:10.21203/rs.3.rs-4115308/v1

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Consolidation process of uncemented backfill slurry in a mine stope considering hydro-geotechnical properties of rockmass in adjacent stopes

https://doi.org/10.21203/rs.3.rs-4115308/v1

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A reasonable assessment on pore water pressure (PWP) and effective stresses of backfill slurry during consolidation process is critical to ensure a secure and economic backfilling in mine stopes. This task can be accomplished by analytical or numerical simulations, but most of the previous simulations did not take into account the hydro-geotechnical properties of rockmass in adjacent stopes, which was mainly simplified to an impervious boundary. This treatment may not be representative of the field conditions in underground mine stopes because of the presence of geological joints and/or mining induced cracks in surrounding rockmass that serve as seepage paths for pore water discharged from the filled slurry. In this paper, numerical modeling was conducted with FLAC3D to investigate consolidation process of uncemented backfill slurry in a vertical stope considering the surrounding rockmass with different permeability, initial saturation, porosity, and the rockmass width. The results show that the PWP and effective stresses of backfill slurry in a mine stope considering adjacent rockmass can be very different with numerical outcomes by simplifying the rockmass as impermeable or permeable boundaries assumed in previous studies. For the same backfill slurry in mine stopes with different drainage conditions along side walls, the peaks of the PWP and effective stress differ by a factor of three to five for each consolidation process. This would make the evaluations on backfill slurry consolidation either too conservative, with impermeable side walls, or too aggressive, with free drainage side walls, ignoring the actual rockmass hydro-geotechnical parameters. Different hydro-geotechnical properties of the rockmass have different impacts on the evolutions of the PWP and effective stresses of the consolidating backfill slurry. However, when the hydraulic conductivity of the surrounding rockmass is lower than 10^− 8 m/s, the simulated PWP and effective stresses for the backfill slurry will be comparable to the numerical models that simplify the rockmass to a watertight boundary. Furthermore, the influences of different hydro-geotechnical properties of adjacent rockmass on the lateral earth pressure coefficient of consolidated backfill were also discussed. In addition to the validations of simulated PWP and stresses against the analytical results with Gibson model and an arching model respectively, the numerical results were compared with the previous published in-situ monitoring benchmarks to validate the consolidation process simulated by FLAC3D here.

backfill slurry

consolidation

pore water pressure

effective stress

rockmass

FLAC3D

Valuable minerals are extracted from ore rocks excavated mostly from underground stopes, which will lead to additional creations of large mined voids and huge number of solid wastes including mine tailings and waste rocks. Under this condition, underground mining methods with backfill have been increasingly employed in worldwide mines, which allows the tailings to be backfilled into the excavated stopes (known as backfill), thereby reducing the surface disposal of mine wastes, improving ground stability around underground voids and increasing ores recovery rate (Aubertin et al. 2002; Belem and Benzaazoua 2008; Shahsavari and Grabinsky 2014, 2015).

Mine tailings blended with water and/or binders are transported from surface backfill plants primarily by pipelines and then poured into underground stope voids where access to the mine stopes should be pre-blocked with man-made structures (known as barricades) to retain the slurried tailings. During and after filling operations, the barricades must remain stable until the slurry tailings have reached the desirable consolidation state under self-weight loading. Even with this clear purpose, accidents of barricades cracking occur from time to time, mainly caused by the pressure from the unconsolidated tailings slurry, which not only poses a serious safety hazard to miners and equipment, but also results in a significant economic loss to the mines in cleaning up the rushed-out slurry during shutdowns (Potvin et al. 2005; Revell and Sainsbury 2007; Government of Western Australia 2020). Therefore, it is significant to correctly evaluate the pore water pressure (PWP) dissipation of the backfill slurry especially in large scale stopes of mass mining, as maintaining high PWP for a long time may aggravate the serious crack accidents of the barricades in underground workplaces (Potvin et al. 2005; Yumlu and Guresci 2007).

To analytically calculate the PWP during the consolidation process of backfill slurry in mine stopes, one can refer to the Gibson model (1958), which was initially proposed to investigate the self-weight consolidation of an accreting clayey layer based on one dimensional consolidation assumptions of Terzaghi (1943) theory. The quasi-analytical solution of Gibson (1958) contains an integral part that can only be numerically evaluated (cannot be solved by hand calculations or commonly available calculation tools) to calculate the PWP of ongoing slurry sedimentation, and this limitation was recently overcome by Zheng et al. (2018a, b), who formulated the true analytical equations for slurried materials consolidation with pervious or impervious base respectively. In addition, Fahey et al. (2010) updated the analytical solution of Gibson model by modifying the constant coefficient of consolidation c_v to a varying value based on the tested permeability and constrained modulus changed with consolidating time of slurried materials from two mine sites. Cui and Fall (2016, 2020) proposed coupled analytical models to calculate the PWP and effective stress of paste backfill considering consolidation behavior under thermal, hydraulic, mechanical and chemical (THMC) processes. The Gibson model and its following modifications can reasonably represent the one-dimensional consolidation process for backfill slurry, but mostly assume that the slurry is in a simplified stope with impermeable side confining walls that allow water to drainage freely from the top and/or bottom of the backfilled stope.

Numerical modeling has proven to be an effective and efficient tool to investigate the consolidation processes of backfill slurry in mine stopes. Helinski et al. (2007a, a) applied the Minefill-2D code (non-commercial) based on a self-developed finite element program to investigate the coupled processes of consolidation and hydration of cemented tailings backfill, in which the water was allowed to be discharged from the barricade and top surface of slurry, but with a stope model having impermeable side walls. El Mkadmi et al. (2014) studied the consolidation behavior of backfill slurry using SIGMA/W (commercial software in Geo-studio), comparing rapid complete filling of stopes under subsequently progressive drainage conditions with continuous backfilling of slurries at varying rates of filling under simultaneous drainage conditions. In their models, free drainage faces were applied on the stope floor and top surface of filled slurry, but with water-proof boundaries for side walls. Li (2013) numerically modeled, also in SIGMA/W, the effects of wick drain in stopes on the drainage process of slurried backfill. The wick drains together with the top and base planes of the stopes were simulated with a fixed zero PWP (free drainage boundaries), while the side walls of stopes were considered impervious. Doherty (2015) carried out a numerical study with ABAQUS (commercial software) into the soil water retention properties affecting the PWP and effective stress of backfill in a single mine stope with free drainage on backfill top surface and barricade, and with impervious boundaries on the stope base and side walls. Veenstra (2013) built a model with FLAC3D (typical commercial software widely used in mining engineering) to numerically investigate the pressure of early age paste backfill exerting on the barricades during the filling process. The hydraulic boundary consists of a fixed zero PWP along the backfill-rock interface as well as at the backfill top surface. As can be seen from the above numerical simulations on backfill slurry consolidation in mine stopes, most of the previously reported simulations did not consider the hydro-geotechnical properties of adjacent rockmass in nearby stopes, which were arbitrarily simplified to the impermeable side boundaries in an individual mine stope. This assumption may not be representative of the reality of underground mining, because the side rockmass walls usually contain geological faults, joints and/or mining induced cracks that allow excess pore water pressure to dissipate through these fractures.

In terms of physical tests, Wickland and Wilson (2005) fabricated four cylindrical columns with 1 meter in diameter and 6 meters in height by keeping the top and base planes of the columns as free drainage boundaries to test the permeability and self-weight consolidation process of blended waste rocks and tailings with different mixing ratios. Belem et al. (2016) built three columns with different drainage boundaries on side walls (full-height sealed, lower half-height sealed and upper half-height free drainage, and free drainage along the full-height) to carry out physical model tests on the gravity driven consolidation of slurry prepared with tailings and binders from two Canadian mines, which contributed to well understanding on the effects of vertical settlement and drainage on the final cured backfill strength. Physical modeling tests on consolidation process also help to reveal its effects on the settlement and strength properties of tailings slurry to work out an optimal backfilling strategy in mine stopes (Ghirian & Fall 2016; Islam et al. 2020; Qin et al. 2021; Deng et al. 2022).

Furthermore, in-situ measurements of PWP and total stress in mine stopes can be of great help in revealing the occurrence of consolidation in tailings slurry and in characterizing the variations of drainage parameters during practical filling processes (Belem et al. 2004; Thompson et al. 2009, 2012; Helinski et al. 2010b; Doherty et al. 2015). These efforts were instrumental in designing barricade structures, controlling schemes of filling rates in backfill plant and underground stopes, and determining reasonable time to excavate the ore rocks in nearby stopes based on the real-time monitored pressure development during the consolidation of filling slurry.

Summarily, previous analytical solutions, numerical models and physical tests have shed light on the understanding of backfill slurry PWP dissipation over time. However, current works considered the consolidation process of backfill slurry in the vertical direction along a single mine stope, mostly with a fixed zero PWP boundary at the top surface, totally pervious or impervious boundaries on the bottom plane, and waterproof constraints on the side walls.

However, in the multiple steps of excavating and filling procedures of the divided mine stopes in open stoping with subsequent backfill mining methods, the backfill slurry in one stope is typically constrained by the rockmass and/or cured backfill body in adjacent stopes. Hydro-geotechnical properties such as permeability, saturation, and drainage boundaries of adjacent rockmass vary depending on geological structures and other fractures, and may differentially affect the consolidation process of the backfill slurry in one stope. As stated in previous publications (e.g., Abdelghani et al. 2015; Jaouhar and Li 2019), these factors should be considered in the practical mining process, but no studies have been reported on their influences on the consolidation process of tailings backfill slurry.

In this study, numerical simulations are firstly conducted with FLAC3D to investigate the consolidation process of uncemented backfill slurry in a vertical mine stope considering the hydro-geotechnical properties of rockmass in adjacent stopes (including permeability, initial saturation, porosity, width of the rockmass and external drainage boundaries) under the practical mining procedures of multiple stopes. Pore water pressure (PWP), total and effective stresses of the uncemented backfill slurry are comprehensively analyzed. Numerical outcomes on PWP are validated against the analytical results from the Gibson model (1958) and the in-situ monitoring results from Helinski et al (2010b). Some simulated effective stresses are further compared with the analytical results for submerged backfilled stopes after considering the arching effect by Li and Aubertin (2009a, 2009b). The influences of cement hydration on the consolidation of backfill slurry are not emphasized here but with necessary discussions. Coupled analyses about the thermal, chemical or mechanical factors, and the man-made drainage structures (e.g., wick drains, drainage holes, barricades arrangements) are not the concern of this paper.

2.1 Model construction and boundary conditions

As shown in Fig. 1(a), in multiple excavating and filling steps of an open stoping with subsequent backfill mining method, the large and thick ore-body is usually divided vertically into several stages, which are separated from each other by crown (or sill) rock pillars to isolate the mining activities. At each stage, the ore rock will be further divided into primary stopes (stope ① and stope ②) and secondary stopes (stope ③ and stope ④) which can be synchronously excavated at interval of one stope or three stopes. For some multilayer or vein style ore-bodies, if the planned stopes are prospected to be barren rocks, these stopes will be left for ground control with no excavation, which will also have possible effects on the seepage paths of the tailings slurry in adjacent filled stopes.

The above excavating and filling procedures can lead the drainage boundaries and the consolidation processes of the backfill slurry in one typical vertical stope to the following conditions, especially after considering the lateral drainage boundaries of adjacent rock walls, as shown in Fig. 1(b):

If the backfill slurry during drainage and consolidation in one of a stope is confined by intact non-fractured rockmass or dense cemented fine tailings backfill, the drainage boundaries of the filled slurry along side walls will be nearly impermeable, which will result in a relatively slower consolidation and a higher PWP in the backfill slurry, because the bleed water from tailings slurry may only be able to drain through the barricades in the bottom of the stopes, or just accumulate on the top surface of tailing slurry to form a water pond (Yang and Li 2017; Ma et al. 2023).

If the backfill slurry in a stope is surrounded by fractured rockmass or backfill bodies cured with coarse waste rocks, water from the tailings slurry will be able to flow across one or more stopes via possible drainage paths. In these cases, the hydro-geotechnical properties of the rockmass and/or existing backfill body are expected to have different effects on the consolidation process of the filled slurry, which are important and necessary to be investigated. However, these practical factors have rarely been reported in most previous numerical simulations (Helinski et al. 2007a, 2010a; Li 2013; El Mkadmi et al. 2014; Doherty 2015; Zheng et al. 2018a, 2018b, 2020a, b).

Except for the drainage conditions for side boundaries, the top surface of the filling slurry is fixed at zero PWP as usual, while the base plane of the stope is set to be impervious due to the crown rock pillars between stages which are commonly used for the top and base drainage boundaries in previous models (Gibson 1958; Helinski et al. 2010a; Doherty 2015; Zheng et al. 2018b; Jaouhar and Li 2019).

As shown in Fig. 2(a), a typical vertical stope in the mining procedure of Fig. 1 was idealized as a physical model to evaluate the development of PWP and stresses during backfill slurry consolidation. The excavated stope void which is gradually filled with slurry has a fixed stope width B, a constant stope height H and confined by side rockmass matrix of a variable width W. Accordingly, a plane strain numerical model was constructed in FLAC3D, as shown in Fig. 2(b), with a vertical symmetry plane (VSP) along the vertical central line of the stope width, to simulate the consolidating properties of the uncemented backfill slurry progressively deposited in the excavated stope void.

As shown in Fig. 2(b), the mechanical and hydraulic boundaries of the numerical models were set as follows:

For the bottom plane of the backfill slurry and the adjacent rockmass matrix illustrated by the red line, the mechanical boundary was set by fixing displacements in all directions together with impervious hydraulic simulations.

For the left side plane of filling slurry along VSP (vertical symmetry plane) illustrated by the red line, only the horizontal displacement in its normal direction was fixed, and the hydraulic boundary was kept impermeable to simulate the symmetric issue.

For the right-side plane of rockmass matrix illustrated by the blue line, only the horizontal displacement in its normal direction was fixed, and the hydraulic boundary was set to be fully pervious (kept constant to zero PWP) to simulate the free drainage conditions of nearby excavated voids shown in Fig. 1(b).

For the top surface of the rockmass matrix illustrated by the red line, which is free to move in all directions, the hydraulic boundary was set to be waterproof due to the crown rock pillar between the two mining stages shown in Fig. 1(b).

For the continuously deposited backfill slurry in the excavated stope void, the top surface of each newly added backfill layer (0.5m per layer in height) illustrated by the blue line was set to be fully pervious (zero PWP) and was allowed free deformations without fixed displacements. Besides, it should be noticed that after adding a new slurry layer to the previously deposited backfill layer, the zero PWP boundary on the top surface of the previous layer should be removed and re-assigned to the top surface of the newly added backfill layer.

Under the above mechanical and hydraulic boundaries, a series of sensitivity analysis about model meshing in FLAC3D were performed to ensure stable numerical results. The hexahedral elements were applied with 0.25 m in Z-direction and 0.5 m in X-direction per grid. A 0.25 m element in Y-direction (perpendicular to the page) was used for all models and set to a fixed Y-displacement and impervious boundary to simulate the plane strain problem.

2.2 Material parameters and numerical cases

In all the numerical models here, the backfill slurry and rockmass were assumed to be homogeneous, isotropic elasto-plastic materials, obeying the Mohr-Coulomb criterion, with mechanical and hydraulic parameters as shown in Table 1. These typical values were selected mainly based on the reports given in the previous literature (Aubertin et al. 1996; Belem et al. 2006; Ghirian and Fall 2013; Jaouhar and Li 2019; Zheng et al. 2019) and partly based on the authors’ experiences gained during the realization of several mining projects with backfill.

Table 1

Mechanical and hydraulic parameters of the backfill slurry and rockmass
No.	Items	Parameters	Symbols	Values	Unit	References
1	Uncemented backfill slurry	Dry density	ρ_df	1500	kg/m³	(Zheng Jian, 2019)
2		Bulk modulus	K_f	480	MPa
3		Shear modulus	G_f	360	MPa
4		Cohesion	c_f	0	kPa
5		Internal friction angle	φ_f	30	°
6		Dilation angle	ψ_f	0	°
7		Hydraulic conductivity	k_f	5×10^− 6	m/s	(Aubertin, 1996)
8		Porosity ratio	n_f	50%	-	(Ghirian, 2013)
9		Initial saturation ratio	s_f	100%	-	(Ghirian, 2013)
10	Rockmass	Dry density	ρ_d	2700	kg/m³	(Zheng Jian, 2019)
11		Bulk modulus	K	2.8	GPa
12		Shear modulus	G	1.68	GPa
13		Cohesion	c	9.4	MPa
14		Internal friction angle	φ	38	°
15		Dilation angle	ψ	0	°
16		Hydraulic conductivity	k	VAR	m/s	(Goodman, 1989)
17		Porosity ratio	n	VAR	-
18		Initial saturation ratio	s	VAR	-
19	Water	Density	ρ_w	1000	kg/m³	Constant
20	Water	Bulk modulus	K_w	2×10⁶	kPa
21	Other	Gravitational acceleration	g	10	m/s²

Besides, it is worth emphasizing that the real structural planes in the practical rockmass representing geological joints and/or mining induced fractures (shown in Fig. 1) were not modeled here, but idealized with varying values of permeability, porosity and initial saturation, which is a common simplification used in previous numerical simulations (Wang and Narasimhan 1985; Goodman 1989; Naqa 2001; Jaeger et al. 2007; Cai et al. 2013).

The hydro-geotechnical properties of the rockmass were key variable factors schemed in numerical program of Table 2 which were considered to investigate their effects on the consolidation process of confined backfill slurry in a typical mine stope. Moreover, the stope width (B = 12m) and the final backfilled stope height (H = 30m) were held constant in all the numerical models of Case1, Case2 and Case3 shown in Table 2. But the width of the rockmass, W, was varied in Case4 based on the proposed simulation program to represent the different seepage paths for backfill slurry drainage.

Table 2

Simulation scenarios for the consolidation process of backfill slurry in mine stopes considering the hydro-geotechnical properties of adjacent rockmass
Cases	Figures	Properties of rockmass laterally confining backfill slurry				Hydraulic boundaries on side walls of filled stope
Cases	Figures	Width W (m)	Hydraulic conductivity k (m/s)	Porosity ratio n	Initial saturation ratio s	Hydraulic boundaries on side walls of filled stope
Case0	4, 5, 6	0	/	/	/	impermeable
Case1	7, 8	12	1×10^− 5, 1×10^− 6, 1×10^− 7, 1×10^− 8	25%	40%	Based on assigned hydraulic properties of the rockmass.
Case2	10, 11	12	1×10^− 6	10%, 25%, 40%	40%
Case3	12, 13	12	1×10^− 6	25%	40%, 60%, 80%, 100%
Case4	15	12, 36	1×10^− 6	25%	40%

3.1 Simulated PWP compared with analytical results of Gibson model

A world-recognized model to analytically calculate the PWP of accreting sediment layers consolidating with its increasing thickness was proposed by Gibson in 1958, which can be employed to investigate the consolidation process of the backfill slurry in mine stopes.

In analogy with the Gibson model (1958), Fig. 3 can be used to illustrate the deposition of backfilling slurry on an impermeable base of a mine stope. The initial thickness of the slurry at the beginning time is zero. After a deposition time t (hour) and a constant increasing rate m (meter per hour, simplified as m/h), the backfilled slurry reaches a certain thickness h (m), which means the current height of the slurry can be expressed as h = m×t. The slurry will continue to rise up to a final height of H (m) under the same increasing rate m (m/h) in the vertical direction.

As the height of the backfill slurry increases, a part of water can be only drained from the top permeable surface in Gibson model with the assumed impermeable side and base boundaries. In this condition, Eq. (1) was proposed to calculate the excess PWP at an elevation z (m) and deposition time t (hour) in the backfilled slurry.

$${c_{\text{v}}}\frac{{{\partial ^2}u}}{{\partial {z^2}}}=\frac{{\partial u}}{{\partial t}} - \gamma ^{\prime}\frac{{dh}}{{dt}}$$

where u (kPa) is the excess PWP defined as the value of the current total PWP in the filled slurry minus the hydrostatic water pressure at the same position; c_v (m²/h) is the consolidation coefficient of the slurry; γ′ =γ_f −γ_w, γ_f and γ_w (kN/m³) are the unit weight of the filled slurry and the water respectively.

Considering the zero PWP of the constant free drainage boundary at the top permeable surface of backfilled slurry, Eq. 1 can be further transformed to Eq. 2 to calculate the excess PWP u of the slurry.

$$u=\gamma ^{\prime}mt - \gamma ^{\prime}{(\pi {c_{\text{v}}}t)^{ - \frac{1}{2}}}\left[ {\exp \left( {\frac{{ - {z^2}}}{{4{c_{\text{v}}}t}}} \right)} \right] \times \int_{0}^{\infty } {\xi \tan h\left( {\frac{{m\xi }}{{2{c_{\text{v}}}}}} \right)} \cos h\left( {\frac{{z\xi }}{{2{c_{\text{v}}}t}}} \right)\exp \left( { - \frac{{{\xi ^2}}}{{4{c_{\text{v}}}t}}} \right)d\xi$$

where ξ (dimensionless) is an integral variable (0 < ξ < ∞).

Gibson defined a dimensionless time factor T to further interpret the calculated results about the excess PWP at any accreted thickness h and relevant time t of the deposited slurry, which can be expressed as the Eq. 3.

$$T=\frac{{{m^2}t}}{{{c_{\text{v}}}}}=\frac{{m \times \left( {m \times t} \right)}}{{{c_{\text{v}}}}}=\frac{{m \times h}}{{{c_{\text{v}}}}}$$

Before numerically investigating the consolidation process of backfill slurry in a mine stope considering the hydro-geotechnical properties of adjacent rockmass, the applicability and reliability of the FLAC3D program should first be validated. The Gibson model mentioned above can give acceptable analytical results of the PWP in backfill slurry to verify the numerical outcomes.

The self-weight consolidation problem presented by Gibson was firstly modeled in FLAC3D. The width of the surrounding rockmass W was set to zero shown as the Case0 in Table 2. The hydraulic boundaries were set to a fixed zero PWP (free drainage) at the top surface of each filled layer and fixed impermeable side and base surfaces for the filled slurry which were kept consistent with Gibson’s analytical model. Besides, the mechanical boundaries for the filled slurry were set to be completely fixed at the bottom surface in all directions and fixed at the side walls in horizontal directions. These assumptions were all consistent with the settings of Gibson’s analytical model.

The parameters used in the analytical and numerical models were kept the same with the values shown in Table 1. In FLAC3D models, the unit weight γ_f (kN/m³) and consolidation coefficient c_v of the simulated backfill slurry can be obtained by Eq. 4 and Eq. 5 based on the parameters given in Table 1.

$${\gamma _{\text{f}}}={\text{(}}{\rho _{{\text{df}}}}+{n_{\text{f}}}{s_{\text{f}}}{\rho _{\text{w}}})g$$

$${c_{\text{v}}}=\frac{{{k_{\text{f}}}}}{{{\rho _{\text{w}}}g\left( {\frac{{{n_{\text{f}}}}}{{{K_{\text{f}}}}}+\frac{1}{{{K_{\text{f}}}+4{G_{\text{f}}}/3}}} \right)}}$$

Figure 4 illustrates the comparisons of the numerical simulated excess PWP u with analytical results of the Gibson solution under different time factors T. When the value of T is close to zero, it represents the beginning period of the accreted slurry and the filled height is relatively small. With the increase of the time factor T, the height of the accreted slurry will also be added under the increasing rate m (m/h). Among the continuous filling and consolidating processes, Fig. 4 illustrates only some typical outcomes of PWP at discontinuous certain time factor T (= 0.5, 1, 2, 4, 8, 32). The vertical axis represents the ratio of an elevation z (m) at any selected position to the current filled slurry height h (m). Along the vertical ordinate value, a value of 0 indicates that the analyzed location is at the base plane of the backfilled stope and a value of 1 indicates that the analyzed location is at the top surface of the currently filled slurry. In addition, the horizontal axis represents the ratio of the excess PWP u to the effective self-weight stress γ′×h of the currently filled slurry at different times.

It can be seen from Fig. 4 that there are good agreements for the numerical and analytical results about the excess PWP among different filling and consolidating periods represented by the dimensionless time factor T. The comparisons demonstrate that the constructed numerical model using FLAC3D in this study is a reliable method to investigate the excess PWP and the consolidating process for the backfill slurry in mine stopes.

3.2 Simulated stress compared with analytical results of arching model

Together with the validation of the simulated excess PWP u for backfill slurry, the effective stress distribution of the consolidating backfill is another key issue to be verified, because the stresses close to the bottom of the slurried backfill are proved to be a crucial factor affecting the stability of man-made barricade structures in access drives to stopes, and the stresses along the backfill height in stopes are significant for understanding the ground control behaviors of backfill and its strength requirement after side exposure in mining procedures (Liu et al. 2016a, 2016b, 2017, 2018, 2021).

For fully drained and totally consolidated dry granular materials, the Marston model (1930) and the Terzaghi model (1943) initially derived from soil mechanics have been widely used to analytically calculate the backfill stress distribution (Li et al. 2005, 2013). On the basis, after considering the effect of PWP, Li and Aubertin (2009a) further proposed a modified analytical solution to assess the total and effective stresses in a submerged cohesionless backfill, which assumed a specified phreatic surface in the backfill to calculate the stresses above and below the phreatic line where the PWP equals to zero.

Eq. 6 was suggested by Li and Aubertin (2009a) to analytically calculate the effective vertical stress σ′_v (kPa) at a depth h (m) of the backfill in a mine stope with a width B (m), a totally filled stope height H (m) and a specified phreatic surface at vertical depth H_p (m) from the top surface of backfill.

$$\begin{gathered} {{\sigma ^{\prime}}_{\text{v}}}=\frac{{B{\gamma _{{\text{subf}}}}}}{{2{{K^{\prime}}_{{\text{sf}}}}\tan {{\phi ^{\prime}}_{\text{f}}}}}\left[ {1 - \exp \left( { - \frac{{2{{K^{\prime}}_{{\text{sf}}}}\left( {h - {H_{\text{p}}}} \right)}}{B}\tan {{\phi ^{\prime}}_{\text{f}}}} \right)} \right] \hfill \\ {\text{ }}+\frac{{{\gamma _{{\text{mf}}}}B}}{{2{K_{{\text{sf}}}}\tan {\phi _{\text{f}}}}}\left[ {1 - \exp \left( { - \frac{{2{K_{{\text{sf}}}}{H_{\text{p}}}}}{B}\tan {\phi _{\text{f}}}} \right)} \right] \times \exp \left( { - \frac{{2{K_{{\text{sf}}}}\left( {h - {H_{\text{p}}}} \right)}}{B}\tan {{\phi ^{\prime}}_{\text{f}}}} \right) \hfill \\ \end{gathered}$$

where γ_subf (=γ_satf−γ_w, kN/m³) is the unit weight of the submerged backfill under the phreatic surface, γ_satf is unit weight of saturated backfill and γ_w is unit weight of water; γ_mf (kN/m³) is the unit weight of wet backfill above the phreatic surface; K′_sf (= tan²(45°−φ′_f/2)) is the effective coefficient of lateral earth pressure for the submerged backfill under the phreatic surface and K_sf (= tan²(45°−φ_f/2)) is the active coefficient of lateral earth pressure for the wet backfill above the phreatic surface; φ′_f is effective friction angle of the submerged backfill under the phreatic surface and φ_f is the friction angle of wet backfill above the phreatic surface.

When the backfill is completely under water at the moment of the stope void being fully filled, which means the assumed phreatic surface is at the top of the backfill (i.e., H_p=0), the effective vertical stress σ′_v (kPa) of the submerged consolidated backfill can be further determined by Eq. 7. This equation can be used as an analytical reference to validate the numerically simulated effective vertical stress of the slurried backfill at different accreting and consolidating times.

$${\sigma ^{\prime}_{\text{v}}}=\frac{{B{\gamma _{{\text{subf}}}}}}{{2{{K^{\prime}}_{{\text{sf}}}}\tan {{\phi ^{\prime}}_{\text{f}}}}}\left[ {1 - \exp \left( { - \frac{{2{{K^{\prime}}_{{\text{sf}}}}h}}{B}\tan {{\phi ^{\prime}}_{\text{f}}}} \right)} \right]$$

To validate the numerical program of simulating effective stresses in the slurried backfill during consolidation, the same condition corresponding to Eq. 7 was numerically modeled with FLAC3D. According to Fig. 2, the width W of the surrounding rockmass was set to zero. The hydraulic boundaries were set to a fixed zero PWP (free drainage) at the top surface of the filled slurry, and fixed impermeable side and base surfaces (Case0 in Table 2). In addition, the displacement of the base of the backfill was completely fixed in all directions, the two side walls of the backfill were fixed in the normal direction and all elements were fixed in the Y-direction (perpendicular to the paper). The backfill is considered as an elastic-plastic material obeying the Mohr Coulomb criterion. The backfill properties used in the analytical equation and numerical model remain consistent with the values in Table 1.

Figure 5 shows the evolution of the numerically simulated effective vertical stress monitored at the bottom of the stope (illustrated as the blue star monitoring point in Fig. 2a). The curve was started from the beginning of the layer-by-layer accreting increase of the backfill slurry in the excavated stope void, to the moment when the stope void was fully filled over the entire height H, and then to the gradual development of the effective stress during the subsequent consolidation of the backfilled slurry.

Based on the given program in FLAC3D here (a constant filling rate of 0.5 m/h), it took 60 hours to fully fill the stope void to a final height of H = 30m. During this filling period, the effective vertical stress built up as the slurried backfill rises and the PWP was obtained in parallel with the drainage and consolidation process. And it was defined as the 0 day at the moment of the stope void just being fully filled throughout entire stope height H, after which the drainage and consolidation will continue to have an effect on the effective vertical stress.

It can be seen from Fig. 5 that the effective vertical stress at the stope bottom increases rapidly within the period from 0 hour to 60 hours following the backfill slurry accretion layer by layer in the stope void. After 60 hours, the effective vertical stress continues to increase up to 396 hours, i.e., 14 days after the stope void is completely filled throughout the entire height H. In this period, the increase of the effective stress was mainly caused by the water drainage and gravity conduction from top part slurry to the bottom area of stope. Then, from 396 hours to 732 hours (i.e., 14d to 28d after full filled stope), the effective vertical stress increases marginally, indicating that the water drainage and consolidation process for slurried backfill is coming to an end. And after 28 days starting from the moment of fully filled the stope void, the simulated effective vertical stress at stope bottom hardly changes, which means the backfill in the bottom area of the stope is close to a fully drained and totally consolidated state.

Figure 6 illustrates the variations of the effective vertical stress along the vertical center line of the whole height in backfilled stope at different times after the moment of fully filling the stope void. In addition, the effective vertical stress calculated analytically with Eq. 7 is also presented as black solid line in Fig. 6 for comparison.

It can be seen from Fig. 6 that the effective vertical stresses simulated with FLAC3D models at 60h (i.e., moment of just fully filled stope void defined as 0 d) represented by blue squares are much smaller than the analytical stress with Eq. 7 which is assumed for a submerged fully consolidated backfill. However, it is very interesting to note that with the increase of the consolidating time, the numerically simulated effective stress along the stope height gradually increases and approaches to the analytical stress of Eq. 7. These processes clearly illustrate that the gradual self-weight consolidation of the backfill slurry with water drainage from backfill slurry to dissipate excess PWP and increase effective stress. When the time comes to 732h (i.e., 28d after full filled the stope void), it can be observed from Fig. 6 that the numerical and analytical results of effective vertical stress have a good agreement, especially in the lower half height of the backfilled stope. This agreement can also be corresponded to the curve shown in Fig. 5 to illustrate the fully drained and totally consolidated state of backfill near stope floor. In addition, the simulated effective vertical stress in the upper half height of the backfilled stope at the time of 732h is still smaller than the analytical results, which implies that some additional time is still needed for the upper filled slurry to reach the fully drained and totally consolidated state.

The comparisons shown in Fig. 5 and Fig. 6 can prove that the proposed numerical program with FLAC3D here is competent to simulate the excess PWP and effective stress states of the slurried backfill in mine stopes at different filling and consolidation times. Subsequently, the numerical method is applied to investigate the consolidation process of uncemented backfill slurry in a mine stope considering the hydro-geotechnical properties of adjacent rockmass.

4.1 Hydraulic conductivity k

Figure 7 shows the evolution of the simulated PWP monitored at the bottom (illustrated as the blue star monitoring point in Fig. 2a) of the backfilled stope surrounded by the rockmass with different hydraulic conductivity k in adjacent stopes (Case1 in Table 2). The simulated PWP by numerical models without considering surrounding rockmass but with an idealized impermeable (water-proof) or permeable (free-draining) boundary which were commonly used in previous numerical studies (Helinski et al. 2007a, 2010a; Li 2013; El Mkadmi et al. 2014; Doherty 2015; Zheng et al. 2018a, 2018b, 2020a, b) is also presented in the Fig. 7 for comparison.

As can be seen from Fig. 7, regardless of the drainage boundary conditions along side walls of the backfilled stope, there are typically four regions of change in the simulated PWP curves as the filling and consolidation time progresses.

(1) The first region shows a linear and rapid increase of the PWP from the start point of depositing slurry in the stope void which is mainly caused by the gravity of the poured backfill slurry layer by layer. Within this region, the lower for the permeability along the side drainage boundary, the faster for the PWP increases and the steeper for the obtained curve. For the extreme condition of totally impermeable side walls confining the backfill slurry used in most previous studies (e.g., Helinski et al. 2007a, 2010a; Li 2013; El Mkadmi et al. 2014; Doherty 2015; Zheng et al. 2018a, b), the steepest slope and longest duration of the linear rise imply that the highest rise in PWP is monitored at stope bottom.

(2) The secondary region carries a marked feature that the continued increasing slope of the PWP curve slows down until to the peak value, accompany with water drainage from the top surface and/or side boundary of filled slurry. It is also worth mentioning that the peak PWP values in the current model under totally impermeable and permeable side drainage conditions are 468 kPa and 102 kPa respectively, and this nearly 5-times difference in peak PWP proves, once again, that it is essential to consider the practical drainage conditions along side walls of backfilled slurry, otherwise the simulated PWP of backfill will be over conservative with impermeable side walls or too aggressive with totally free drainage side walls assumed in most previous analytical and numerical models. In addition, Fig. 7 illustrates that the higher for the hydraulic conductivity k of rockmass, the smoother for the slope increase to the peak PWP, and this is because the potential to increase pore pressure has been consumed by drainage along the side boundary through rockmass in adjacent stopes.

(3) After the peaks, the simulated PWP curves gradually decline to steady states with time, forming the third region. The peak values commonly occur at the moment when the void is fully filled throughout the stope height H, except the model with totally permeable side walls in which the peak was reached earlier due to the free drainage ability of the side walls. Moreover, it is clear that the smaller the hydraulic conductivity k of the rockmass, the slower the PWP decreases until a steady constant PWP is reached, which means the pressure exerted by the backfill slurry at the stope bottom on the barricade structures will last a longer time, which will have an adverse impact on the stability and safety.

(4) The fourth region is the final steady state of the simulated PWP which means the poured backfill slurry in stopes has reached a totally drained and consolidated state under specific conditions. From Fig. 7, it can be seen that the ideal model with totally permeable side walls has a constant PWP value about 36 kPa after 4 days (96 hours) starting from the original slurry pouring into the stope void. Furthermore, it takes about 7 days (168 hours) to obtain a steady constant PWP of 94 kPa for the same filled stope but with a hydraulic conductivity k = 1×10^− 5 m/s of the surrounding rockmass. However, the steady constant PWP of backfilled stopes cannot be reached within the simulated 10 days (240 hours) for the filled stopes with confining rockmass of hydraulic conductivity 1×10^− 6, 1×10^− 7 and 1×10^− 8m/s, which means it needs some extra time for the slurry to reach the drained and consolidated state. The smaller the hydraulic conductivity, the longer it takes to go through the consolidation process to a constant PWP in the fourth region.

Figure 8 presents the evolution of the effective vertical σ′_v and horizontal σ′_h stresses of the backfill slurry monitored at stope bottom confined by the rockmass with different hydraulic conductivities. The effective stresses yielded from the idealized models with totally impermeable and permeable side boundaries are also presented for comparison.

It can be seen from Fig. 8 that the vertical and horizontal effective stresses follow the similar upward trend, increasing steadily with time before reaching the plateaus. In addition, with a higher hydraulic conductivity of the side rockmass, both the vertical and horizontal stresses experience a much steeper increment which means the final stable stress state will be reached faster. This, combined with the lower PWP for the higher hydraulic conductivity of the adjacent rockmass shown in Fig. 7, suggests a load transfer from the pore water to the backfill matrix, which results in the development of effective stresses. Since the rate at which consolidation occurs dictates the rate of stress transfer to the backfill matrix (Fourie et al. 2007), higher permeability of the surrounding rockmass facilitates the consolidation of the backfill in one stope. If the surrounding rockmass is simplified to the totally impermeable or permeable boundary, unreasonable consolidation rate will inevitably produce as shown in Fig. 8, which is not conducive to accurately assessing the effective stresses of the backfill slurry in practical stopes.

A smooth increasing trend of effective stresses before reaching a stable value can be seen in Fig. 8, and there is no distinct peak like the PWP curves shown in Fig. 7. This is because the increment of effective stresses within the slurry comes mainly from the drainage and consolidation driven by gravity, independent of the filling process. Therefore, once the backfill is placed in the stope, the effective stresses continue to increase smoothly as the drainage occurs. The filling process is equivalent to loading on the top surface of the backfill (Fourie et al. 2007), and then the increase in load by placing a new backfill layer is carried mainly by the pore water due to its much higher bulk modulus (2 GPa shown in Table 1) compared with that of the backfill (0.48 GPa shown in Table 1), resulting in typically continuous increase in PWP during filling and a peak value at the end of filling. The sensitivity of the PWP to external loading makes it commonly measured in field monitoring during and after stope filling to prevent safety issues, such as liquefaction and barricade failures (Thompson et al. 2012; Doherty et al. 2015).

In Fig. 8, the model with permeable side wall and a hydraulic conductivity of 10^− 5 m/s in the adjacent rock mass can reach a stabilized value of effective stress, while others cannot. This is similar to the variation of PWP shown in Fig. 7 and means the backfill has reached a totally drained and consolidated state. In addition, the highest effective stresses of the permeable boundary show more load have been transferred to the backfill matrix, indicating a greater degree of consolidation and more stable backfill structure. Therefore, the permeability of the surrounding rockmass of a backfilled stope should be carefully modeled in numerical simulations, and using an ideally permeable side wall can produce aggressive outcomes.

It is interesting to see that the increment of effective stresses in Fig. 8 is smaller than the corresponding changes in PWP in Fig. 7. For example, the vertical effective stress for k = 10^− 6 m/s increases by 5.5 kPa from 144 hours to 228 hours, but the PWP is reduced by 31.85 kPa during the same period. According to Terzaghi's effective stress principle, the decrease in PWP should be equal to the increase in effective stress if the total stress remains constant. The difference between the changes in vertical effective stress and PWP can be caused by the arching effect developed in the backfill as shown in Fig. 9. In Fig. 9a, a “stress arch” is set up in the backfill where the vertical effective stress in the middle of the stope (x = 0) is greater than that near the right-hand side wall (x = 6 m) on the same elevation. Additionally, the big difference between the vertical effective stress and self-weight stress of the backfill in Fig. 9b (ρ_df × g × h, where ρ_df is the backfill density, g is the gravitational acceleration, and h is the vertical height from top surface of the backfill) clearly illustrates the formation of an arching effect developed in the backfill during consolidation, whereby the settlement of the backfill is held by the stiffer adjacent rockmass (the bulk modulus of rockmass and backfill is 2.8 GPa and 0.48 GPa as shown in Table 1). Due to the arching, a part of the load is transferred to the adjacent rockmass, which results in the difference between changes of the effective stress and PWP. The consolidation-induced arching has also been reported by Helinski (2010a). In his study, two cases, a fully rough stope wall (fixed-BC) and a completely smooth stope wall (free-BC), are considered to simulate the consolidation of the backfill during and after filling. The results show that as consolidation proceeds, some of the vertical stress within the backfill is redistributed to the fixed boundary (arching), and the arching formed prevents further increase in the vertical stress in the fixed-BC, while the vertical stress in the free-BC is similar to the self-weight stress at all stages.

4.2 Porosity ratio n

Figure 10 shows the evolution of the PWP monitored at the bottom of the backfill in the stope surrounded by the rockmass with porosity of 10%, 25% and 40%. The PWP obtained from the models with the permeable and impermeable side walls are also presented.

In Fig. 10, the PWP has a considerable increase during the filling process and reach the peak value when the stope is fully filled and then decrease continuously, which is consistent with the PWP variation in Fig. 7. It is found that the PWP decreases as porosity of the surrounding rockmass increases. This can be explained by the fact that a larger porosity of the surrounding rockmass can provide more space for the accommodation of the drainage water from the backfill, which is favorable to the drainage and consolidation of the backfill, then the PWP decreases as porosity increases.

In practice, the backfilled stopes can be surrounded by either cemented backfill or rockmass. Cemented backfill generally has a porosity varying from 30–50% (Belem 2004; Ghirian 2013), whereas the porosity of rockmass can vary from close to 0 to as high as 90%, depending on the mineral composition, depth and geological structures (e.g., joints and fractures) (Goodman 1989). The voids in the adjacent cemented backfill or rockmass can provide storage space and seepage paths for the drainage water from the backfill slurry during consolidation (Farouk et al. 2015). In Fig. 10, there is a large gap between figures for the backfill confined by the rockmass with varied porosity and figures for the impermeable and permeable boundary condition, indicating the pronounced impact of the porosity on the PWP. The impermeable boundary means that the adjacent stope has no water storage capacity with very small porosity, while the permeable boundary in numerical simulations means that the adjacent stope has unlimited water storage capacity. Neither of them is realistic.

Figure 11 presents the evolution of the vertical and horizontal effective stresses of the backfill confined by the rockmass with different porosities. It shows that the effective stresses increase steadily and smoothly once the backfill is placed in stopes and, as expected, the effective stresses increase with the porosity of the rockmass. As the porosity varies, the effective stresses show similar upward trend, but cannot reach an apparent plateau as shown in Fig. 8. This means that the evolution of the effective stresses in Fig. 11 is not controlled by the porosity of the rockmass, and could be dominated by the constant hydraulic conductivity (k = 10^− 6 m/s) of the rockmass which limits the development of the effective stresses.

4.3 Initial saturation s

Figure 12 shows the evolution of the PWP monitored at the bottom of the backfill surrounded by the rockmass with varied initial saturation of 40%, 60%, 80% and 100%. Clearly, the PWP increases with the initial saturation of the adjacent rockmass. This is because the initial saturation represents the initial water storage capacity of the rockmass with a given porosity. When the backfill is surrounded by the rockmass with a high initial saturation (e.g., s = 100%), the pore water in the backfill cannot flow into the adjacent rockmass in a timely manner because it takes time for the pore water originally stored in the surrounding rock to drain out. But for the rockmass with low initial saturation that means the adequate water storage capacity, the drainage water of the backfill slurry can enter the rockmass more easily, which leads to a stronger drainage of the backfill and more rapid PWP dissipation during consolidation, and then the PWP decreases with the decrease of the initial saturation of the rockmass.

It can also be observed in Fig. 12 that the initial saturation of the rockmass has a significant effect on the PWP peak value. For example, the PWP peak value increases by 39.2% from 270.53 kPa to 376.74 kPa when the initial saturation increases from 40–100%. This pronounced difference shows that to accurately estimate the PWP of the backfill for barricades design, it is important to consider the saturation of the adjacent rockmass, especially when mining in extreme environments, such as desert areas where the rockmass is less saturated, or groundwater-rich areas where the rockmass may be saturated.

Figure 13 presents the evolution of the vertical and horizontal effective stresses of the backfill slurry confined by the rockmass with varied initial saturations. As expected, the effective stresses increase when the initial saturation decreases from 100–40%. In addition, the effective stresses of the backfill confined by rockmass with different initial saturations present apparent differences during 72 ~ 144 hours after the backfill is placed, and tend to concentrate after the 216th hour. This shows the dynamic influence of the initial saturation of the rockmass on the development of effective stresses. As illustrated in Fig. 14, at t = 84 h there is a large unsaturated area, which accommodates the drainage water from the backfill, in the adjacent rockmass with the initial saturations of 40% and 60%, and there is no continuous and fully saturated seepage path from the backfill to the right-hand permeable boundary of the rockmass, then for these two cases the effective stresses are controlled by the saturation of the rockmass and show an apparent difference. But for the rockmass with initial saturations of 80% and 100%, the continuous and fully saturated areas are formed, then the development of effective stresses are mainly controlled by the hydraulic conductivity (k = 10^− 6 m/s) of the rockmass and are similar with each other. At t = 228 h, since more drainage water from the backfill enters the rockmass, continuous and fully saturated areas are formed in the rockmass in each case, then the effective stresses are controlled by the constant hydraulic conductivity of the rockmass and tend to reach an identical value.

In the simulations, the hydraulic conductivity, porosity, and initial saturation of the rockmass are considered to be independent of each other. However, they are coupled in the practical rockmass. For example, the geological faults, joints and other discontinuities in rockmass can lead to a higher porosity as well as hydraulic conductivity (Goodman 1989). Experimental results on unsaturated soil also show that the magnitude of the hydraulic conductivity will differ for different saturation (Fredlund 1993). The coupling of these three parameters of the adjacent rockmass affects the consolidation of the backfill slurry, but was not considered in the simulations.

4.4 Confining width W

Figure 15 presents the PWP monitored at the bottom of the backfilled stope confined by the rockmass different stope width and varied initial saturation. It can be seen that figures for the rockmass with width W = 12 and 36 m coincide exactly when the initial saturation of the rockmass equals 40% (Table 2, Case 4), indicating the rockmass width has little effect on the PWP evolution. To explain this phenomenon, more simulations in which the initial saturation of the rockmass varying in the range of 60%-100% are conducted, and the PWP obtained from these simulations are presented in Fig. 15. Interestingly, differences in PWP between W = 12 and 36 m increases gradually as the initial saturation of the rockmass increases from 60–100%. This illustrates that the influence of the rockmass width on the PWP evolution of the backfill is related to the initial saturation of the rockmass. Specifically, the greater the initial saturation of the adjacent rockmass, the more significant influence of the rockmass width on the PWP evolution of the backfill, and this can be explained by the following.

Figure 16 plots the saturation contours at t = 132 h for rockmass with varied initial saturations and widths. For s = 40%, there is no continuous and fully saturated seepage path from the backfill to the right-hand permeable boundary of the rockmass because the unsaturated areas in the less initially saturated rockmass for cases of W = 12 and 36 m are both enough to accommodate the drainage water from the backfill, then the PWP for W = 12 and 36 m shows no difference. For s = 60% and 80%, the continuous and fully saturated seepage paths are formed at the bottom, then the rockmass width can have an influence on the PWP evolution because the shorter seepage path (W = 12 m) promotes dissipation of PWP in the backfill. For the rockmass that is initially fully saturated (s = 100%), the influence of the seepage length (rockmass width) on the PWP evolution appears earliest and is most pronounced.

5.1 Lateral earth pressure coefficient of consolidated backfill

Lateral earth pressure coefficient K′ plays an important role in estimating the stress state within the backfill or the horizontal pressure exerted on barricades. In previous studies, some researchers suggested to use Rankine’s active earth pressure coefficient K_a=tan²(45°−φ′_f/2) in the analytical solution (Li L 2009a, Sobhi et al. 2017, Liu G S et al. 2018), while others proposed to take Jaky’s at-rest earth pressure coefficient K₀ = 1-sin(φ′_f) in some cases (Yang P et al. 2017b and 2018). To quantitatively understand the K′, it is necessary to discuss the effect of hydro-geotechnical properties of adjacent rockmass.

The effective horizontal and vertical stresses at the bottom of the backfill after 228-hours consolidating were used to calculate the K′ of the consolidated backfill, and the results obtained from the backfill surrounded by rockmass with varied hydro-geotechnical properties are presented in Fig. 17, against the benchmark of K_a=1/3 calculated using φ′_f = 30°. It is found that the K′ of the backfill generally increases with the hydraulic conductivity regardless of the initial saturation and porosity. The adjacent rockmass with higher hydraulic conductivity facilitates the consolidation of the backfill slurry, thus contributing to the development of K′. In addition, the K′ in all cases is closer to the K_a = 1/3 than to the K₀ = 1/2.

Figure 18 presents the evolution of K′ for the backfill surrounded by the rockmass with varied hydraulic conductivity k. The effective vertical and horizontal stresses used to calculate the K′ are from the results of Case0 and Case1 in Table 2.

During filling, the K′ values for different k are similar to each other and close to K_a. After the end of filling, the K′ values for k = 10^− 5 and 10^− 6 m/s jump sharply and reach stable values, respectively, while those for k = 10^− 7 and 10^− 8 m/s emerge invisible changes. This shows that the K′ of the backfill is not constant, but evolves with the filling process and consolidation. These results are consistent with the field monitoring results reported by Thompson (2012). In his study, the K′ calculated by the monitored vertical and horizontal effective stresses changes during filling, and the K′ at the lower portion of the stope appears to be near K_a while the upper portion is closer to the K₀. Some numerical simulations conducted without considering the backfill consolidation also show that the K′ of the backfill confined by the rockmass is related to the position (Yang P et al. 2017b and 2018). Therefore, it is difficult and possibly unreasonable to assume that a constant value of K′ is representative of the entire stope during consolidation of the backfill.

For the backfill with impermeable and permeable side walls in Fig. 18, K′ shows a totally different pattern than those from numerical models considering the adjacent rockmass. The figures for the impermeable and permeable side walls decrease remarkably from rather high values (more than 0.5 but not shown in Fig. 18 for visual clarity) at the beginning of the filling to stable values. This specific trend may be attributed to the mechanical boundary condition of the backfill. When considering the rockmass, the lateral displacement can occur near the right-hand boundary of the backfill since the bulk modulus of the rockmass and backfill are comparable (2.8 and 0.48 GPa respectively). However, for the backfill with impermeable and permeable side walls, no rockmass is modeled and the lateral displacement at the right-hand boundary is totally fixed. The difference in the mechanical boundary condition could lead to different stress state within the backfill, then the K′ shows a different evolution pattern. More work is needed to explain this discrepancy.

5.2 Comparison of simulated PWP and stress with in-situ monitored results

To further validate the reliability of the numerical simulation, comparisons of simulated results with monitored values of PWP and total stresses are made. The field monitoring data was collected from the work at a gold mine reported by Helinski (2010b). The monitored stope is filled with cemented tailings slurry to a height of 40 m, with plane dimensions of 15 m × 18 m and with a single 6 m wide × 6 m tall draw-point in the middle of the stope length. The filling sequence consisted of filling the first 10 m at a vertical rate of ascent of 0.2 ~ 0.5 m/h followed by a 24-h rest period. After the rest period, filling continued at a rate of 0.3 ~ 0.6 m/h until the stope was filled. A corresponding numerical model similar to that shown in Fig. 2b was constructed with FLAC3D and the drawpoint was considered, and the adjacent rockmass was not included but replaced by an impermeable boundary. The backfill slurry was characterized by dry density ρ_d = 1220 kg/m³, bulk modulus K_f = 35 MPa, shear modulus G_f = 18 MPa, internal friction angle φ_f = 35°, cohesion c_f = 0 and dilation angle ψ = 0°, hydraulic conductivity k = 5×10^− 7 m/s, porosity ratio n = 0.5 and initial saturation s = 1. These parameters were from the laboratory tests in Helinski’s study.

Figure 19 compares simulation results with monitored values of PWP and total vertical stress (TVS), and the self-weight stress of the backfill is also presented. As shown in Fig. 19, starting from the commencement of the placement of backfill slurry to the end of the rest period, simulation results are consistent well with monitored values. This indicates that the numerical model constructed with FLAC3D is qualified for the simulation of PWP and TVS at the early age of cemented backfill slurry.

After the rest period, the monitored values of PWP and TVS fluctuated and then stabilized, while the simulation results increased over time, followed by a considerable difference between the two. The stabilization of the monitored values of PWP and TVS towards the end of backfilling illustrates the effect of cement hydration on consolidation behavior. Some researches have reported that cement hydration can promote PWP dissipation in backfill slurry during consolidation (Helinski et al. 2007b, Ghirian A et al. 2013, Doherty J P 2015), but the numerical model here did not consider the effect of cement hydration because there is currently no commercial simulation software around the world that can simulate the whole process of cement hydration, then the simulated PWP and TVS continued to increase as the uncemented slurry filling proceeds. The gap between simulated results and monitored values shows the limitation of the current numerical model, but the good agreement at the early age demonstrates the reliability and accuracy of the numerical model.

It should be noted that the numerical model did not consider the influence of the adjacent rockmass because there are no related descriptions about the rockmass in Helinski’s study. As analyzed above, the simulated PWP of the backfill confined by rockmass is always smaller than that obtained from the numerical model with an impermeable side wall. Therefore, in addition to the effect of cement hydration, the gap between simulated results and monitored values in Fig. 19 could also be caused by faults, joints or cracks in adjacent rockmass, which was not considered in the numerical simulation here.

Numerical simulations were conducted with FLAC3D to investigate evolution of pore water pressure (PWP) and effective stress of uncemented backfill slurry in a vertical stope considering adjacent rockmass with different hydraulic conductivity, initial saturation, porosity, and rockmass width. The main conclusions are summarized as follows.

(1) The PWP and effective stresses of backfill slurry in a mine stope considering adjacent rockmass are always greater than numerical outcomes by simplifying the rockmass as permeable boundaries and lower than those in the case of impermeable boundaries. If adjacent rockmass is ignored, the evaluation of backfill slurry consolidation will be either too conservative with impermeable side walls or too aggressive with permeable side walls.

(2) The hydraulic conductivity of adjacent rockmass highly affects the stress state within backfill slurry. When the hydraulic conductivity of adjacent rockmass varies from 10^− 8 m/s to 10^− 5 m/s, there are about three-fold difference in the peak values of PWP and effective stresses during consolidation for the same backfill slurry. At lower hydraulic conductivity (10^− 8 m/s), evolution of PWP and effective stresses in backfill slurry during consolidation is comparable to that for the impermeable boundary. The similar correspondence can also be observed between cases of the high hydraulic conductivity of the rockmass (10^− 5 m/s) and the permeable boundary. Therefore, it is reasonable to simplify the surrounding rockmass as boundary conditions in certain cases.

(3) Higher porosity and lower initial saturation of the adjacent rockmass are both conducive to the PWP dissipation and effective stresses development in backfill slurry, but the influences of them are not as pronounced as that of the hydraulic conductivity of the rockmass. The PWP and effective stresses in backfill slurry confined by the rockmass with varied porosity and initial saturation can show apparent differences between each other in the early time, but will tend to approach an identical value as the adjacent rockmass becomes gradually saturated, and after that, the consolidation of backfill slurry is controlled by the hydraulic conductivity of the rockmass.

(4) The influence of the rockmass width on the PWP evolution of backfill slurry is related to the initial saturation of the adjacent rockmass. When the initial saturation of the adjacent rockmass is low (40%), the rockmass width has no impact on the PWP evolution of backfill slurry. But as the initial saturation of the rockmass increases from 60–100%, an increasing influence of the rockmass width on the PWP evolution is observed.

(5) The lateral earth pressure coefficient of backfill slurry confined by rockmass is closer to the active earth pressure coefficient than to at-rest earth pressure coefficient, and it is not constant but evolves with the filling process and consolidation.

Author Contribution

Guangsheng Liu and Qinghai Ma wrote the main manuscript text. Xiaocong Yang and Lijie Guo reviewed the manuscript. Xuehao Yuan prepare the Figures. Li. Li review and improve the written English.

Acknowledgements

The authors would like to acknowledge the financial supports from the Young Scientist Project of National Key Research and Development Program of China (Grant No. 2021YFC2900600) and the Beijing Nova Program (Grant No. 20220484057).

Abdelghani F B, Aubertin M, Simon R, & Therrien R. (2015). Numerical simulations of water flow and contaminants transport near mining wastes disposed in a fractured rock mass. International Journal of Mining Science and Technology, 25(1), 37–45.
Aubertin M, Bussière B, & Chapuis R. (1996). Hydraulic conductivity of homogenized tailings from hard rock mines. Canadian Geotechnical Journal. 33(3): 470-482.
Aubertin M, Bussière B, Bernier L. (2002). Environnement et gestion des rejets miniers, Presses Internationales Polytechnique, Montréal.
Belem T, Aatar O E, Bussiere B, Benzaazoua M, Fall M, & Yilmaz E. (2006). Characterisation of Self-Weight Consolidated Paste Backfill. In 9th International Seminar on Paste and Thickened Tailings, 3-7th April, Limerick, pp 333–345.
Belem T, Aatar O E., Bussière B, & Benzaazoua M. (2016). Gravity-driven 1-D consolidation of cemented paste backfill in 3-m-high columns. Innovative Infrastructure Solutions, 1(1), 1–12.
Belem T, and Benzaazoua M. (2008). Design and application of underground mine paste backfill technology. Geotechnical and Geological Engineering, 26(2): 147-174.
Belem T, Harvey A, Simon R, & Aubertin M. (2004). Measurement and prediction of internal stresses in an underground opening during its filling with cemented fill. In symposium on ground support in mining and underground construction. Taylor and Francis Group, London, Australia, pp. 619–630.
Cai M F, He M C, & Liu D Y. (2013). Rock Mechanics and Engineering (2nd Edition). Chinese science press, Beijing, China.
Cui L, & Fall M. (2016). Multiphysics model for consolidation behavior of cemented paste backfill. International Journal of Geomechanics, 17(3), 04016077.
Cui L, & Fall M. (2020). Numerical Simulation of Consolidation Behavior of Large Hydrating Fill Mass. International Journal of Concrete Structures and Materials, 14(1), 1–16.
Deng X, Li Y, Wang F, Shi X, Yang Y, Xu X, & de Wit B. (2022). Experimental study on the mechanical properties and consolidation mechanism of microbial grouted backfill. International Journal of Mining Science and Technology, 32(2): 271-282.
Doherty J P, Hasan A, Suazo G H, & Fourie A. (2015). Investigation of some controllable factors that impact the stress state in cemented paste backfill. Canadian Geotechnical Journal, 52(12), 1901-1912.
Doherty J P. (2015). A numerical study into factors affecting stress and PWP in free draining mine stopes. Computers and Geotechnics, 63, 331-341.
El Mkadmi N, Aubertin M, Li L. (2014). Effect of drainage and sequential filling on the behavior of backfill in mine stopes. Canadian Geotechnical Journal, 51(1): 1-15.
El Naqa, A. (2001). The hydraulic conductivity of the fractures intersecting Cambrian sandstone rock masses, central Jordan. Environmental Earth Sciences, 40(8), 973–982.
Fahey M, Helinski M, & Fourie A. (2010). Consolidation in accreting sediments: Gibson's solution applied to backfilling of mine stopes. Géotechnique, 60(11), 877-882.
Farouk BA, Michel A, Richard S, & Rene T (2015). Numerical simulations of water flow and contaminants transport near mining wastes disposed in a fractured rock mass. International Journal of Mining Science and Technology, 25(2015), 37-45.
Fourie A B, Helinski M, & Fahey M (2007). Using effective stress theory to characterize the behaviour of backfill. In Proceedings of the Minefill Conference, Perth, 2007, p. 27.
Fredlund DG, Rahardjo H. Soil mechanics for unsaturated soils: John Wiley & Sons; 1993.
Ghirian A, & Fall M. (2013). Coupled thermo-hydro-mechanical–chemical behaviour of cemented paste backfill in column experiments. Part I: Physical, hydraulic and thermal processes and characteristics. Engineering Geology, 164, 195–207.
Ghirian, A., & Fall, M. (2016). Strength evolution and deformation behaviour of cemented paste backfill at early ages: effect of curing stress, filling strategy and drainage. International Journal of Mining Science and Technology, 26(5), 809-817.
Gibson R E. (1958). The progress of consolidation in a clay layer increasing in thickness with time. Géotechnique. 8(4): 171-183.
Goodman R. (1989). Introduction to Rock Mechanics (2nd Edition). John Wiley & Sons Inc., New York, USA, Chapter2.5, page35.
Government of Western Australia. (2020). Significant Incident Report No. 279 about paste wall failure. www.dmp.wa.gov.au/Documents/Safety/MSH_SIR_279.pdf.
Helinski M, Fahey M, & Fourie A. (2010b). Behavior of cemented paste backfill in two mine stopes: measurements and modeling. Journal of Geotechnical and Geoenvironment Engineering, 137(2), 171–182.
Helinski M, Fahey M, Fourie A. (2007a). Numerical Modeling of Cemented Mine Backfill Deposition. Journal of Geotechnical and Geoenvironmental Engineering, 133(10): 1308-1319.
Helinski M, Fahey M, Fourie A. (2010a). Coupled two-dimensional finite element modelling of mine backfilling with cemented tailings. Canadian Geotechnical Journal, 47(11): 1187-1200.
Helinski M, Fourie A, Fahey M, & Ismail M. (2007b). Assessment of the self-desiccation process in cemented mine backfills. Canadian Geotechnical Journal, 44(10): 1148–1156.
Islam S, Williams D J, Llano-Serna M, & Zhang C. (2020). Settling, consolidation and shear strength behaviour of coal tailings slurry. International Journal of Mining Science and Technology, 30(6), 849-857.
Jaeger J C, Cook N G W, & Zimmerman R W. (2007). Fundamentals of rock mechanics (4th Edition). Blackwell Publishing Ltd, Oxford, UK, Chapter 7, page186.
Jaouhar E M, & Li L. (2019). Effect of Drainage and Consolidation on the Pore Water Pressures and Total Stresses within Backfilled Stopes and on Barricades. Advances in Civil Engineering, 2019, 1–19.
Li L, & Aubertin M. (2009a). Influence of Water Pressure on the Stress State in Stopes with Cohesionless Backfill. Geotechnical and Geological Engineering, 27(1), 1–11.
Li L, & Aubertin M. (2009b). A Three-Dimensional Analysis of the Total and Effective Stresses in Submerged Backfilled Stopes. Geotechnical and Geological Engineering, 27(4), 559–569.
Li L, Aubertin M, & Belem T. (2005). Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings. Canadian Geotechnical Journal, 42(6), 1705-1717.
Li L, Dubé J S, & Aubertin M. (2013). An Extension of Marston’s Solution for the Stresses in Backfilled Trenches with Inclined Walls. Geotechnical and Geological Engineering, 31, 1027–1039.
Li L. (2013). A new concept of backfill design—Application of wick drains in backfilled stopes. International journal of mining science and technology, 23(5): 763-770.
Liu G S, Li L, Yang X C & Guo L J. (2016a). Stability analyses of vertically exposed cemented backfill: A revisit to Mitchell’s physical model tests. International Journal of Mining Science and Technology, 26(6), 1135-1144.
Liu G S, Li L, Yang X C & Guo L J. (2016b). A numerical analysis of the stress distribution in backfilled stopes considering nonplanar interfaces between the backfill and rock walls. International Journal of Geotechnical Engineering, 10, 271–282.
Liu G S, Li L, Yang X C & Guo L J. (2017). Numerical analysis of stress distribution in backfilled stopes considering interfaces between the backfill and rock walls. International Journal of Geomechanics, 17, paper 06016014.
Liu G S, Li L, Yang X C & Guo L J. (2018). Required strength estimation of a cemented backfill with the front wall exposed and back wall pressured. International Journal of Mining and Mineral Engineering, 9(1), 1-20.
Liu G S, Yang X C & Guo L J. (2021). Stiffness determination of backfill-rock interface to numerically investigate backfill stress distributions in mine stopes. Advances in Civil Engineering, paper 6460764.
Ma Q, Liu GS, Yang XC, & Guo LJ. (2023). Physical model investigation on effects of drainage condition and cement addition on consolidation behavior of the tailings slurry within backfilled stopes. International Journal of Minerals, Metallurgy and Materials, 30(8): 1490-1501.
Marston A. (1930). The theory of external loads on closed conduits in the light of latest experiments. Bulletin No. 96, Iowa Engineering Experiment Station, Ames, IA,.
Potvin Y, Thomas E, Fourie A. (2005). Handbook on mine fill. Perth: Australian Centre for Geomechanics.
Qin J, Zheng J, & Li L. (2021). An analytical solution to estimate the settlement of tailings or backfill slurry by considering the sedimentation and consolidation. International Journal of Mining Science and Technology, 31(3), 463-471.
Revell M B, & Sainsbury D P. (2007). Paste bulkhead failures. 9th International Symposium on Mining with Backfill, Minefill 2007, Montréal, Canada, .
Shahsavari M, & Grabinsky M. (2014). Cemented paste backfill consolidation with deposition-dependent boundary conditions. Paper presented at the 67th Canadian Geotechnical Conference, Canadian Geotechnical Society, Regina, Saskatchewan, Canada.
Shahsavari M, & Grabinsky M. (2015). Mine backfill porewater pressure dissipation: numerical predictions and field measurements. 68th Canadian Geotechnical Conference, Quebec City, Quebec, Canada, 1-8.
Sohbi M A, Li, L, & Aubertin M. (2017). Numerical investigation of the earth pressure coefficient along the central line of backfilled stopes. Canadian Geotechnical Journal, 54(1): 138-145.
Terzaghi, K. (1943). Theoretical Soil Mechanics, John Wiley and Sons, New York, NY, USA.
Thompson B D, Bawden W F, & Grabinsky M W. (2012). In situ measurements of cemented paste backfill at the Cayeli Mine. Canadian Geotechnical Journal, 49(7), 755-772.
Thompson B D, Grabinsky M W, Bawden W F, & Counter D B. (2009). In-situ measurements of cemented paste backfill in long-hole stopes. Paper presented at the 3rd CANUS Rock Mechanics Symposium, Toronto, Canada, paper 199.
Veenstra R. (2013). A design procedure for determining the in situ stresses of early age cemented paste backfill (PhD Thesis). Toronto: University of Toronto, Canada.
Wang J S Y, & Narasimhan T N. (1985). Hydrologic Mechanisms Governing Fluid Flow in a Partially Saturated, Fractured, Porous Medium. Water Resources Research, 21(12), 1861–1874.
Wickland B E & Wilson G W. (2005). Self-weight consolidation of mixtures of mine waste rock and tailings. Canadian Geotechnical Journal, 42(2): 327-339.
Yang P, & Li L. (2017a). Evolution of Water Table and Pore-Water Pressure in Stopes with Submerged Hydraulic Fill. International Journal of Geomechanics, 17, 04017052.
Yang P, Li L, & Aubertin M. (2017b). Stress ratios in entire mine stopes with cohesionless backfill: A numerical study. Minerals, 10(7): 1-14.
Yang P, Li L, & Aubertin M. (2018). Theoretical and numerical analyses of earth pressure coefficient along the centerline of vertical openings with granular fills. Applied Sciences, 10(8): 1-11.
Yumlu M, & Guresci M. (2007). Paste Backfill Bulkhead Monitoring – A Case Study from Inmet’s Cayeli Mine, Turkey. 9th International Symposium on Mining with Backfill, Minefill 2007, Montréal, Canada , 2479-2489.
Zheng J, Li L, & Li, Y C (2019). Total and Effective Stresses in Backfilled Stopes during the Fill Placement on a Pervious Base for Barricade Design. Minerals, 9(1), paper 38.
Zheng J, Li L, Mbonimpa M & Pabst T. (2018a). An analytical solution of Gibson's model for estimating the pore water pressures in accreting deposition of slurried material under one-dimensional self-weight consolidation. Part I: Pervious base. Indian Geotechnical Journal, 48(1), 72-83.
Zheng J, Li L, Mbonimpa M & Pabst T. (2018b). An analytical solution of Gibson's model for estimating pore water pressures in accreting deposition of slurried material under one-dimensional self-weight consolidation. Part II: Impervious base. Indian Geotechnical Journal, 48(1), 188-195.
Zheng J, Li L. & Li, YC (2020a). Solutions to estimate the excess PWP, settlement and volume of draining water after slurry deposition. Part I: impervious base. Environmental Earth Sciences, 79, paper 124.
Zheng J, Li L. & Li, YC (2020b). Solutions to estimate the excess PWP, settlement and volume of draining water after slurry deposition. Part II: pervious base. Environmental Earth Sciences, 79, paper 275.

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Consolidation process of uncemented backfill slurry in a mine stope considering hydro-geotechnical properties of rockmass in adjacent stopes

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Abstract

Figures

1 Introduction

2 Numerical models and simulation schemes

2.1 Model construction and boundary conditions

2.2 Material parameters and numerical cases

3 Validation on numerical simulated consolidation states of backfill slurry

3.1 Simulated PWP compared with analytical results of Gibson model

3.2 Simulated stress compared with analytical results of arching model

4 Effect of hydro-geotechnical properties of rockmass on backfill consolidation

4.1 Hydraulic conductivity k

4.2 Porosity ratio n

4.3 Initial saturation s

4.4 Confining width W

5 Discussions

5.1 Lateral earth pressure coefficient of consolidated backfill

5.2 Comparison of simulated PWP and stress with in-situ monitored results

6 Conclusions

Declarations

Author Contribution

References

Additional Declarations

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