11
11
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com
ScienceDirect
Underground Space 13 (2023) 121–135
www.keaipublishing.com/undsp
Received 30 November 2022; received in revised form 14 February 2023; accepted 29 March 2023
Available online 29 June 2023
Abstract
Estimating average vertical pillar stresses is a critical step in designing room-and-pillar mines. Several analytical methods can be used
to estimate the vertical stresses acting on the pillars. However, the present analytical methods fail to adequately account for the influence
of abutments on the distribution of vertical stresses, especially when applied to narrow panel widths and pillar layouts comprising evenly
spaced barriers. In this study, a multi-layer perceptron neural network (MLPNN) was applied to predict the vertical loads of regular
pillars more accurately. Hundreds of room-and-pillar mine layouts were modeled using a displacement discontinuity method (DDM),
and a database of 2355 sampled pillar cases was compiled. The MLPNN was trained based on this database, and its prediction capa-
bilities were further validated using simulations by a finite difference code (i.e., FLAC3D). The model predictions and the FLAC3D sim-
ulations reasonably agreed with a regression coefficient of 0.99. The model was also adapted for mine cases with evenly spaced barrier
pillars, and its application to a real case study mine has shown to provide accurate pillar stress estimations; hence, this model is suitable
for practical use at mines. Even though the MLPNN model cannot be applied universally to all mine situations, it seems as a significant
improvement over existing analytical techniques in terms of accounting for the influence of abutments on pillar stresses.
Keywords: Pillar stress; Abutments; Multi-layer perceptron neural network; Numerical simulation; Room-and-pillar mine
https://doi.org/10.1016/j.undsp.2023.03.008
2467-9674/Ó 2023 Tongji University. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
122 N. Dzimunya et al. / Underground Space 13 (2023) 121–135
considering the relative extraction ratio (Hauquin et al., govern pillar stresses are analysed; a database is numeri-
2016). On the other hand, computing the actual pillar cally developed using the displacement discontinuity
strength is also a challenging task due to scale effects and method (DDM); a multi-layer perceptron neural network
other influencing parameters such as in-situ stress, geome- (MLPNN) is then trained on the database; a mine layout
try of pillars, rock mass quality and variation in rock types is simulated in FLAC3D and the results are compared with
(Wang & Cai, 2021). MLPNN predictions for validation purposes; the MLPNN
TAT assumes that the overburden load is evenly dis- model is adapted for use in a mine layout that consists of
tributed and equally shared among the pillars (Brady & evenly spaced barrier pillars; finally, the adapted model is
Brown, 2004; Hedley & Grant, 1972; Salamon & Munro, applied to an actual mine case study. The flowchart of
1967). This method does not consider the influence of ML model development is summarised in Fig. 1.
nearby abutments, and it is well known to overestimate pil-
lar stresses, especially for narrow mine panel widths 2 Database development using 3D DDM
(Wagner, 1980; Wagner et al., 2016). PAT assumes that a
pressure arch is formed between the abutments and that A dataset is an integral part of ML. Datasets house sev-
most of the pillar loads are carried by these abutments. eral data that can be used to train the ML algorithm. This
The method uses an averaged extraction ratio over several study used DDM to simulate numerous mine layouts to
pillars, and as a result, it generally underestimates pillar develop a database for subsequent pillar stress predictions
stresses around an average value (Hauquin et al., 2016). using ML. DDM-based software NUTEX (Fujii et al.,
Applications and modifications of PAT are available 1997; Fujii, 2004) was used, and the code was developed
(Abel, 1988; Poulsen, 2010), and the dependence of the to simulate stresses and displacements in tabular deposits
method on a parameter called the load transfer distance numerically. The software was developed on Microsoft
makes its application uncertain in hard rocks because this Fortran Power Station and is compatible with Microsoft
parameter was calibrated in sedimentary coal seams. Windows. Successful implementations of NUTEX can be
On the other hand, the quadratic equation assumes that found in Fujii et al. (2001) and Sinkala et al. (2019,
a portion of the overburden load is transferred to pillars 2022), and other separate applications of the DDM
and abutments that support the remainder. Despite the (Napier & Malan, 2011; Tuncay et al., 2021).
model’s better performance over TAT and PAT in general
mine conditions, it did not give accurate pillar stresses 2.1 DDM brief theory and model construction
within approximately 72 m from the abutments, indicating
the need for a method that captures the influence of abut- DDM is a variant of the boundary element method
ments to pillar stresses. (BEM) and uses displacement and stress due to displace-
Numerical modelling remains the only tool that can ment discontinuity (difference in displacement between
accurately evaluate the dependability of pillar stresses ana- fracture surfaces) in an infinite medium as fundamental
lytically. However, the main challenge of numerical tools is solutions. The ore is regularly divided by square elements
that they require significant time and expertise, which is and the boundary conditions are assigned. Boundary con-
generally not readily available at mines in practice ditions are described as follows: x- and y-axes are in the
(Potvin & Hudyma, 2017; Sweby et al., 2016). Further- strike and dip directions, respectively, and z-axis is normal
more, numerical modelling is not very convenient for the to the ore seam. b is the displacement discontinuity. bx and
routine stress analysis work in a typical mining environ- by represent slip along x- and y-axes. Negative or positive
ment where highly variable ground control districts bz represents closure or opening of the roof and floor.
(geotechnical zones) are regularly encountered, prompting For the mined ore seam elements and the ground surface,
frequent changes to extraction ratios and pillar outlines.
As a result, design engineers at mine sites recurrently use szx ¼ syz ¼ rz ¼ 0; ð1Þ
the TAT despite the availability of numerical tools, but this
where s and r are shear and normal stresses, respectively. If
technique is conservative and cannot incorporate the influ-
bz surpasses the adjusted working height of the ore seam
ence of abutments to pillar stresses. Consequently, TAT
elements,
remains the most used technique because it is simple, and
it tends to make mine constructions safer by overestimating b0z ¼ at; ð2Þ
pillar stresses.
where a and t are a coefficient and the mining height,
The analytical methods previously mentioned provide
respectively. And
valuable estimations of pillar stresses, but no existing
method effectively considers the influence of abutments in b0z b0z
b0x ¼ bx ; b0y ¼ by : ð3Þ
hard rocks. Based on numerical modeling and machine bz bz
learning (ML), this study proposes a solution to estimate
vertical loads on regular pillars. This solution factors in Conversely,
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
the influence of abutments and assumes linearly elastic
If smax ¼ s2zx þ s2yz P rz tan /;
rock behavior. The study proceeds as follows: factors that
N. Dzimunya et al. / Underground Space 13 (2023) 121–135 123
rz tan / rz tan / required quickly. Even though DDM can take relatively
s0zx ¼ szx qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; s0xy ¼ syz qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; ð4Þ
s2zx þ s2yz s2zx þ s2yz shorter solution times, some of the mine layouts of vast lat-
eral extensions, as simulated in this study, required more
where / is the angle of internal friction. For the unmined than one day to converge.
elements, Model construction in NUTEX is relatively simple. Six
steps must be followed to obtain the average vertical stress
bx by bz of the pillars: (1) create data files related to the layout of
sxz ¼ G; syz ¼ G; rz ¼ E; ð5Þ
t t t the mine (assigning 1’s to unmined elements and 0’s to
E mined elements), (2) setup the number of mining steps,
G¼ ; ð6Þ
2ð 1 þ v Þ (3) divide the ore seam into elements of length with ore
thickness, (4) input mine geometry and rock mass parame-
where E, G, and m are Young’s modulus, shear modulus ters that characterise the mine, (5) analyse with NUTEX,
and Poisson’s ratio, respectively. and (6) record the average pillar stresses.
Displacement discontinuity values can be obtained by
solving boundary integral equations for all the elements.
Displacements and stresses at arbitrary points can be 2.2 Parameter analysis for database feature identification
obtained from these displacement discontinuity values
(Crouch & Fairhurst, 1973; Crouch, 1976). BEM efficiently The essential undertaking in building ML databases is
solves large-scale problems characterised by complicated identifying the attributes/features that constitute the data-
geometries such as room-and-pillar mines. In such cases, base. In this study, feature identification was accomplished
using finite element methods, which depend on discretising via parameter analysis from past studies and through
the entire volume rather than boundaries, as in the case of selecting well-known factors that influence pillar stresses.
BEM, would take very long run times, which are pro- It is well known that pillar stresses depend on mining depth
hibitive, especially at mine sites where solutions may be (H), extraction ratio (e, %), and overburden unit weight (c).
124 N. Dzimunya et al. / Underground Space 13 (2023) 121–135
However, for reasons of simplicity, c was maintained as when studying pillar stress distributions. In a study
2.7 t/m3 for all the DDM simulations. In cases of a predic- (Hauquin et al., 2016), numerical simulations of several
tion involving different overburden c, simple proportions regular pillars revealed that the magnitude of the in-situ
would be considered valid. horizontal stress has a minimal influence on the vertical pil-
Sensitivity analysis of the effect of Poisson’s ratio m on lar stresses. The maximum difference observed of a scenario
pillar stress was done in NUTEX. The analysis indicated where k was 0.5 and 2 amounted to a 2% difference. This
that m has little influence, and thus it was not considered difference was deemed negligible, and k was maintained
an important parameter. A constant m of 0.2 was used for as 1 for all simulations in DDM. Contrariwise, k influences
all the DDM simulations. Young’s modulus E influences stability of the rooms and must be carefully incorporated in
pillar stresses (Yu et al., 2018; Zhou et al., 2017). Modulus such designs. A tensile zone exists in the roof of any tabular
ratio (MR), ratio of the overburden E to that of the seam, mining excavation due to subjection of the hanging wall of
has been reported to influence pillar stresses. However, this the excavation to vertical ‘deadweight’ tensile stresses. The
ratio is more pronounced in coal mines where the coal extend of this tensile zone decreases with the increase of k
seams are usually softer than the surrounding rocks. The ratio (Ozbay et al., 1995).
focus of this study was on hard rock room-and-pillar It is important to note that all numerical simulations in
mines, and in such cases, it has generally been reported that this study were performed assuming linear elastic rock
the ratio is usually very close to unity (similar stiffness of behavior. The target pillars in this study are non-yield pil-
ore seam and host rock) and thus E for host rock and pil- lars. The main consideration in the design of such pillars is
lars was assumed to be equal in the DDM models. to warrant that pillar strength always exceeds, by an appro-
The panel width influence on pillar stresses was also priate FOS, the maximum pillar stress imposed by the
investigated. Three different panel widths of 100, 300, overburden load of the superincumbent rock mass. This
and 700 m were simulated for a layout with 6 m square pil- implies that non-yield pillars are intended to remain essen-
lars, 6 m room width, E of 20 GPa, and 200 m mining tially intact and elastic throughout the mine life. At stress
depth. Figure 2 shows the average vertical pillar stress dis- levels in a pillar below the corresponding pillar strength,
tribution for the three cases. It is clear from the plot that the pillar remains intact and reacts elastically to the
panel width has a considerable influence on pillar stresses. increased state of stress (Brady & Brown, 2004). Conse-
The pillar stresses increase as the distance from the abut- quently, the linear elasticity assumption in this study can
ment increases. Maximum average pillar stress in the panel be reasonable as an initial design approach.
approaches the TAT stress asymptote as the size of the
panel increases. Pillars adjacent to the abutments have sig-
nificantly lower stresses because the abutments carry some 2.3 Database development
of the load. This study focused on an ML model that can
reproduce the trends in Fig. 2. Since numerical modelling is the superior method for
In addition, it is well understood that the horizontal-to- rock mechanics problems, it is acceptably logical to simu-
vertical stress ratio k has an extensive range of values, typ- late numerous combinations of realistic rock mass and pil-
ically at shallow depths (Hoek et al., 1995), where the lar configurations and make future predictions of actual
room-and-pillar mining method is often applicable. This cases based on the simulated data. Other studies founded
fact suggests that the influence of k must be considered on numerically simulated databases include (Hauquin
et al., 2016; Li et al., 2021). The parameters chosen as vari-
able features are H, E, e, and panel width. Numerical sim-
ulations in DDM were then conducted based on a
parametric study of these model variables. Random values
were assigned to these four variable parameters, and exten-
sive numerical simulation was undertaken with all possible
combinations of these parameters, as illustrated in Table 1.
Pillar sizes and room widths typically used in hard rock
mines were chosen, and configurations that satisfy the
extraction ratios in Table 1 were simulated. In total, 180
Table 1
Summary of the variable values and the total number of DDM
simulations.
Variable Values Count Total simulations
e (%) 55.5, 75, 80, 84, 88 5 5 3 4 3 = 180
E (GPa) 20, 50, 75 3
H (m) 100, 200, 500, 800 4
Panel width (m) 100, 300, 700 3
Fig. 2. Effect of panel width on pillar stress distribution.
N. Dzimunya et al. / Underground Space 13 (2023) 121–135 125
Table 3
RF and MLPNN comparison on testing data.
Regressor R score MAE RMSE
RF 0.99 0.24 0.61
Fig. 3. Normal stress distribution on an example of sampled pillars in one
MLPNN 0.99 0.78 1.14
of the DDM simulations.
126 N. Dzimunya et al. / Underground Space 13 (2023) 121–135
MLPNN is the most used ANN for a wide variety of where w+ij and b+k are the updated weight and bias, respec-
problems. MLPNNs are established on a supervised learn- tively. Weights and biases are updated using one training
ing procedure and contain three fully connected types of example at a time. That cycle is called an epoch when
layers: input, hidden, and output. The processing elements the entire training data has been used in forward and
in ANN are called perceptron or neurons (Walczak & backpropagation. Thus, to fully train the MLPNN, multi-
Cerpa, 2003). Each connection between neurons is associ- ple epochs must be achieved. Training is stopped when the
ated with a weight (wij), and every neuron is associated with errors of the cost function hardly change. The architecture
a bias (bk). The basis of MLPNN training involves two of the MLPNN used in this study is indicated in Fig. 4,
steps: forward propagation and backpropagation. Training signifying the fully connected input, hidden and output
means continuously adjusting the weights and biases until layers.
the error between the predicted output and the actual is The MLPNN was built in the scikit-learn open-
minimal. In the forward propagation, the input data is source ML library. GridSearchCV was used to obtain
fed into the network and gets transmitted into each neuron the best model hyperparameters. The optimum model
through a linear operation (Eq. (9)) and outputted from the hyperparameters were selected and are summarised in
neuron by a non-linear operation via the activation func- Table 4.
tion (e.g., rectified linear unit (ReLu), sigmoid, and hyper-
bolic tangent (Tanh)). 3.3 MLPNN training, testing, and validation
X
Y inp ¼ bk þ wij xi ; ð9Þ A perfect MLPNN model denotes that the predicted pil-
lar stresses be infinitely close to the actual values. In other
where Yinp is the input to the neuron, bk is the kth bias words, the MLPNN model must learn as much as possible
associated with that neuron, xi is the ith input from the pre- from the database to minimise errors in future prediction
vious layer, and wij is the weights associated with connec- applications. In supervised ML, the performance of an
tions to that neuron. algorithm must be assessed on a given dataset before using
When an initial forward pass of the first training exam- it to make predictions on new data. This criterion is satis-
ple is wholly transmitted through the network, an initial fied by splitting the original database into three subsets:
prediction is achieved. This initially predicted output is training, testing, and validation datasets. The training set
then compared with its corresponding actual value. At this is used to build the model and to set model hyperparame-
point, a method is implemented that can update weights ters, while the testing and validation sets are used as inde-
(wij) and biases (bk), so that the error between prediction pendent checks for assessing the model performance on
and actual is reduced. This procedure is the backpropaga- new unseen data. For this study, the 2355 data points were
tion step. Backpropagation is typically achieved by per- divided into 70% training, 20% testing, and 10% validation.
forming gradient descent. Gradient descent is a Figure 5 indicates the regression plots of the MLPNN
mathematical first-order iterative optimisation algorithm model for the testing and validation sets. The R-value is
to find a local minimum of a differentiable function. In limited to two decimal places, and as indicated in Fig. 5,
the case of MLPNN, the differentiable function is the R-values of 0.99 (testing) and 0.99 (validation) are realised
error/cost function (Eq. (10)). for predicting average pillar stresses. These high R-values
2 indicate the high performance of the MLPNN model in
cost ¼ Y pred Y act ð10Þ predicting average vertical pillar stresses.
The error margins of the MLPNN model are also indi-
Gradient descent is made by calculating the partial cated in Table 5. The error margins are reasonably small;
derivatives of the cost function for the parameters (wij thus, the MLPNN model has been sufficiently trained
and bk) (Eq. (11)) and moving in the negative direction of and can make good generalisations when presented with
these derivatives (slopes), shown as below: new data.
N. Dzimunya et al. / Underground Space 13 (2023) 121–135 127
Table 4
MLPNN model hyperparameters and architecture.
Max_iterations Activation Architecture Solver Learning rate Alpha
2000 ReLu 7–150–150–50–1 Adam Adaptive 0.05
Fig. 7. Vertical stress contours in FLAC3D. (a) Entire model, (b) closest pillar to the abutment, and (c) most center pillar.
It is visible from Fig. 9 that rmax can never approach the between the maximum pillar stress in a large panel
TAT stress because the barrier pillars, with their higher (700 m panel width according to the database) and the
stiffness, are carrying the extra load that was supposed to maximum stress (IBSmax) in a panel with a width equiva-
be exerted on the panel pillars. From previous simulations
and predictions, it became evident that pillar loads increase
with the increasing size of the panel. Thus, it is understand-
ably logical to assume that rmax and rmin are bound
lent to IBS. This logical assumption is made more evident designation (RQD) value of 90 (according to the mine
by visualising Fig. 10. reports). The mine employs a robust pillar layout system
The average (b u ) of the MLPNN predictions of the max- to ensure regional stability; thus, panel pillars are accom-
imum stresses in a large panel and IBSmax is reasonably panied by evenly spaced barrier pillars, as indicated in
close to rmax. Similarly, the average of b u and IBSmax is Fig. 11.
approximately equivalent to rmin. This average of b u and The steps to determine rmax and rmin for this mine are as
IBSmax is termed b a . The above trend was the same when follows:
comparing DDM simulations and MLPNN predictions
for other pillar layouts. Multivariate regression analysis (1) Identifying the features of the mine layout and rock
of these comparisons was then performed to develop mod- mass properties to input into the MLPNN model.
els that can estimate rmax and rmin. The hydraulic radius of For this case study (e = 83.3%, E = 75 GPa,
the barrier pillars was also considered as an independent H = (180, 200, 250, 300, and 350 m), panel
variable, but its observed significance level (P-value) of width = (700 m and IBS), m = 1.5, TAT = (28.59,
the test statistic, from the statistical analysis, was more 31.76, 39.71, 47.65, and 55.59 MPa), DfA = (350 m
than 0.05, and thus, it was dropped from the subsequent and 48 m for 700 m and IBS panel widths respec-
models of estimating rmax and rmin. Equations (13) and tively)). Notice, H is taken to represent the range of
(14) are the adapted MLPNN model equations to estimate mining depths at the mine, and the corresponding
rmax and rmin, respectively, in any large panel layout with TAT stress is calculated using a density of 2700 kg/
equally spaced barrier pillars. m3, according to the database. However, the pre-
dicted stresses by MLPNN must be corrected to
rmax ¼ 0:36 þ 1:02^
u; ð13Þ
reflect a density of 3200 kg/m3 at the mine using sim-
rmin ¼ 1:12^
a 1:57; ð14Þ ple proportions.
(2) Prediction of maximum pillar stress for a large panel
where rmax, rmin, b
u and b
a are all in MPa. at a depth of 180 m. The MLPNN prediction was
obtained as 28.73 MPa and corrected to 34.05 MPa
4.2 Case study application by proportion.
(3) Prediction of IBSmax at a depth of 180 m. This was
Equations (13) and (14) were applied to an actual room- predicted as 15.46 MPa and corrected to 18.32 MPa
and-pillar mine used for case study in Zimbabwe. The mine by proportion.
is a large-scale hard rock operation with typical mining (4) Calculation of averages, b u (26.19 MPa) and b a
depths averaging 180 to 350 m. Pillars at the mine are usu- (22.25 MPa).
ally 6 m 6 m and the rooms are with 6 m vent holings and (5) Substitution of b u and ba into Eqs. (13) and (14) to
12 m boards. The average uniaxial compressive strength obtain rmax and rmin. Finally, rmax and rmin were
(UCS) of the pyroxenite rocks at the mine is 205 MPa (ac- obtained as 27.07 and 23.35 MPa, respectively.
cording to mine reports and tests by the authors). The den-
sity of the rock is approximately 3200 kg/m3. E varies Step 2 to 5 were repeated for the other mining depths of
between 90 and 130 GPa. However, the deformation mod- 200, 250, 300, and 350 m, and the results are summarised in
ulus of the rock mass (E0 = 75 GPa) was estimated, accord- Table 7. FOS is used at the mine to judge the stability of
ing to Zhang and Einstein (2004), using a rock quality pillars. Pillar strength at the mine is calculated using the
Hedley and Grant formula (Eq. (15)) (Hedley & Grant,
1972):
0:5
w
P s ¼ K 0:75 ; ð15Þ
h
Table 7 specific pillar stress measurements, the FOS values are rea-
Summary of pillar stress estimations for the case study mine. sonably within similar magnitudes, thus proving that the
MLPNN TAT MLPNN-adapted pillar stress estimation procedure can
Depth, H Ps rmax FOS rmin FOS Stress FOS approximate pillar stresses in similar applications. Table 7
(m) (MPa) (MPa) – (MPa) – (MPa) – also indicates the calculations for the TAT approach. It is
180 106.63 27.07 3.9 23.35 4.6 28.59 3.7 evident that the TAT method tends to be conservative
200 106.63 30.29 3.5 26.39 4.0 31.76 3.4 because the panel pillars near the lines of barrier pillars
250 106.63 37.73 2.8 33.63 3.2 39.71 2.7 or any permanent abutments carry smaller stresses than
300 106.63 44.36 2.4 40.68 2.6 47.65 2.2
predicted by the TAT method, regardless of the IBS.
350 106.63 51.46 2.1 47.99 2.2 55.59 1.9
Fig. 12. Mine-wide FLAC3D simulation at the case study mine (mine reports).
132 N. Dzimunya et al. / Underground Space 13 (2023) 121–135
increasing the extraction ratios in narrow panels and areas ommended as a first approach to design. During mining,
close to the abutments. The maximum distance from the when the pillars have been fully excavated, the importance
abutment where this increased extraction can occur is sub- of physical inspections, deformational and stress measure-
ject to further studies. ments can never be over emphasised. This model is also
limited to design of non-yield pillars where all the analysed
5.3 Limitations pillars are intended to remain intact. However, in some
cases the pillars can attain their strength level and fail; thus,
The MLPNN model has some limitations based on how deviating from linear elastic behavior. Additionally, if fail-
the database was developed. The model cannot accurately ure of other pillars in the system occurs, the model cannot
estimate stresses for pillars with irregular shapes because handle the redistributed stresses, and other separate studies
the model does not include irregular pillar outlines. Also, may be needed in such scenarios.
the MLPNN model can only be used for single exploited
ore seams and cannot be used for multiple mined ore 6 Conclusion
seams. The MR was considered a unity in developing the
database; thus, this MLPNN model cannot be accurately This study presented the development of an MLPNN
applicable in cases of different modulus ratios. However, model to estimate average vertical pillar stresses while con-
to establish the model’s reasonable range of applicability, sidering the influence of abutments. The database used to
effect of MR was simulated in DDM. The simulations com- train the model was numerically developed using DDM.
prised models situated at a mining depth of 200 m, and all The features constituting the database were extraction ratio
other parameters were unchanged except MR (MR = 0.5, (e), Young’s modulus (E), mining depth (H), panel width,
0.75, 1, 1.25, 1.5, and 2). Taking MR = 1 as the actual the ratio of room to pillar width (m), tributary area theory
result, absolute percent error was used to illustrate the pillar stress (TAT), and distance of pillar from abutment
effect of MR. If the acceptable error margin is within 5% (DfA). The MLPNN model was successfully trained, and
the model can be judiciously used within a MR range of its performance on the testing and validation datasets
0.5–2 as indicated in Fig. 13. was acceptable, yielding R score values of 0.99 each. Fur-
It should be noted that the elastic and homogenous rock ther validation of the MLPNN model was done through
mass conditions assumed in this study are a simplification a comparison with FLAC3D results. Predictions of the
of actual rock mass conditions and may have a consider- MLPNN model and the FLAC3D pillar stresses reason-
able impact on the predictions that this model can produce. ably agreed with a regression coefficient of 0.99. The
Rock masses are generally discontinuous (bedding planes MLPNN model was also adapted to mine layouts consist-
and discontinuities may separate pillars and host rock) ing of large panel widths with evenly spaced barrier pillars.
and often have anisotropic and heterogeneous properties. The adapted model was then applied to an actual mine case
The elastic and homogenous assumption adopted in the study in Zimbabwe, and the estimated pillar stresses by the
development of MLPNN model may not accurately repre- model satisfactorily agreed with simulations done at the
sent the actual stress field and the model is particularly rec- mine.
In a typical mining setup where routine pillar stress esti-
mations are inevitable, numerical modelling does not pro-
vide simple procedures for determining pillar stresses.
Models are naturally difficult to setup and usually onerous
computer run times are unavoidable. Such a scenario is not
convenient at mine sites where quick solutions are usually
demanded. The MLPNN model thus affords an approach
that features easily accessible mine geometrical and rock
mass parameters that can quickly be applied in under-
ground mines. Though serving as an indirect route to
attaining almost similar results as numerical modelling, this
model can sufficiently be used as an initial pillar stress esti-
mation approach as substantiated by the series of success-
ful training, testing, validation, and actual case study
application of the model.
Furthermore, the development of the MLPNN model
has unearthed the DfA beyond which abutments cease to
influence pillar stresses. This opens new prospects for
future studies aimed at optimising the distances between
barrier pillars for improved safety against large-scale pillar
collapses. Additionally, further studies are required in
Fig. 13. Effect of MR on vertical pillar stresses. developing pillar design guidelines and extraction ratios
134 N. Dzimunya et al. / Underground Space 13 (2023) 121–135
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