Superiority of artificial neural networks over statistical methods in prediction of the optimal length of rock bolts.
Hasanzadehshooiili, Hadi ; Lakirouhani, Ali ; Medzvieckas, Jurgis 等
1. Introduction
Geotechnical and mining engineering cover a wide range of fields
(Amsiejus et al. 2009; Zarzojus, Dundulis 2010; Zavadskas et al. 2010;
Kelevisius et al. 2011; Hasanzadehshooiili et al. 2012; Sivilevicius et
al. 2012). They are generally related to design and control of surface
or subsurface structures. Furthermore, use of rock bolts in underground
constructions has been one of the most popular support methods applied
by geotechnical and mining engineers (Barton et al. 1974; Unal 1983;
Chua et al. 1992; Cai et al. 2004a, b). As soon as the rock bolting
method was developed in the 1920s, it was proposed as a systematic
method for weak roof support by Weigel (1943). This method has numerous
advantages in comparison to other methods. For instance, one of such
advantages manifests through a more cost-efficient use of materials and
manpower. Furthermore, this active support method is more effective and
efficient as it utilises the rock to support itself by applying internal
reinforcing stress. Besides, it can be used under different geological
conditions (Barton et al. 1974; Luo 1999).
However, the variety of geological conditions is inexhaustible
(Susinskas et al. 2011). Actually, due to the complexity of geological
conditions and mechanisms of bolting technology and since most decisions
are made based on previous experiences, the design of rock bolts could
be attributed to an art form rather than a science (Peng, Tang 1984; Luo
1999). In order to select a suitable bolting system, design
parameters--such as the bolt length, bolt density and bolt pretension
during installation--are usually considered to be optimal.
In this paper, the length of rock bolt, which is one of the most
important design parameters, is considered to be optimal.
As a matter of fact, from a theoretical viewpoint, a bolted beam is
as strong as a solid beam made out of the same material. Thus, finding
the optimal length of a bolt is equivalent to finding the minimum solid
beam thickness (Luo 1999). Besides, independent parameters that affect
the strength of a solid beam include Young's modulus,
Poisson's ratio, overburden thickness, cohesion, friction angle and
tensile strength (Luo 1999).
Thus, to produce a comprehensive study of the optimal length of
rock bolts, professor Luo (1999) computed the minimum solid beam
thickness during an experiment that involved random sampling of each of
the independent variables for each of the data series.
Then, to efficiently and cost-effectively predict the optimal
length of rock bolts, some statistical analyses--such as multiple linear
regression analysis, polynomial regression analysis, dimensionless
analysis and the optimised statistical analysis--were undertaken (Luo
1999). Although numerous efforts have been made to predict the optimal
bolt length, low value of the correlation coefficient obtained by
statistical models reveals the urgent need for a substitute forecasting
method.
Also, to select the optimal bolting system, the mathematical
programming theory and methods can be applied. Such techniques have been
used to solve a similar problem, i.e. optimisation of beams in grillage
structures (Kim et al. 2005; Belevicius et al. 2002). Also, solving
optimisation problems, promising results have been achieved with Genetic
Algorithms (GA) (Belevicius, Sesok 2008). Global optimisation of
grillages using simulated annealing and high performance computing is
given in Sesok et al. (2010). Besides, the method of object-oriented
programming (OOP) for optimal design of steel frame structures had been
suggested by Jankovski, Atkociunas (2010).
As mentioned earlier, the ultimate goal for the bolt design
paradigm, achieving a minimum solid beam thickness, is gained by
optimising the bolt length, bolt density and bolt pretension during
installation (Stankus, Guo 1997). Bolt binding effects are accomplished
using three basic mechanisms: suspension, beam building and keying. In
most situations, both suspension and beam building effects coexist. The
keying effect mainly depends on active bolt tension. To determine the
bolt length, pretension and spacing required for the optimal beaming
effect, the abovementioned global optimisation methods can be used.
On the other hand, because of their multidisciplinary nature,
artificial neural networks are commonly applied by the majority of
researchers working in different branches of science (Goh et al. 1995;
Maity, Saha 2004; Schabowicz, Hola 2008; Baalousha, Celik 2011).
Besides, high capabilities of this tool in prediction of complicated
functions have been broadly proved (Abu Kiefa 1998; Malinowski et al.
2006; Malinowski, Ziembicki 2006; Mang et al. 2009; Dikmen, Sonmez
2011). Thus, to attain a rugged, cost-effective and timely prediction of
the optimal bolt length, the applicability of ANNs has been
investigated. For this purpose, using the data sets prepared by Luo
(1999) and training numerous 1-layer and 2-layer back-propagation
networks, several networks were created and for all the built networks,
the value of the correlation coefficient, the root mean squared error,
the mean absolute error and the fitting line's slope were
calculated.
In order to show the superiority of the neural network modelling
over other statistical methods, values of the correlation coefficient
for all of the built models were presented and compared. Moreover, the
sensitivity analysis was made using the cosine amplitude method to
obtain parameters that have the greatest and the least impact on the
optimal bolt length (Yang, Zhang 1997).
2. Input and output parameters
To gain the minimal thickness of a solid beam or the optimal length
of a rock bolt, roof bolts used for an underground opening with a
constant roof span amounting to 20 feet was considered (Luo 1999). Since
parameters that impact on the strength of a solid beam primarily include
Young's modulus, Poisson's ratio, overburden thickness,
cohesion, friction angle and tensile strength, these six variables were
considered as independent variables that impact on the optimal bolt
length (Luo 1999). By means of a completely randomised design technique,
each independent variable was sampled 50 times to construct a
comprehensive database consisting of 50 groups of independent variables.
Then, for each group, the minimal thickness of a solid beam was computed
as an output parameter (Luo 1999). Ranges of variation of six
independent sampled variables together with the corresponding values of
the optimal bolt length are shown in Table 1 (Luo 1999).
3. Statistical analysis
Based on obtained results, linear and polynomial multiple variable
regression analyses as well as dimensionless modeling and optimum
modeling based on three other aforementioned models were undertaken to
gain a prediction of the optimal bolt length based on independent input
variables.
3.1. Linear multiple variable regression analysis
Using the SAS programme, the multiple variable regression analysis
was carried out to estimate the minimal solid beam thickness (Luo 1999).
According to this analysis, the value of the minimal beam thickness or
the optimal length of a rock bolt in terms of six aforementioned input
parameters could be calculated using Eq. 1 (Luo 1999):
OL = (-1.26 x [10.sup.-6]) x (E) + 0.7721 x (PR) + 0.0016 x (OB) -
0.0001 x (C) - 0.0023 x (TS) - 0.0402 x (FA) + 5.0537. (1)
For this model, the correlation coefficient [R.sup.2] amounted to
0.7182, which is somewhat low (Luo 1999).
3.2. Polynomial multiple variable regression analysis
Polynomial analysis was carried out in order to improve the quality
of estimation produced using the linear regression model. Nevertheless,
it did not improve the prediction accuracy and the coefficient of
correlation amounted to 68%, which was even less than the value in case
of the linear model (Luo 1999).
According to this modelling, the optimal bolt length in terms of
inputs could be computed using Eq. 2 (Luo 1999):
OL = 30.32 x [(E).sup.-0.02] +1.13 x [(PR).sup.0.4] - 0.4126 x
[(OB).sup.-0.5] + 6.87 x [(C).sup.-0.05] + 6.43 x (2) [(TS).sup.-0.27]
+16.00x [(FA).sup.-0.2] - 33.29.
3.3. Dimensionless analysis
Using a dimensionless analysis on independent input variables,
Poisson's ratio becomes redundant in predicting the value of the
optimal bolt length (Luo 1999), the value of which could be approximated
using Eq. 3:
OL = [(OB).sup.0.55]/[(E).sup.0.04][(C).sup.0.05][(TS).sup.0.12][(FA).sup.0.26] (3)
The value of the correlation coefficient for this analysis, just as
for other previously mentioned statistical methods, was somewhat low as
well and amounted to 70%.
3.4. Optimised statistical analysis
As it was shown earlier, use of the above described statistical
methods leads to an approximation of the optimal length of a rock bolt.
Considering each of the results estimated by these analyses as separate
independent variables and assigning a certain weight to each of them,
the optimised model can be achieved through optimisation of the newly
obtained mixed model (Luo 1999).
Thus, the optimised model would look as described below:
[OL.sub.0ptimized] = 0.3452 x ([OL.sub.Linear]) + 0.3941x
([OL.sub.Polynomial]) + 0.2679 x ([0.2679.sub.Dimensionless]), (4)
where:
([OL.sub.Linear]): result of the linear model;
([OL.sub.Linear]): result of the polynomial model;
([OL.sub.Linear]): result of the dimensionless model.
Although this modeling improved the accuracy of prediction and
increased the value of the correlation coefficient to 78% (Luo 1999), it
has not reached the desired level to be acceptable. Subsequently, the
need for a highly capable prediction tool that could be used to
effectively and efficiently predict the value of the optimal bolt length
became obvious.
4. Artificial neural networks
Artificial neural networks are a branch of the field known as
Artificial Intelligence. These powerful tools were firstly introduced by
McCulloch and Pitts (1988) for calculation of logic functions. Yet, now
they are broadly applied by a considerable number of researchers to
model a target function based on available datasets (Khandelwal, Singh
2006; Young-Su, Byung-Tak 2006; Monjezi et al. 2010). In this method, a
real experimental database is used to acquire relationships between
involved parameters. The greater is the database of results, the more
accurate is the prediction (Heshmati et al. 2009; Dikmen, Sonmez 2011;
Khosrowshahi 2011).
The main role of artificial neural networks is to predict outputs
based on inputs and the rules, which are learnt during the training
phase.
In the attempt to prove that neural networks are able to recognise
patterns, Rosenblatt (1958) built a perception network. One of the main
benefits of neural networks in comparison to the statistical methods is
the absence of a need to have prior knowledge about the nature of the
problem, which is to be solved (Funahashi 1989). Besides, multilayer
perception (MLP) networks are believed to be the best type of neural
networks, which can be broadly used to predict any continuous function
(Yasrebi, Emami 2008). This kind of network is composed of three types
of layers: the input, the hidden and the output layer. In a MLP network,
the number of layers depends on the type and complexity of a problem.
However, at least one each--the input, the hidden and the output
layers--are required (Yasrebi, Emami 2008). Each of these layers
contains elements named neurons. These neurons are connected to each
other; however, neurons in a layer cannot be connected to other neurons
in the same layer. Subsequently, they can only be connected to neurons
in other layers. Such nodes are connected by links. Each of these nodes
has a specific weight vector, which is multiplied into the processed
information. Transformation of the sum of the weighted input signals to
each neuron is carried out by activation functions (Monjezi et al.
2010).
As the hidden layer uses nonlinear activation functions such as the
logistic function, the model becomes genuinely nonlinear (Sarle 1994). A
MLP can also have multiple inputs and outputs, as shown in Fig. 1.
In order to predict outputs, neural networks need to be trained
using prepared datasets. Firstly, these datasets are fed into the
network and then, by detecting the similarities, network gets trained;
and while a new dataset is available, the network can predict the
corresponding outputs based on what it has learnt during the training
phase (Sarle 1994).
[FIGURE 1 OMITTED]
To create a true network, three following major components should
be accurately defined and assigned, i.e. the transfer function, the
learning law and the network architecture (Simpson 1990).
4.1. Training the network
One of the most and widely suggested training algorithms, which
have been implemented by a variety of researchers for learning purposes,
is backpropagation also known as BP (Neaupane, Adhikari 2006). This
technique is composed of two passes: the forward pass and the
backpropagation pass. In a forward pass, the network predicts the
outputs assigning a preliminary value for connections between neurons.
Then, in a backpropagation pass, the error--the computational difference
between the calculated output and that of the target pattern, which is
calculated in the forward pass--is backpropagated to update the weights.
This procedure continues to reach the pre-defined threshold (Yang,
Rosenbaum 2002).
It should be noted that in order to build the model, before the
training phase begins, the contributing parameters--inputs and
outputs--should be normalised on the scale of 0-1. Eq. 5 can be used to
normalise the data and make it dimensionless (Monjezi et al. 2010).
Scaled Value = (unsealed value - min. value)/ (max. value - min.
value). (5)
[FIGURE 2 OMITTED]
Once data was normalised, 85% of the entire data were randomly
chosen for training and cross-validation purposes. The remaining data
was kept for testing of the built model. Besides, subsequent to a large
number of trials on different networks, the nonlinear tangent sigmoid
function TANSIG, which shows the minimal error, was considered as the
transfer function. Fig. 2 shows the nonlinear
TANSIG transfer function. The TANSIG transfer function formula is
presented in Eq. 6 (Demuth et al. 1996):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII](6)
where [e.sub.x] is the weighted sum of the inputs for a processing
unit (Demuth et al. 1996).
Other controlling problems, which should be avoided during the
network training, include under-fitting and over-fitting. Over-fitting
occurs as a result of using too many training epochs, which can be
conducive to memorising the outputs. Under-fitting is a consequence of
using insufficient number of training epochs, which results in
model's inaccuracy (Maulenkamp, Grima 1999).
4.2. Network architecture
To gain the best model architecture, lots of 1-layer and 2-layer
MLP networks were created. For all the built models, the value of root
mean squared error, RMSE, and the mean absolute error, MAE, also,
coefficient of correlation, R , were calculated and compared. The
applied formulas for calculating RMSE and MAE are presented as Eqs 7 and
8, respectively (Monjezi et al. 2010):
RMSE = [square root of ([([O.sub.i] - [T.sub.i]).sup.2])/n]; (7)
MAE = [absolute value of [T.sub.i] - [O.sub.i]], (8)
where [T.sub.i] and [O.sub.i] represent computed and predicted
outputs, respectively. Also, n is the number of data sets.
The values of RMSE and MAE as well as the correlation coefficient
together with the slope of fitting line for different network
architectures are given in Table 2.
As Table 2 suggests, the optimal model is the network with the
architecture of 6-18-3-1, as it has the minimum RMSE and MAE as well as
the maximum [R.sup.2] with a slope of 1.0002 for the fitting line A.
To better describe the topology of the optimal network, its
schematic architecture is demonstrated in Fig. 3.
[FIGURE 3 OMITTED]
4.3. Model performance
To evaluate the optimal model's performance for testing of
data series, the normalised predicted values of the optimal bolt length
versus its normalised computed values are depicted in Fig. 4.
[FIGURE 4 OMITTED]
Also, as it is shown in Fig. 5, the value of [R.sup.2] for the
network with the topology of 6-18-3-1 is 0.926, which proves the
superiority of artificial neural network modelling over other
aforementioned statistical methods in prediction of optimal bolt length.
[FIGURE 5 OMITTED]
In addition to high correlation with the computed optimal bolt
length, which is confirmed by high value of the correlation coefficient,
the values calculated for RMSE, 0.0781, and MAE, 0.0682, show high
capability and performance of applied ANN model.
5. Sensitivity analysis
Knowledge of the most influencing parameters and the parameters
with the least effect on the optimal rock bolt length considerably
impacts the entire design procedure and makes it more cost-effective as
well as timely.
Thus, the sensitivity analysis was made using the cosine amplitude
method (CAM).
This method is used to achieve the express similarity relations
between the input parameter and the goal function (Yang, Zhang 1997). In
this method, each input parameter is expressed as one of X array
elements, as demonstrated in Eq. 9 (Khandelwal, Singh 2006):
X = {[sub.x1, X2, X3,..., Xi,... Xn]}, (9)
where each of its elements is a vector with the length of m and is
presented in Eq. 10:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Then, the strength of the relationship between [x.sub.i] and
[x.sub.j] can be calculated using Eq. 11 (Khandelwal, Singh 2006):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
Using these procedures, the most and the least sensitive parameters
on the optimal rock bolt length were attained. The calculated strength
of the relationship between input parameters and the optimal length of a
rock bolt is shown in Fig. 6. According to the Fig. 6, the influence of
Poisson's ratio, overburden thickness, cohesion and tensile
strength on the optimal bolt length is approximately the same.
On the other hand, it was found that the friction angle has the
least influence in determining the optimal length of a rock bolt.
6. Conclusions
An artificial neural network was introduced as a capable tool for
prediction of the optimal length of a rock bolt.
It was discovered that the optimal model is a multilayer perception
network with the architecture of 6-18-3-1.
High value of the correlation coefficient for the optimal created
network, namely 0.926, as well as acceptable values of RMSE, 0.0781, and
MAE, 0.0681, proved the superiority of the artificial neural network
modelling over the conventional statistical methods in prediction of the
optimal bolt length. Besides, the 6-18-3-1 network trained by the feed
forward backpropagation method was introduced as a capable tool in
forecasting of the optimal length of a rock bolt.
Moreover, by means of sensitivity analysis based on the cosine
amplitude method, the friction angle was reported as the least impacting
parameter for the optimal bolt length. Besides, the influences of
Poisson's ratio, overburden thickness, cohesion and tensile
strength on the value of the optimal bolt length are almost the same.
However, the effect of the overburden thickness is slightly higher
than others. Moreover, it plays a more important role in prediction of
the optimal length of rock bolts.
doi:10.3846/13923730.2012.724029
References
Abu Kiefa, M. A. 1998. General regression neural networks for
driven piles in cohesionless soils, Journal of Geotechnical and
Geoenvironmental Engineering ASCE 124 (12): 1177-1185.
http://dx.doi.org/10.1061/(ASCE)1090-0241 (1998)124:12(1177)
Amsiejus, J.; Dirgeliene, N.; Norkus, A.; Zilioniene, D. 2009.
Evaluation of soil shear strength parameters via triaxial testing by
height versus diameter ratio of sample, The Baltic Journal of Road and
Bridge Engineering 4(2): 55-60.
Baalousha, Y.; Celik, T. 2011. An integrated web-based data
warehouse and artificial neural networks system for unit price analysis
with inflation adjustment, Journal of Civil Engineering and Management
17(2): 157-167.
Barton, N.; Lien, R.; Lunde, J. 1974. Engineering classification of
rock masses for the design of tunnel support, Journal of Rock Rock
Mechanics Felsmechanik Mecanique des Roches [Mechanics and Rock
Engineering] 6(4): 189-236.
Belevicius, R.; Sesok, D. 2008. Global optimization of grillages
using genetic algorithms, Mechanika 6: 38-14.
Belevicius, R.; Valentinavicius, S.; Michnevic, E. 2002. Multilevel
optimization of grillages, Journal of Civil Engineering and Management
8(2): 98-103. http://dx.doi.org/10.1080/13923730.2002.10531259
Cai, Y.; Esaki, T.; Jiang, Y. 2004a. A rock bolt and rock mass
interaction model, International Journal of Rock Mechanics and Mining
Sciences 41(7): 1055-1067.
http://dx.doi.org/10.1016/j.ijrmms.2004.04.005
Cai, Y.; Esaki, T.; Jiang, Y. 2004b. An analytical model to predict
axial load in grouted rock bolt for soft rock tunnelling, Tunnelling and
Underground Space Technology 19(6): 607-618.
http://dx.doi.org/10.1016/j.tust.2004.02.129
Chua, K. M.; Aimone, C.; Majtabai, N. 1992. A numerical study of
the effectiveness of mechanical rock bolts in an underground opening
excavated by blasting, in Proc. of the 33th U.S. Symposium on Rock
Mechanics (USRMS), 3-5 June, 1992, Santa Fe, NM, American Rock Mechanics
Association, Paper 92-0285. 10 p.
Demuth, H.; Beal, M.; Hagan, M. 1996. Neural network toolbox 5
user's guide. The Math Work, Inc., Natick. 852 p.
Dikmen, S. U.; Sonmez, M. 2011. An artificial neural networks model
for the estimation of formwork labour, Journal of Civil Engineering and
Management 17(3): 340-347.
http://dx.doi.org/10.3846/13923730.2011.594154
Funahashi, K.-I. 1989. On the approximate realization of continuous
mappings by neural networks, Neural Networks 2(3): 183-92.
http://dx.doi.org/10.1016/0893-6080(89)90003-8
Goh, A. T. C.; Wong, K. S.; Broms, B. B. 1995. Estimation of
lateral wall movements in braced excavation using neural networks,
Canadian Geotechnical Journal 32(6): 1059-1064.
http://dx.doi.org/10.1139/t95-103
Hasanzadehshooiili, H.; Lakirouhani, A.; Medzvieckas, J. 2012.
Evaluating elastic-plastic behaviour of rock materials using Hoek--Brown
failure criterion, Journal of Civil Engineering and Management 18(3):
402-407. http://dx.doi.org/10.3846/13923730.2012.693535
Heshmati, A. A.; Alavi, A. H.; Keramati, M.; Gandomi, A. H. 2009. A
radial basis function neural network approach for compressive strength
prediction of stabilized soil, in Road Pavement Material
Characterization and Rehabilitation: Selected Papers from the 2009
GeoHunan International Conference ASCE 191: 147-153.
Jankovski, V.; Atkociunas, J. 2010. SAOSYS toolbox as MATLAB
implementation in the elastic-plastic analysis and optimal design of
steel frame structures, Journal of Civil Engineering and Management
16(1): 103-121. http://dx.doi.org/10.3846/jcem.2010.10
Kelevisius, K.; Amsiejus, J.; Skuodis, S. 2011. The influence of
changing shaft friction of the pile to wave propagation, Engineering
Structures and Technologies 3(2): 64--71. (in Lithuanian)
Khandelwal, M.; Singh, T. N. 2006. Evaluation of blast-induced
ground vibration predictors, Soil Dynamics and Earthquake Engineering
27(2): 116--125. http://dx.doi.org/10.1016/j.soildyn.2006.06.004
Khosrowshahi, F. 2011. Innovation in artificial neural network
learning: Learn-On-Demand methodology, Automation in Construction 20(8):
1204-1210.
Kim, Y.; Gotoh, K.; Kim, K.; Toyosada, M. 2005. Optimum grillage
structure design under a worst point load using real-coded micro-genetic
algorithm, in Proc. of the 15th International Offshore and Polar
Engineering Conference, 19-24 June, 2005, Seoul, Korea, 730-735.
Luo, L. 1999. A new rock bolt design criterion and knowledge-based
expert system for stratified roof. PhD Dissertation, Virginia
Polytechnic Institute and State University, Blacksburg, Virginia. 189 p.
Maity, D.; Saha, A. 2004. Damage assessment in structure from
changes in static parameters using neural networks, Sadhana 29, Part 3:
315-327. http://dx.doi.org/10.1007/BF02703781
Malinowski, P.; Ziembicki, P. 2006. Analysis of district heating
network monitoring by neural networks classification, Journal of Civil
Engineering and Management 12(1): 21-28.
Malinowski, P.; Polarczyk, I.; Piotrowski, J. 2006. Neural model of
residential building air infiltration process, Journal of Civil
Engineering and Management 12(1): 83-88.
Mang, H. A.; Jia, X.; Hoefinger, G. 2009. Hilltop buckling as the A
and O in sensitivity analysis of the initial postbuckling behavior of
elastic structures, Journal of Civil Engineering and Management 15(1):
35-16. http://dx.doi.org/10.3846/1392-3730.2009.15.35-46
Maulenkamp, F.; Grima, M. A. 1999. Application of neural networks
for the prediction of the unconfined compressive strength (UCS) from
Equotip hardness, International Journal of Rock Mechanics and Mining
Sciences 36(1): 29-39. http://dx.doi.org/10.1016/S0148-9062(98)00173-9
McCulloch, W. S.; Pitts, W. 1988. A logical calculus of the ideas
immanent in nervous activity, Bulletin of Mathematical Biophysics 5:
115-133. http://dx.doi.org/10.1007/BF02478259
Monjezi, M.; Bahrami, A.; Varjani, A. Y. 2010. Simultaneous
prediction of fragmentation and flyrock in blasting operation using
artificial neural networks, International Journal of Rock Mechanics and
Mining Sciences 47(3): 476-480.
http://dx.doi.org/10.1016/j.ijrmms.2009.09.008
Neaupane, K. M.; Adhikari, N. R. 2006. Prediction of
tunneling-induced ground movement with the multi-layer perceptron,
Tunnelling and Underground Space Technology 21(2): 151-159.
http://dx.doi.org/10.1016/j.tust.2005.07.001
Peng, S. S.; Tang, D. H. Y. 1984. Roof bolting in underground
mining: a state-of-the-art review, Geotechnical and Geological
Engineering 2(1): 1-42.
Rosenblatt, F. 1958. The perception: a probabilistic model for
information storage and organization in the brain, Psychological Review
65: 386-408. http://dx.doi.org/10.1037/h0042519
Sarle, W. S. 1994. Neural networks and statistical models, in Proc.
of the 19th Annual SAS Users Group International Conference, 10-13
April, 1994, Dallas, Texas. 13 p.
Schabowicz, K.; Hola, J. 2008. Application of artificial neural
networks in predicting earthmoving machinery effectiveness ratios,
Archives of Civil and Mechanical Engineering 8(4): 73-84.
http://dx.doi.org/10.1016/S1644-9665(12)60123-X
Sesok, D.; Mockus, J.; Belevicius, R.; Kaceniauskas, A. 2010.
Global optimization of grillages using simulated annealing and high
performance computing, Journal of Civil Engineering and Management
16(1): 95-101. http://dx.doi.org/10.3846/jcem.2010.09
Simpson, P. K. 1990. Artificial neural system: foundation,
paradigms, applications and implementations. New York: Pergamon Press.
209 p.
Sivilevicius, H.; Daniunas, A.; Zavadskas, E. K.; Turskis, Z.;
Susinskas, S. 2012. Experimental study on technological indicators of
pile-columns at a construction site, Journal of Civil Engineering and
Management 18(4): 512--518.
http://dx.doi.org/10.3846/13923730.2012.709958
Stankus, J.; Guo, S. 1997. New Design Criteria for Roof Bolt Syste
. in Proc. of the 16th Conference on Ground Control in Mining, 3-5
August, 1997, Morgantown, WV, 158-166.
Susinskas, S.; Zavadskas, E. K.; Turskis, Z. 2011. Multiple
criteria assessment of pile-columns alternatives, The Baltic Journal of
Road and Bridge Engineering 6(3): 77-83.
Unal, E. 1983. Development of design guidelines and roof-control
standards for coal-mine roofs. Ph issertation, Pennsylvania State
University, University Park, PA. 380 p.
Weigel, W. 1943. Channel irons for roof control, Engineering and
Mining Journal 144(5): 70-72.
Yang, Y.; Rosenbaum, M. S. 2002. The artificial neural network as a
tool for assessing geotechnical properties, Geotechnical and Geological
Engineering 20(2): 149-168. http://dx.doi.org/10.1023/A:1015066903985
Yang, Y.; Zhang, Q. 1997. A hierarchical analysis for rock
engineering using artificial neural networks, Rock Mechanics and Rock
Engineering 30(4): 207-222. http://dx.doi.org/10.1007/BF01045717
Yasrebi, S. S. H.; Emami, M. 2008. Application of Artificial Neural
Networks (ANNs) in prediction and interpretation of pressuremeter test
results, in Proc. of the 12th International Conference of International
Association for Computer Methods and Advances in Geomechanics (IACMAG),
1-6 October, 2008, Goa, India, 1634-1638.
Young-Su, K.; Byung-Tak, K. 2006. Use of artificial neural networks
in the prediction of liquefaction resistance of sands, Journal of
Geotechnical and Geoenvironmental Engineering ASCE 132(11): 1502--1504.
http://dx.doi.org/10.1061/(ASCE)1090-0241(2006)132: 11(1502)
Zarzojus, G.; Dundulis, K. 2010. Problems of correlation between
Dynamic Probing Test (DPSH) and Cone Penetration Test (CPT) for cohesive
soils of Lithuania, The Baltic Journal of Road and Bridge Engineering
5(2): 69--75. http://dx.doi.org/10.3846/bjrbe.2010.10
Zavadskas, E. K.; Turskis, Z.; Valutiene, T. 2010. Multiple
criteria analysis of foundation instalment alternatives by applying
Additive Ratio Assessment (ARAS) method, Archives of Civil and
Mechanical Engineering 10(3): 123-141.
http://dx.doi.org/10.1016/S1644-9665(12)60141-1
Hadi Hasanzadehshooiili (1), Ali Lakirouhani (2), Jurgis
Medzvieckas (3)
(1,2) Department of Civil Engineering, University of Zanjan,
Zanjan, Iran (3) Faculty of Civil Engineering, Vilnius Gediminas
Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania
E-mails: (1) h.hasanzadeh.shooiili@gmail.com; (2) rou001@znu.ac.ir; (3)
jurgism@vgtu.lt (corresponding author)
Received 25 Jan. 2012; accepted 17 Jul. 2012
Hadi HASANZADEHSHOOIILI. PhD student of the Dept of Civil
Engineering, Faculty of Engineering, University of Guilan, Rasht,
Guilan, Iran. He obtained his BSc in Mining Engineering from Urmia
University in 2008 and his MSc in Geotechnical Engineering from
University of Zanjan in 2011. His research interests include rock
mechanics and geomechanics, geotechnical engineering (deep foundations),
computational plasticity and mechanics, Hoek-Brown plasticity, numerical
modeling, constitutive modeling of geo-materials and using ANNs in
prediction of complicated civil engineering problems.
Ali LAKIROUHANI. PhD Assist. Prof. of the Dept of Civil
Engineering, University of Zanjan, Zanjan, Iran. A graduate of Civil
Engineering Faculty of Amirkabir University of Technology, Tehran, Iran
(1998), MSc in geotechnical engineering (2000) and PhD in geotechnical
engineering (2008). Research interests: hydraulic fracturing modeling
(initiation of hydraulic fractures at a borehole to improve the
interpretation of the in-situ stress from a hydraulic fracturing stress
test.), tunnelling, rock slope stability.
Jurgis MEDZVIECKAS. Dr, Assoc. Prof. of the Geotechnical Dept of
Vilnius Gediminas Technical University. A graduate of Civil Engineering
Faculty of Vilnius Civil Engineering Institute (now--Vilnius Gediminas
Technical University), Lithuania (1978). Dr in Structural Engineering
(1989). Fields of research: foundation underpinning, relationship
between ground and structures, estimation of soil mechanical properties.
Table 1. Input and output parameters (Luo 1999)
Type of Parameter Symbol Range
data
Input Young's modulus (Lb/[Inch.sup.2]) E 147941-1160320
Poisson's ratio PR 0.1-0.48
Overburden thickness (feet) OB 266-1184
Cohesion (Lb/[Inch.sup.2]) C 580-5686
Friction angle (degree) FA 20-60
Tensile strength (lbs/[in.sup.2]) TS 29-1204
Output Optimal bolt length (feet) OL 0.033-7.611
Table 2. The value of RMSE, MAE, R2 and the slope of fitting
line for different model's architecture
Architecture RMSE MAE [R.sup.2] A
6-9-7-1 0.2212 0.1597 0.520 0.1717
6-3-8-1 0.1892 0.1286 0.588 0.3288
6-10-1 0.1445 0.1111 0.510 0.3143
6-5-1 0.1499 0.1224 0.585 0.3418
6-4-1 0.1220 0.0885 0.552 0.4483
6-9-1 0.1209 0.1052 0.635 0.4233
6-7-1 0.1065 0.0975 0.426 0.4206
6-12-3-1 0.1061 0.0921 0.545 0.8932
6-13-1 0.0897 0.0784 0.734 0.9193
6-4-13-1 0.0872 0.0768 0.687 0.4185
6-18-5-1 0.0880 0.0659 0.893 0.4744
6-4-9-1 0.0866 0.0643 0.738 0.6019
6-18-3-1 0.0781 0.0682 0.926 1.0002
Fig. 6. Strength of the relationship between input parameters
and the length of a bolt
Young's modulus 0.669
Poison's ratio 0.867
Overburden thickness 0.933
Cohesion 0.889
Friction angle 0.491
Tensile strength 0.906
Note; Table made from bar graph.
