DETERMINING THE OPTIMAL SOLUTION FOR THE EXECUTION OF UNDERGROUND [613412]

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DETERMINING THE OPTIMAL SOLUTION FOR THE EXECUTION OF UNDERGROUND
MINING CONSTRUCTIONS, GIVEN THE GEOLOGICAL AND MINI NG CONDITIONS

*N. Dobritoiu and I.S. Mangu

University of Petrosani
20 Universitatii Street
Petrosani, Romania
(*Corresponding author: [anonimizat] )

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DETERMINING THE OPTIMAL SOLUTION FOR THE EXECUTION OF UNDERGROUND
MINING CONSTRUCTIONS, GIVEN THE GEOLOGICAL AND MINI NG CONDITIONS

ABSTRACT

The modern methods used in designing underground mi ning constructions are using graph
structure-based models. The graph structure-based m odels contain: the environmental conditions of the
area where an underground mining construction is to be built and the technological elements involved i n
the process of building an underground mining const ruction. The usage of the graph-structure model in
mining design creates a great number of options for the construction process. Therefore, these options
ought to be evaluated and based on a decision crite rion, an optimal choice can be made.

KEYWORDS
Matrix of connections, graph, critical path, mining work, optimum solution, natural conditions.

GENERAL IDEAS

To build an underground mining construction one can choose between various digging methods at
their disposal. The selection of the digging method is being done taking into consideration the geolog ical
and mining conditions of the types of rock from the digging site.
Having chosen the digging method, one can select th e type of technological means corresponding
to the selected method.
The dynamics of the environmental changes that will affect the geological and mining conditions
of a mining construction will result in the alterin g of the digging methods and the technologies selec ted for
those methods.
Selecting the best digging method and the correspon ding technological means can be done using
the graph structure models. Due to the high number of digging methods and various technologies, the
graph structure methods usage to select the best is required.
The graph structure models allow one to determine t he geological and mining conditions of the
rock layers where the mining construction will be l ocated.
The usage of graph structure methods in designing o f mining constructions when the geological
and mining conditions are known results in a high n umber of design solutions.
From the high number of options generated using the conditions-solutions connection matrix ,
large number can be set aside because of the exitin g incompatibilities between the nodes of the non-
adjacent columns of the conditions-solutions graph.
Quantifying every admissible variant of solution b y using a system of indicators and knowing an
optimization criterion, one can determine the optim al solution for building an underground mining
construction when the environmental conditions are given.

MODEL OF GENERATION, EVALUATION AND ESTABLISHMENT O F AN OPTIMAL
VARIANT OF ACTION FOR CAPITALIZATION OF DEPOSIT

General ideas regarding the classification of the i nformation used for the graphs design

The information used to design the building of an u nderground mining construction can be
classified using the following criteria:
1. The classification of the information according to the nature of the state variables

3 Any complex system can be characterized by a determ ined number of parameters which, at a
certain moment, take on different values and define a certain state of the system, hence, they are als o called
state variables. Variables of state describe the sy stem from two points of view: a qualitative and a
quantitative one. Depending on the described domain , variables of state can be grouped under: category
variables, continuous variables and discrete variab les.
The category variables represent that group of variables of state which d escribe the complex
system from a qualitative point of view, for exampl e: the nature of the face rocks, the type of coal, the rate
of methane emanation, the type of support in a face , the type of underground transport, etc.
The continuous variables represent that group of state variables which desc ribe the complex
system from a quantitative point of view (mass, vol ume, length and time). Continuous state variables c an
get any value within a given interval, for example: the thickness of the seam, the length of the worki ng
face, the length of a borehole, etc.
The d iscrete variables describe the quantitative side of the system but d iscretely, i.e. number of
items elements or number of component parts. Discre te variables can get only certain values within a g iven
interval without going through intermediate values, for example: the number of seams, the number of fa ce
advances, the number of support units, the number o f workers needed on a work site, etc.
2. The classification of the variables according to the time dependent variation
Modifications in time of the value of one or severa l continuous or discrete variables are leading to
the modification of the state of the complex system from a quantitative point of view only. Any comple x
system is known to evolve in the course of time, to change both qualitatively and quantitatively. The
evolutions in time of the variables describing the state of a complex system can be: dynamic, quasi-st atic
and static.
Dynamic variables of state are those variables which in the course of a perio d of time change
continuously, so they are functions of time. The tr ajectories of these variables are not constant thro ughout
the time interval being analysed.
Quasi-static variables of state are those variables which in the course of a perio d of time undergo
only changes of a discrete nature. The trajectories of these variables look like a stepped graph throu ghout
the period of time under consideration.
Static variables of state are those variables of state which in the course o f a period of time remain
constant. The trajectories of these variables are c onstant throughout the period of time under conside ration.
3. The classification of variables of state accordi ng to their relation to the decision-maker
Throughout the existence of a certain complex syste m, changes are brought about frequently or
periodically with a view to modify its state qualit atively as well as quantitatively, depending on the
purpose. There are variables of state that can or c annot be modified using man’s intervention. Thus,
variables of state can accordingly be grouped under : stimulus variables and response variables.
Stimuli variables represent the multitude of the variables of state that cannot be modified by the
intervention of man, for example: the number of str ata, the nature of the rocks from the stope, the de pth of
the deposit, etc.
Response variables represent the multitude of the variables of state that can be modified by man’s
intervention, for example: the number of drills bei ng used simultaneously for drilling holes in the st ope, the
work force needed on the work site, etc.
4. Variables that can indicate the result
The purpose of the management of any system is to t ransform the multitude of stimuli, S, into
admissible responses, R. Any operator that can turn objective stimuli into responses is called a deter miner.
The determiner is the man or group of people that t ransform stimuli S into responses R using certain r ules.
The transformation stimuli-responses: S → M → R is expected to result in the most effective
transformation. The variables characterizing the re sults depend on the S and R set and are called resu lt
indicators.

The database required to design the conditions grap h

The information required to determine the graph str ucture model that is to be used for the design
of the conditions where the underground mining cons truction is being built can be systematized and
classified in the following groups:

4 1. the group of information of static and category stimuli includes:
– the relief on the surface of the deposit where th e underground mining construction is to be built;
– the type of depth of the deposit;
– the type of rocks from the strata covered by the underground mining construction etc.
2. the group of information of static and continuous stimuli includes:
– the mean value of the depth of the stratum where the underground mining construction is to be
built;
– the flow of the accumulation of the underground w ater etc.
3. the group of information of static and discrete sti muli includes:
– the number of reserve units that form the rock be d where the underground mining construction is
situated;
– the number of tectonic accidents of the same type in the underground strata where the mining
construction is to be built etc.
4. the group of information of dynamic and category st imuli includes:
– the category of variation of the ground stability per deposit direction and deposit slope;
– the category of variation of the tectonic acciden ts per deposit direction and deposit slope etc.
5. the group of information of dynamic and continuo us stimuli includes:
– the variation of the absolute water flow of water bearing sheets located in the roof of deposit;
– the variation of the water pressure in a water be aring sheet located in the rock bed;
– the variation of the absolute volume of mine gase s emanation in the deposit and in the rock bed
etc.
6. the group of information of dynamic and discrete stimuli includes:
– the variation of the number of accidents of the s ame type per deposit direction and deposit slope;
– the variation of the number of water deposits per deposit inclination and deposit slope etc.

The database required to design the solutions graph

The “Reactions categories” type of information is r equired to design the graph structure model
used to generate solutions for building of an under ground mining constructions. For example:
– the digging method and the exploitation options;
– the method used to cut the rocks from the rock be d;
– the method used to partially ventilate the work s ite;
– the method used to supply the work site;
– the method of using temporary means temporary con solidation of the galleries resulted after the
cutting of the rocks from the work site;
– the method used to temporarily reinforce the wall s of the underground mining construction;
– the method of definitive consolidation of the und erground mining construction;
– the method used in the underground mine developme nt.

GRAPHICAL-ANALYTICAL MODEL USED TO GENERATE THE MET HOD, OPTIONS OF
DIGGING AND TECHNOLOGICAL MEANS TO EXECUTE AN UNDER GROUND MINING
CONSTRUCTION

Presentation of the graphical-analytical model used to generate the digging conditions of an
underground mining site

The site of the underground mining building can be represented through a descriptive model that
contains: the series of rock strata, the tectonics of the ground, the gas dynamics of the ground, the
hydrogeology of the ground.
The description of the rocks formation includes the description of the following data: the nature
and type of rocks, the physical, mechanical and che mical characteristics of each type of rock, the
geometrical parameters of the rock formation, the m ineralogical and petro-graphical description of the rock
formation, the dynamic of the gases in the rock for mations and the hydro-dynamic of the ground, the
occurrence of tectonic accidents, etc.

5 Once we have the descriptive model of the ground wh ere the underground mining workings are to
be dug, we can attempt to transpose it into a graph ical-analytical model.
In order to transpose the data presented in the des criptive model into a graph structure model,
these data have to be systematized according to the aforementioned presentation (2).
Once the systematization of the data from the descr iptive model has been done, the next step is the
plotting of the graph of conditions.
START C11
C12
C13 C21
C15 C14 C32 C31
C23 C22
C42 C41
C33 STOP C1 C2 C3 C4

Figure 1 – Graph example

This graph enables the generation of a high number of conditions under which the underground
mining construction can be dug.
A graph represents a graphical construction created from columns of nodes linked with left-to-
right oriented arcs (figure 1).
A column of nodes represents the values of a parame ter that is used to describe the natural
conditions under which the mining construction is b eing built The number of columns of nodes in the
graph is equal to the number of parameters used to describe the natural environment where the mining
construction is being dug.
A column of nodes represents the values of a parame ter that is used to describe the natural
conditions under which the mining working is dug. T he number of columns of nodes in the graph is equal
to the number of parameters used for describing the natural environment in which the mining working is
being dug.
The order of the columns of nodes is based on the d egree of relationship of the data, while the
order of nodes in the column depends on the values taken on by the parameter attached to that column.
The graph begins with a single node column which re presents the starting node of the graph called
”START” and it also ends in a single node column ca lled ”STOP”.
The arcs of a graph link the nodes belonging to two adjoining columns. The order of linking is
from left to right. These arcs can take the followi ng values:
– "1" when there is a relationship between the two nodes, i.e. the nodes are compatible;
– "0" when there is no relationship between the two nodes, i.e. the nodes are incompatible. (e.g.:
Consider the nodes column containing the type of th e rocks from the deposit. For the node “foliated ma rl”
and the adjoining node, “the values of the coeffici ent of abrasiveness of the types of rocks situated at the
underground mining construction site”, with the fol lowing values: high abrasiveness, medium
abrasiveness, decreased abrasiveness and no abrasiv eness. We notice that there is no compatibility bet ween
the “foliated marl” node and the nodes from the adj oining column, with the following values: high
abrasiveness, medium abrasiveness, decreased abrasi veness and no abrasiveness).
Remarks
1. All the arcs having their origin in the ”START” node and their destination the ”STOP” node
have the value ”1”.
2. The ”START” and ”STOP” nodes are compatible with nodes in the graph, as a result of the
graph construction.

6 The graph representation of the parameters describi ng a massif through which a mining working is
dug solves only the compatibility between adjacent nodes. Under the circumstances, the number of
conditions that would be generated by this graphica l construction is:
∏
==n
ii dnN
1
where: i=1, 2, 3, , n –represents the number of columns in the graph;
ni – represents the number of nodes in the column “i” .
For the graph in figure 1 it is to generate N d =1 ·5·3·3·2·1=90 paths.
Obviously, not all the paths generated by the graph in fig. 1 are admissible.
In order to determine the number of paths admitted, one will have to solve the compatibility of the
nodes in a column with all the nodes belonging to t he non-adjacent column. This is not possible using the
model with a graph structure. However, the problem can be solved by means of the connection or conting ence
matrix which represents the transposition of the gr aph structure model to analytical form.
The connection matrix representing the analytical t ransposition of the graph structure model in figure
1 is presented in figure 2.

Nr.
crt. Specifica-
tions Parameter
values C1 C 2 C 3 C 4 C 5
c11 c12 c13 c14 c15 c21 c22 c23 c31 c32 c33 c41 c42 c51
C0 c 01 1 1 1 1 1 1 1 1 1 1 1 1 1 1
C1 c11
1 1 1 1 1 0 1 0 1
c12 1 1 1 0 1 1 0 0 1
c13 1 1 1 1 0 1 1 1 1
c14 1 1 1 1 1 1 0 1 1
c15 1 1 1 0 1 1 1 0 1
C2 c21
1 1 1 1 0 1
c22 1 1 1 0 1 1
c23 1 1 1 1 0 1
C3 c31
1 1 1
c32 1 1 1
c33 1 1 1
C4 c41 1
c42 1
Figure 2 – The connection matrix
Remark . The data necessary to draw the graph (fig. 1) and t he connection martix (fig. 2) are
taken at random. The connection matrix is composed of two modules:
– the first module of the matrix represents the con nection module resulting from the analytical
transposition of the graph structure model and it i s the dark part in the matrix;
– the second module of the matrix is ”the module of the added matrix” and it solves the
compatibility of the nodes from non-adjacent column s.

The graphical-analytical model for generating techn ological solutions and technological options for
executing underground mining construction

Given the group of methods for digging an undergrou nd mining site and the sets of operations of
the digging process, we identify for each set of op erations all the types of mining equipment (simple and
complex), installations, devices, tools and we crea te a list with all this data.
For each group of mining equipment on the list, we identify all the types of equipment belonging
to each group. Also, for each type of equipment we identify the existing typo-dimensions.
Having the list of equipment with all the data abou t a group of equipment, the types of equipment
and the typo-dimensions of each piece of equipment, we will draw the “solution graph”.
The “solution graph” is identical to the graph in f igure 1.

7 In order to solve the problem of the compatibility of the nodes belonging to the non-adjacent
columns, we can use the connection matrix. Under th ese circumstances, the compatibility between two
nodes belonging to adjacent and non-adjacent column s result in a technological coupling which can be
used in the digging operations. The information req uired to determine the compatibilities between the
nodes of the adjacent and non-adjacent columns can be found in technical books where one can find
descriptions of the technical-economic characterist ics and of the natural conditions in which this equ ipment
can work. These compatibilities are determined by t he specialists in this field.
The graph of solutions, the way it has been plotted , generates solutions to technologies and
technological options. In order for these technolog ies to be applicable i.e. to be admitted, the conne ction
matrix is used. The way of generating and determini ng the admissible solutions is identical to the one used
for generating the digging conditions for an underg round mining site.

The model with the graph structure for generating a technology or technological variants for digging
underground mining workings when the natural condit ions under which they are executed are
known

Given the two graph structure models for generating the conditions of execution of an
underground mining construction, technologies and t he technological options for the digging of a minin g
work; the following question arises: how does one u se the two types of models with a graph structure f or
determining the technology and the technological op tion for the digging of an underground mining site,
given the natural conditions of the digging?
The answer to this question is: the two graphs are combined into one, resulting a new graph called
“the graph conditions-solutions”. However, this new graph cannot be used for solving the aforementione d
problem. To be able to use it to determine technolo gies or technological options given the natural
conditions of the underground mining construction, we also need the connection matrix resulting from t he
analytical transposition of the “conditions-solutio ns” graph. The new matrix solves the connection bet ween
the graphs “conditions” and “solutions”. This conne ction is created by completing the matrix with the
module “added matrix”. This connection is solved us ing the module “added matrix”, also called the
“connecting module” i.e. it connects “condition mat rix” to “solution matrix” and it is situated on the right
of the modules of the condition matrix, figure 3.

Figure 3 – The connections conditions-solutions mat rix
Remarks
1. The data used to draw the graph solutions and th e matrix of connections of the graph solutions
belong to “Responses” type according to the “the na ture of variables (or the values they can take on)”
criterion used for the classification of data.
2. The type of data corresponding to the “variation in time” and “relation to the decision-maker”
criteria is the same as in the case of the construc tion of the conditions graph.

EXAMPLE
For this example, we have used information from the “Indicative of estimate and costs per unit for
work articles for underground mining constructions, C. M. 1982”, Romania. CONDITION
MATRIX MODULE OF
CONNECTION BETWEEN
CONDITION MATRIX AND
SOLUTION MATRIX
SOLUTION
MATRIX
Nr.
crt Specifications Parameter
Values Columns of
condition matrix Columns of
Solution matrix
Lines of
condition
matrix
Lines of
solution
matrix C0 Sf

8 Due to the complexity of the conditions-solutions g raph, we will not describe it here.
Nevertheless, we will describe the analytical trans position of the graph into a table, “the conditions –
solutions matrix”, appendix 1. Depending on the con ditions under which the underground mining
construction is to be built, we have identified a w ay to determine the method, the optimal technology to be
used for the building of the underground mining con struction.
In order to determine the best options of building the underground mining construction, we will
use the cost per unit building criterion. For certa in situations, to determine the best solution to bu ild the
underground mining construction, we can use various simple and complex optimization criteria.
From the connections matrix presented in appendix 1 , we select the set of conditions for the
building of the underground mining construction, i. e. the natural conditions set corresponding to 0101
code. The segments of this code correspond to:
– first 01 segment – the type of the rocks from the mining site;
– second 01 segment – the value of the type of rock – hard rocks.

Creating the conditions-solutions matrix correspond ing to the set of determined conditions

To create the conditions-solutions matrix correspo nding to the determined set of conditions, see
appendix 2, we need to follow the next steps:
– step 1. In appendix 1, we identify the line conta ining the 0101 code. We follow the line to the
right and delete all columns that contain the “0” v alue in the cells corresponding to this line,
– step 2. We focus on the line containing the 0001 variable. From the columns that belong to the
01 variable, we delete all the lines that are part of the set of conditions that describe the rock bed where the
underground mining construction is located.
– step 3. We identify the column “variable code seg ment” and we go down vertically until we
reach the 02 variable lines. We delete all the line s matching to the columns deleted from the group of
columns corresponding to the 02 variable. We do the same for all the variables.
Remark
– the set of columns that correspond to the STOP va riable has one value. This value appears only
in that set of columns;
– the group of lines corresponding to the START var iable has one value. This value appears only
in that set of lines;
– the nodes corresponding to the START and STOP art ificial variables are compatible with every
node of the graph.
The matrix presented in appendix 2 was graphically converted into a graph and can be seen in
appendix 3.
The number of solutions generated by the graph in a ppendix 3 can be obtained using the relation:
N= ∏n
in
1=1 ⋅1⋅6⋅1⋅1⋅3⋅1⋅2⋅1⋅2⋅3⋅3⋅1=648 paths
where n i represents the number of nodes from the graph pres ented in appendix 3.
From the maximum number of solutions that can be ge nerated using the graph from appendix 3,
only a small number of them are admissible solution s.
In order to eliminate the impossible solutions, we use the analysis for the compatibility of the
nodes with the non-adjacent columns for every path generated by the matrix presented in appendix 2.

Identifying the optimal solution for the building o f the underground mining construction

Let us consider the problem of identifying the opti mal solution for the building of an underground
mining construction under a certain set of conditio ns.
In order to determine the best option to build an u nderground mining construction, given the set of
conditions, we must determine the values of the cos t per unit function for every node in the graph. Th ese
values are based on the given set of conditions and the values from every node.
In appendix 3, for every node that belongs to the c olumns of nodes that form the solutions graph,
you can find attached the values of the costs per u nit (for column 2 – 12 we have attached random valu es
for the costs per unit, depending on the given set of conditions).

9 We notice that for the column of nodes “12” (“STOP” ), the value of the 01 node is equal to the
value of the costs per unit, i.e. 0.
There are situations when, for a set of given condi tions, there is not compatibility between the
nodes of two adjoined columns. In order to build a graph, for the given conditions, we use a false nod e for
the column that has no compatibilities with the nod es of the adjoined column. This node will have the
value of the costs per unit function, 0. The false node will be compatible with all the nodes in the g raph.
Remark . The best solution for building an underground minin g construction can also be
determined using another type of evaluation of the execution options (time, productivity, production, etc.).
The values of the evaluation partial functions for every of the nodes of the columns that describe
the solutions matrix will be completed in the modul es of the section belonging to the solutions matrix and
the compatibilities matrix (see the matrix presente d in appendix 4).
As we have seen, two adjoined columns form a module in the connections matrix. Example: the
group of lines of variable 10 and the group of colu mns of variable 11 combine into a module composed o f
three lines and three columns (see figure 3).

Figure 4
a. The module presented in appendix 2 b. The module presented in appendix 4

We fill in the cells of the 10-11 module from appen dix 5 following the next steps:
– in the cells of the figure 3 module, with 0 value , we add ∞, see the module in figure 3.b;
– in the cells from figure 3.a., with 1 value, we a dd the values corresponding to the nodes from
column 11 of the graph presented in appendix 3, see figure 3.b.
Remark . If all the cells from the module presented in figur e 3.a had the 1 value, then in the 1101
column we would add only the value 7, in the column 1102 – the value 15, and in the column 1103 – the
value 8.
For the matrix in appendix 4, we add, horizontally, the following types of columns:
– a column to separate the compatibility matrix and the rest of the columns;
– a column for each variable;
– a column for “critical path value”.
And after line 1201, we will add, horizontally, a l ine which will contain the “value of the critical
path”.

The algorithm used to determine the optimal solutio n

Given the matrix presented in appendix 5 and the g raph in appendix 4, we can determine the
critical path. The critical path can have minimum a nd maximum values. These values are determined by
the functions used to evaluate the solutions genera ted by the type of matrix presented in appendix 5.
The algorithm used here is taken from the critical path analysis (CPA) and is combined with a test
of compatibility between the nodes of the columns n on-adjacent that describe an option of building a
mining construction.
The algorithm used to determine the best solution u sing an evaluation function consists of the
following situations:
– situation 1 . We identify the first column of nodes that belong s to the conditions matrix – in our
example 0101 (in the given case, the conditions mat rix is represented by one group of values and this group

10 contains one column). We move down on the 0101 colu mn until we reach the 0101 line. We add the 0
value in the cell resulted from the intersection of the 0101 line and the “critical path value” column . In the
cells of the columns 00 and 01 we add the path that has the 01, 01 values.
– situation 2. We identify the first group of columns that belong to the 02 solutions matrix. We
move down on column 0203 until we reach the 0101 li ne, where we see the 13 value. When we encounter
the 13 value, we add the value from the cell result ed from the intersection of the 0101 line and the “ critical
path value” column, 13+0=13. We follow the same pro cedure for all the columns of the 02 variable: 0204
column, 16+0=16. We add the result in the cell resu lted from the intersection of the “critical path va lue”
column and the 0204 line. We follow these steps unt il we go through all the columns from the first gro up
of columns of the solutions matrix.
While add the values in the “critical path value”, we add in the 0203 – 0208 lines, in the cell from
the 00 columns, the path 01 from the line 0101. For the 02 column, we add to these lines the 03, 04, 0 5, 06,
07, 08 codes.
Example: For the group of lines described by the 02 variable, we have the following nodes:
0203 – with the codes sequence: 01, 01, 03
0204 – with the codes sequence: 01, 01, 04
–
0208 – with the codes sequence: 01, 01, 08
– situation 3 . We move to the right of the first group of column s of the solutions matrix and we
identify the group of columns for the 03 variable. Then we move down on the first column of this group of
columns until we meet the 0 value. We add 13 to 0. We move down until we meet the 0204 line, where we
reach the ∞ value. We add 16 to the values we find on the same line corresponding to the last column. We
continue until we reach the last line that belong t o the 02 variable and we get the following set of v alues:
(13. ∞, 14, ∞, 14, ∞). From this set of values we select the minimum va lue, 13. We add this value in the
0302 cell, the “critical path value” column.
We check the compatibility of the nodes that form t he critical path. The critical path is given by
the values: 0001, 0101, 0203, to which we add the 0 302 value. This verification can be done following the
next steps:
– we move down on column 0302 and we check the comp atibility between node 0101 and node
0302. It results compatibility. In this situation w e fill in the critical path on line 0302, in the ar ea of the
added columns. We also add value 13 in the cell “03 – critical path value”.
These two stages are to be repeated for the 04, 05, 06, 07, 08, 09. Therefore, we get the values in
the corresponding lines and columns.
– situation 4. This refers to the general situation. We follow th e next steps:
– step 1. We move down on column 1001 until we rea ch line 0902. To value 15 we add
the 43 value, from the same line, in the “critical path value” column. We get value 58. We continue to
move down until we reach the 0903 line, until we re ach value 15. We add to it value 38, from the same line
in the last column. We get value 53. From the set o f values (58, 53), we select the minimum value, 53.
– step 2. We check the compatibilities of the exis ting non-adjacent nodes that belong to
the path corresponding to the minimum value, 53. Th is is the road given by the 0903 line. The line 090 3
contains of: 0001, 0101, 0203, 0302, 0406, 0502, 06 01, 0702, 0802, 0902, to which we add the code of t he
1001 column.
We repeat these two steps and for columns 1002, 100 3. We get the values from the columns that
have been added.
In the cell resulted from the intersection of colum n 10, that belongs to the group of added
columns, and the “critical path value” line, we add the minimum value that results from the set of val ues
from the group of lines of variable 10, i.e. (53, 5 0, 51), the minimum value is 50 and it corresponds to line
1002. The path described by the 1002 line is a mini mum path. The 50 value is added to the cell resulte d
from the intersection of the “critical path value” line and column 10.
We use the same path for the group of columns corre sponding 11, thus getting the values from the
group of lines that belong to variable 11. The mini mum path from the group of lines that belong to var iable
11 is given by line 1103, (0001, 0101, 0203, 0302, 0406, 0502, 0601, 0702, 0802, 0902, 1002, 1103) and it
has the 58 value.

11 When we reach the last column of nodes, column nr. 12, we use the same steps as in situation 3.
We get the set of values (60, 66, 58). We determine the minimum value, which is 58. This value
corresponds to the accepted path that belongs to li ne 1103. Both the accepted path (0001, 0101, 0203,
0302, 0406, 0502, 0601, 0702, 0802, 0902, 1002, 11 02) that belongs to line 1103, and the minimum
value 58 will be written down in line 1201. We will add the code of line 1201 to the path that has bee n
written down. This accepted path is the shortest ro ad described by the graph in appendix 4 and generat ed
by matrix 5. Its value is 58 monetary units.

CONCLUSIONS

The model with graph structure:
– allows us to synthesize the description of the e nvironmental conditions of a rock bed where an
underground mining construction is to be built;
– allows us to synthesize the elements of the solu tions used to build an underground mining
construction;
– connects the environmental conditions elements a nd the components of the solutions used to
build an underground mining construction;
– allows us to quickly update the data with the ne w pieces of information that appear in the
conditions group and in the “Categories reactions” group;
– allows us to determine the optimal solution to b uild an underground construction, given the
environmental conditions;
– needs a small amount of time to determine the op timal solution.
The model presented can be applied in a software a pplication.

References
[1] Burceacov, A.C., Proiectirovanie Șaht, Izdatelstva Nedra, Moskva, 1989 (in Russian).
[2] Dogaru, Metode noi în proiectare. Elemente de g rafic ă 3D, Editura Știin țific ă și Enciclopedic ă,
Bucure ști, 1988 (in Romanian).
[3] Dobri țoiu, N., The use of the graphical-analytical models to determine the methods and the
technologies of execution of the underground mining works when the set of natural conditions of diggin g
are known, Proc. of the International Conf. on Ener gy and Environment Technologies and Equipment
(EEETE '10), Univ. Politehnica, Bucharest, Romania, April 20-22, 2010. Published by WSEAS Press,
www.wseas.org
[4] Dobri țoiu, N., How to generate and evaluate the optimal m ethod for the capitalization of a
deposit of available mineral substances, 22 nd WORLD MINING CONGRESS 11-16 Sept. 2011 Istanbul.
[5] Dobri țoiu, N., Cercet ări în vederea structur ării și integr ării informa țiilor geologico-miniere și
topografice într-un sistem CPAC (Cercetarea și Proiectarea Asistate de Calculator) pentru z ăcământul de
cărbune Valea Jiului. Tez ă Doctorat, Universitatea din Petro șani, 1998 (in Romanian).
[6] Kagramanian, A., Modelirovanie i upravlenie gor norudnimi predpriiatiiami, Editura Nedra,
Moskva, 1989 (in Russian).
[7] Murgu, M., Evaluarea geologic ă și industrial ă a z ăcămintelor minerale, Editura Tehnic ă,
Bucure ști, 1986 (in Romanian).
[8] Nabradov, I. P., Principiile de construire a mo delelor economico- matematice ale minelor în
func țiune, Ugoli, nr.12/1984 (in Romanian).
[9] Popa, A. (coord.), Manualul inginerului de mine , vol. I, II, III, IV, V, Editura Tehnic ă, Bucure ști,
1984-1989 (in Romanian).
[10] Rozniacenko, S. S., Modelarea matematic ă în industria minier ă, Editura Nedra, Moscova, 1981
(in Romanian).
[11] Simionescu, A., Modelarea matematic ă în proiectarea minelor, Litografia I.M.P., Petro șani, 1980
(in Romanian).
[12] Țoi, C., Matematiceskie Osnovs Automatizirovannoi Si stems Proiectirovania Șaht, Alma-Ata,
1979 (in Russian).
[13] *** Indicatoarele de norme de deviz și pre țuri unitare de deviz pe articole de lucr ări pentru
construc ții miniere și montaje în subteran C.M. 1982 (in Romanian).

12 Annex no. 1

The graph conditions-solutions for generating techn ologies and technological variants for digging a ho rizontal mining working code of variabe Name of variable Name of element variable
code of elem.
vari. 01 02 03 04 05 06 07 08 09 10 11 12
01 02 03 04 05 01 02 03 04 05 06 07 08 01 02 01 02 03 04 05 06 01 02 03 04 05 06 07 01 02 01 02 03 04 05 01 02 01 02 03 01 02 03 01 02 03 01
00 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
01 Type of
roks and the values extra-hard rocks
01 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1
very hard rocks 02 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1
hard rocks 03 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1
semi-hard rocks 04 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1
soft rocks 05 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1
02 Method of
executing the profile of the mining workings and temporary suport seting with the values cutting the profile by means of a drifting machine and temporary support setting
01 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by means of a drifting machine without temporary support setting 02 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, hand load ing and temporary support setting 03 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, hand load ing without temporary support setting 04 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, pneumatic mechanical loading and temporary support setting 05 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, pneumatic mechanical loading without temporary support setti ng 06 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, electrica l mechanical loading and temporary support setting 07 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, electrica l mechanical loading without temporary support sett ing 08 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
03 Dismantling
temporar with dismantling temporary support 01 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
without dismantling temporary support 02 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
04 Setting
shutterings and skeleton ribs with the values setting fir squared timber shuttering for brick and concrete masonery
01 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
setting fir squared timber shuttering for brick and concrete masonery 02 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
setting steel shuttering for concrete work 03 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
setting panel shuttering for concrete work and bric k masonry 04 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
setting plank and fir board shuttering for concrete work and masonery 05 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1
without setting shutterings and skeleton ribs 06 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
05 Type of
permanent support with or withant shuttering with the values support by guniting
01 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1
wooden support 02 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
support by ring 03 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
support by precast concrete-block walling and shutt ering 04 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1
support by concrete cast in position and shuttering 05 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1
support by concrete cast in position, floor concret ing and shuttering 06 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1
support by precast concrete-block walling, floor in cluded and shuttering 07 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1
06 Dismantling
shutterinds … without dismantling shutterings and skeleton ribs 01 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1
with the dismantling of shuttering and skeleton rib s 02 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1
07 Type of
lagging used with the values cover board lagging
01 1 1 1 1 1 1 1 1 1 1 1 1
steel-mesh lagging 02 1 1 1 1 1 1 1 1 1 1 1 1
oak or fir plank lagging 03 1 1 1 1 1 1 1 1 1 1 1 1
steel lagging (IUMP type) 04 1 1 1 1 1 1 1 1 1 1 1 1
without lagging 05 1 1 1 0 1 1 1 1 1 1 1 1
08 Type of floor
with the values cover board lagging
01 1 1 1 1 1 1 1 1 1 1
steel-mesh lagging 02 1 1 1 1 1 1 1 1 1 1
09 Type of
dewatering channel with concrete channel
01 1 1 1 1 1 1 1
unsustenable channel 02 1 1 1 1 1 1 1
without channel 03 1 1 1 1 1 1 1
10 Type of
transport used in the values with mine locomotive
01 1 0 0 1
conveyor belt transportation 02 0 0 1 1
conveyor belt transportation and locomotive 03 0 1 0 1
11 Type of
mining workings furnishing mine railway and planking furnishing
01 1
mine railway and conveyor belt furnishing 02 1
belt conveyor furnishing 03 1

13 Annex no. 2

Reduced matrix Code of variables Name of variable Name of element variable "I"
cod elem. varia. i 00 01 02 03 04 05 06 07 08 09 10 11 12
01 01 03 04 05 06 07 08 02 06 01 02 03 01 02 05 02 02 03 01 02 03 01 02 03 01
00
01 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
01 Type of roks and
the values extra-hard rocks 01 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

02
Method of executing the profile of the mining workings and temporary suport seting with the values cutting the profile by drilling -blasting, hand loadi ng and temporary support
setting 03
1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling -blasting, hand loading without temporary support
setting 04 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling -blasting, pneuma tic mechanical loading and
temporary support setting 05 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling -blasting, pneumatic mechanical loading without
temporary support setting 06 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling -blasting, electrical mechanical loading and
temporary support setting 07 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1
cutting the profile by drilling-blasting, electrica l mechanical loading without
temporary support setting 08 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
03 Dismantling temporar without dismantling tempora ry support 02 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
04 Setting shutterings and skeleton ribs with the values without setting shutterings and skeleton ribs 06
1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1
05 Type of permanent support with
or withant shuttering with the values support by guniting 01 1 0 1 1 1 1 1 1 1 1 1 1 1
wooden support 02 1 1 1 1 1 1 1 1 1 1 1 1 1
support by ring 03 1 1 0 1 1 1 1 1 1 1 1 1 1
06 Dismantling shutterinds …
without dismantling shutterings and skeleton ribs 01 1 0 1 1 1 1 1 1 1 1 1 1
07 Type of lagging used with the
values steel-mesh lagging 02 1 1 1 1 1 1 1 1 1 1
without lagging 05 1 0 1 1 1 1 1 1 1 1
08 Type of floor with the values
steel-mesh lagging 02 1 1 1 1 1 1 1 1 1
09 Type of dewatering channel with unsustenable channel 02 1 1 1 1 1 1 1
without channel 03 1 1 1 1 1 1 1
10 Type of transport used in the values with mine locomotive 01 1 0 0 1
conveyor belt transportation 02 0 0 1 1
conveyor belt transportation and locomotive 03 0 1 0 1
11 Type of mining workings
furnishing mine railway and planking furnishing 01 1
mine railway and conveyor belt furnishing 02 1
belt conveyor furnishing 03 1

14 Annex no. 3

03
07 06 05 04
01 01
08 02 06 01
02
03 02
01
05 02 02
03
03 02 01
02 01 0
0
0
0
0
0
0
0
0
0
0
1
1

01
03 1
1
1
1
1
13. 0 0 2
1
1 0 1
∞ 0 5
0 1
1
1 7
0
∞ ∞

15 Annex no. 4 Code of variable
Code of elem.
variable . i
00 01 02 03 04 05 06 07 08 09 10 11 12
00 01 02 03 04 05 06 07 08 09 10 11 12
Critical path
value
01 01 03 04 05 06 07 08 02 06 01 02 03 01 02 05 02 02 03 01 02 03 01 02 03 01
00 01 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 01 0
01 01 13 16 14 15 14 13,5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 01 01 0

02 03
0 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 03 13
04 ∞∞ ∞∞ 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 04 16
05 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 01 01 05 14
06 ∞∞ ∞∞ 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 06 15
07 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 07 14
08 ∞∞ ∞∞ 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 08 13.5
03 02 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 03 02 13
04 06 20 15 18 1 1 0 1 1 1 1 1 1 1 1 1 1 01 01 03 02 06 13
05 01 0 0 1 1 1 1 1 1 1 1 1 1 1 01 01 03 02 06 01 33
02 0 1 1 1 1 1 1 1 1 1 1 1 1 01 01 03 02 06 02 28
03 0 1 0 1 1 1 1 1 1 1 1 1 1 01 01 03 02 06 03 31
06 01 10 ∞∞ ∞∞ 1 1 1 1 1 1 1 1 1 1 01 01 03 02 06 02 01 28
07 02 0 1 1 1 1 1 1 1 1 1 01 01 03 02 06 02 01 02 38
05 0 0 1 1 1 1 1 1 1 1 ∞∞ ∞∞
08 02 5 0 1 1 1 1 1 1 1 01 01 03 02 06 02 01 02 02 38
09 02 15 12 13 1 1 1 1 01 01 03 02 06 02 01 02 02 02 43
03 15 12 13 1 1 1 1 01 01 03 02 06 02 01 02 02 03 38
10 01 7 ∞∞ ∞∞ ∞∞ ∞∞ 1 01 01 03 02 06 02 01 02 02 03 01 53
02 ∞∞ ∞∞ ∞∞ ∞∞ 8 1 01 01 03 02 06 02 01 02 02 03 02 50
03 ∞∞ ∞∞ 15 ∞∞ ∞∞ 1 01 01 03 02 06 02 01 02 02 03 03 51
11 01 0 01 01 03 02 06 02 01 02 02 03 01 01 60
02 0 01 01 03 02 06 02 01 02 02 03 03 02 66
03 0 01 01 03 02 06 02 01 02 02 03 02 03 58
12 01 01 01 03 02 06 02 01 02 02 03 02 03 01 58
Value critical path 0 0 13 13 13 28 28 38 38 38 50 58 58