INTRODUCTION
Approximately 90% of all coal production by underground mines in Iran is derived
directly from longwall mining method in Kerman, Tabas and Albors coal mines.
In the mines, OSD usually varies from 15 to 30%, depending upon the mining,
geological and technical conditions. The amount of OSD substantially reduces
the efficiency of the mines. Also, OSD lowers the quality of the run of mine
coal, raises the cost of concentration, milling, cooking processing, transport
and handling, especially when longdistance hauls are involved (Popov,
1971). Saeedi et al. (2008) reported when
OSD increases 1% at Tabas coal mine, net profit and the efficiency of coal washing
plant decreases by 0.75% and 1.17 $ t^{1}, respectively.
To date, attempts have been rare for a comprehensive understanding of the formation
state and the factors influencing OSD in the longwall mining method. The earlier
studies have only been done by investigators for some of mining methods such
as sublevel stopping. In one of the estimation methods, the content of the useful
constituent in the extracted coal, the useful constituent in the solid coal
in place and the useful constituent in the rock contaminating coal were related
to dilution (Popov, 1971). The main advocate of this idea
was Agoshkov who established a relationship between mentioned parameters and
dilution. Agoshkov proposed that the dilution coal is largely dependent upon
the content of coal in the rocks contaminating it. Therefore high dilution figures
do not always mean low extraction efficiency. Another similar study was presented
by Nazarchik in mining thin ore bodies. Nazarchik investigations is considers
on width of the stope area, mean width of the vein, volume weight of the host
rock, volume weight of the vein matter, content of metal in the vein matter
and host rocks (Popov, 1971). The third dilution approach
proposed by Pakalnis (1986) based on case histories from
the Ruttan mine. This method is not used by industry. However, it is an early
attempt to quantify dilution. Clark developed a new dilution estimation method
based on the format of the modified stability graph and expressed the stope
stability as a dilution estimate (Clark, 1998). Another
study was based on fieldcollected data at Stillwater mine in Montana (Annels,
1996). In this method, the dilution is estimated by the use of a power curve
equation based on studies of the actual dilution associated with different ore
thicknesses. According to the investigations performed by Annels
(1996), the dilution increased when the thicknesses of seam decreased.
Some researchers used numerical modeling techniques to investigate parameters
influencing dilution in open stope method. Suorineni et
al. (1999) investigated faultrelated dilution in open stop mining method
where dominant geological weaknesses or faults exist by using Phase 2. They
proposed that the presence of a fault near an open stope can increase the size
of the distressed zone and dilution around the stope relative to conditions
without a fault.
Another numerical modeling method was based on evaluation stress and hanging
wall geometry on open stope stability and dilution by using two boundary element
method programs (Examine 3D and Examine 2D) (Wang, 2004).
According to the investigations performed by Wang, with an increase in the radius
factor and the stress ratio, dilution increases.
The third numerical approach proposed by Henning and Mitri
(2007). In the method, a series of threedimensional numerical models are
developed and analyzed to examine the effect of mining depth, in situ
stress as well as stope geometry and orientation on ore dilution.
In assessing OSD in longwall mining method, it is necessary to understand factors causing and the main sources of OSD. Therefore, in this study, the main sources and the relative importance of factors influencing OSD was investigated base on the data obtained at coal mines, in Iran. To better understand the how factors increase the OSD, a statistical analysis was conducted using SPSS (Statistics Package for Social Sciences).
THE SOURCES OF OSD IN THE LONGWALL MINING
In longwall mining method, which is the preferred method of mining a flatlying
stratiform orebody when a high area extraction ratio is required, OSD is unavoidable
with extracting the full seam thickness. Especially, when a fully mechanized
face is used for extraction of coal. In this method, the average of OSD is 1025%.
As a first step in evaluation OSD, the sources of OSD must be determined. In
the longwall mining method, the sources of OSD may be divided into three main
classes; primary, secondary and tertiary dilution (Noppe,
2003). Primary dilution includes cutting of the stone floor or roof by the
longwall shearer machine. Secondary dilution is slabbing or breakup of the
roof or floor during mining and tramming and the subsequent loading of this
material together with the coal (rather than being stowed in back areas). Tertiary
dilution includes waste material loaded with the coal during sectioncleaning
operations. Parameters influencing OSD categorization differs among the above
main sources. Figure 1 presents the general and detailed factors
influencing OSD for each source. These factors can be treated as independent
and dependent variables.
Basically, the most significant contributing factors can identified as independent
variables, excluding the human element, such as geologic anomalies, bottom and
roof quality, hardness of seam, depth of seam, height of seam, amount of water
present and dip of seam. To some extent these variables are interrelated.

Fig. 1: 
The main sources of OSD and factors influencing OSD for each
source in longwall coal mines 

Fig. 2: 
Depth of Removing Floor (DRF) by shearer on a soft floor in
longwall 
For
example, roof quality is partially a function of the depth of the seam and floor
quality may be affected by the presence of water. However, each can also be a factor independent of any other.
Primary OSD: The primary OSD plays a significant role among the sources of OSD. It often occurs due to cutting of the stone floor or roof (accidental or planned) by the longwall shearer machine or by the drilling and blasting operations in hard coals. The type of OSD takes place with cutting the coal at the same time. The following seem to be detailed description of factors influencing primary OSD.
Floor quality: While all mining systems operate at optimum efficiency
on firm bottoms, the condition of the floor is most critical for longwall. Because
in massive rock that required heavyduty support and shearer, the bearing capacity
of a weak floor would not be adequate. Consequently, if the floor is soft the
support system and longwall shearer machine may sink into the floor under the
roof pressure. It will not only reduce the supporting capacity of the powered
supports, but will also be removed some material from the floor by shearer.
Figure 2 shows the Depth of Removing Floor (DRF) by shearer
on a soft floor in longwall mining method.
Many factors, such as bedding and foliation, rock joint orientation, rock joint
density, rock type, strength and amount of water pressure can significantly
affect floor quality and hence the primary OSD. A classification of floor quality
proposed by Stefanco (1983) is shown in Table
1.
For the calculation of DRF in soft and plastic rocks, the bearing capacity
of floor and external loadings on the powered supports or support capacity should
be calculated. Since, the material properties of this type of rock are similar
to soil, the theories from the soil mechanics can be applied (Peng
and Chiang, 1984). The most widely used one is the terzaghi’s bearing
capacity equation which when applied to the mine floor for rectangular base
is:
where, σ_{b} is the bearing capacity of floor; C is cohesion of
the floor rock; γ is the weight per unit volume of the soil; B and L are
the width and length of the footing; N_{c}, N_{q} and N_{r}
are bearing capacity factors; r is the uniform loading on both sides of the
base; γ_{1} and Z are the weight per unit volume and thickness
of the strong stratum, respectively. N_{c}, N_{q} and N_{r}
are the bearing capacity factor, γ_{2} is the weight per unit volume
of the weak stratum and η_{0} is stress distribution coefficient.
For determination of support capacity, based on the characteristics of the
roof, a statistical model for describing the interaction between the roof strata
and support has been developed (Peng, 1986). Coal mine
ground control:
where, Δq is the effective increment of load density in t ft^{2},
i.e.,
where, p_{s} is the setting load in tons; Δp is the load increment
from support setting to final load immediately before the support is released
for advance in tons; η is the support efficiency; A is the canopy area
of the support in ft^{2} and a and c are constants related to roof conditions.
Based on this model, the following formulas can be used for calculating the
setting load, load increment and the yield load P_{y}:
The minimum bearing capacity of floor (σ_{b}) required for the
condition in which the basesinking problems will not occur is:
Therefore:
If the bearing capacity of floor is less than the total pressure on canopy,
the support system and longwall shearer machine will sink into the floor under
the roof pressure. In this case, the basesinking depth or DRF is a function
of the total pressure on canopy that can be determined by stressstrain relationships
for materials with plasticity behavior. Therefore:
where, ε is normal strain. Equation 8 means that DRF
is dependent on material behavior, type of floor material and the total pressure
on canopy.
Geologic anomalies: Geologic anomalies are often a major cause of primary OSD in the form of coalbed displacement in underground coal mines. Three main subjects are discussed below in terms of the influence of geological factors on OSD.
When a section of a coalbed becomes constricted by reason of a rising bottom
and a lowering roof, as shown in Fig. 3a, the terms pinch,
squeeze or swell are used to describe this condition (Stefanco,
1983). The underlying stratum or bottom of a coalbed is rarely a smooth
horizontal surface but usually has many undulations or rolls that very considerably
in both horizontal and vertical extent. If the rolls become exaggerated the
term horseback, as shown in Fig. 3b, is used to describe
this condition. The folding of coalbeds results from movements of the earth’s
crust. Folds, as shown in Fig. 3c, are strata that have been
thrown into more or less curved forms.



Fig. 3: 
OSD as resulting from pinch (a) horseback, (b) folding and
(c) in a coalbed (Stefanco, 1983) 

Fig. 4: 
Roof fall as a result of fault in the propfree front of the
face in longwall 
Authorities classify these structural
features as resulting from pressure applied by crustal movement to the bed during
formation, or by strata adjoining the bed. However, in these mentioned cases, with cutting and loading the coal, a significant
amount of the immediate floor and roof strata will be extracted and consequently
OSD would also be increased.
Seam height: In longwall mining method, the seam height H_{c}
should first be considered for properly selecting the dimensions of the shearer,
which includes the diameter of the cutting drum D, body height L_{a}
, ranging arm length B, body depth B and swing angle α of the ranging arm
(Hartman, 1992). The relationship among those parameters
can be expressed by:
If , α_{1}≤α≤α_{2}. Thus the minimum seam
height H_{cm} is:
The seam height should not be less than H_{cm}. Otherwise, the amount
of stone roof and floor should be cut by the shearer to gain height for operator
comfort and a mining area of minimal breadth. Consequently, the primary OSD
increases.
Secondary OSD: The type of OSD includes slabbing or breakup of the roof or floor during mining and the subsequent loading of this material together with the coal. This form of dilution is very common in weak roof and weak floor conditions.
Faulting strata: A fault is a major geologic structure in underground coal mines. In a fault area, as shown in Fig. 4, the surrounding strata are generally brocken; therefore, when the face through a fault, the roof falls in the propfree front can be a major cause of OSD. Many factors, such as the angle between a fault and the face, fault friction angle and fault position are often the most important factors influencing the severity of faultrelated sloughage in longwall.
Roof quality: The major reason for local roof fall at the longwall face is the lack of efficient means for supporting the exposed immediate roof between the faceline and the tip of the canopy and subsequently the failure to prevent the broken rocks from falling into the working space and increasing OSD. Amount of the roof fall depend on bedding and foliation, joint orientation, joint density, rock type, strength and water pressure.
Roof fall in propfree front of the face can be determined by roof fall sensitivity
or roof fallibility. Roof fall sensitivity is a measure of the extent of roof
fall at the face area (Peng and Chiang, 1984). It is defined
as:
where, A is the summation of area of roof fall cavities and A_{t} is
the total area surveyed. A should be measured at the roofline and only those
roof falls with height greater than 20 inch are counted.
However, roof fall cavities are most irregular in shape. They not only take
a longer time to map, but very often can’t be done accurately. For account
this problem, roof fall sensitivity can be represented by the percentage of
roof fall cavity width to the total unsupported roof span, that is:
where, F_{v}, a, b, c and d are roof fallibility, distance from edge
of the canopy to the first roof contact point on the canopy, nominal unsupported
roof span from front edge of the canopy, depth of face sloughing and width of
roof fall cavity, respectively. Table 2 shows a roof classification
scheme based on roof fallibility.
Based on roof fallibility, the following formula can be used for calculating
the percentage of OSD cause by roof falls:
where, h and H are the average cavities depth and coal seam height, respectively.
Underground investigation have shown that there are four types of open roof fractures in longwall faces: R_{1} is parallel to bedding, R_{2} is perpendicular to bedding, R_{3} is dipping toward the faceline and R_{4} is dipping toward the gob (Fig. 5). If R_{1} and R_{2} intersect and form a high wedge shaped cavity, it signifies a loose roof. Each type should be recorded and expressed in terms of the average cavities depth.
Exposed roof area: The exposed roof area in front of the face varies,
depending on the cutting depth and the length of shearer, as shown in Fig.
6. The shape factor is frequently used to quantify the exposed roof geometry.
The shape factor is another word for Hydraulic Radius (HR). The HR is calculated
by dividing the area of exposed roof by the perimeter of that roof. For a rectangular
shaped surface, the HR can be calculated by Eq. 14 (Laubscher,
1977):
where, HR, L and S are the hydraulic radius of the exposed roof area, the length
of shearer (length of the exposed roof area) and cutting depth (width of the
exposed roof area), respectively.
This is due to the fact that under constant conditions, the local roof fall
and consequently the OSD increase with the hydraulic radius and roof exposure
time.

Fig. 6: 
The exposed roof geometry in propfree front of the face (Whittaker,
1974) 
Stress environment: When an underground opening is excavated into a
stressed rockmass, stresses near the new opening are disrupted and redistributed.
Figure 7a shows an interpretation of the distribution of vertical
stress, σ_{zz}, around a single longwall face. The vertical stress
is zero at the face and the rib side (Brady and Brown, 2004).
Therefore, a relaxation zone with low stress exists in propfree front the face.
In the relaxation zone, the absence of significant clamping stresses is often
cited as one of the main reasons for the instability and fall of roof and consequently,
the OSD occur in this relaxation zone (Fig. 7b) (Henning
and Mitri, 2007).
Dip of seam: The influence of hangingwall dip on the roof fall can
be significant. With steeply dipping seams, vertical stresses are shed around
the coalbed. As the dip of the hangingwall becomes shallower, vertical stresses
are shed onto the coalbed, leading to larger displacements and roof falls (Henning
and Mitri, 2007). Therefore, severity of OSD increases as seam dip angle
became increasingly shallow.

Fig. 7: 
Vertical stress redistribution in the plane of the seam around
a longwall coal face (a) and OSD area in front of the face (b) (Richard
et al., 1998) 
Drilling and blasting: When hardness of the coal is high, the coal is
barely capable of being cut with shearer. In this case, it must be cut using
drilling and blasting operations. Drilling and blasting of the coal can significantly
damage the roof falls and overbreak in front of the face. So, some degree of
the OSD can be attributed to blast vibrations and damage.
Many factors, such as drillhole size, drillhole spacing and burden, charging geometry and the drillhole accuracy are often the most important factors influencing the severity of roof falls and overbreaks.
Tertiary OSD: Tertiary OSD includes waste material loaded as a result
of gob area with the coal during sectioncleaning operation by workers. The
type of OSD can be reduced by practices such as management controls, education
and training. Management controls induces type of contract, incentive plans,
management initiatives and coal quality controls. Education and training induces
awareness of dilution impacts and dilution impacts on company profitability
(Chugh and Moharana, 2005).
Statistical analysis: A statistical analysis was conducted to evaluate
the relationship between OSD and some of the effective parameters mentioned
above. The SPSS (Statistics Package for Social Sciences) for windows software
package was used for the statistical analysis. Table 3 and
4 shows the parameters included in the statistical analysis.
Field data of these tables was collected from coal mines in Iran.
Multiple parameter regression analysis was carried out by the parameters shown
in Table 4. The OSD is defined as dependent variable and the
remaining parameters are referred to as independent variables in the study.
The general additive multiple parameter regression model express as the following
(Devore, 1995):
where, Y, β, k, x and ε are the dependent variable, coefficient,
the number of independent variables, the independent variables and the random
error term, respectively. By replacing the dependent variable Y in Eq.
15 by OSD and the independent variables x_{i} by X_{i},
we have the multiple parameter regression model given as Eq.
16:
where, OSD is outofseam dilution and X_{1}, X_{2}, X_{3},
X_{4}, X_{5}, X_{6}, X_{7}, X_{8} and_{
}X_{9} are variation in seam thickness (m), seam thickness (m),
dip of seam (degree), cutting methods (pick, shearer or blasting), roof quality,
floor quality, depth of seam (m), hydraulic radius (m^{2}) and type
of contract, respectively. X_{4}, X_{5}, X_{6} and X_{9}
are string variables. Table 5 shows string variables and its
imported value labels in statistical analysis.
The field data were imported into the statistical analysis package SPSS and
a multiple parameter regression was conducted. The correlations between parameters
and the multiple parameter regression quantitative coefficients were obtained.
Table 6 presents the correlation matrix and the calculated
coefficients for the parameters involved in the analysis. The sign of the correlation
coefficient indicates the direction of the relationship (positive or negative).
The absolute value of the correlation coefficient indicates the strength, with
larger absolute values indicating stronger relationships. Table
6 shows that X_{7} has the strongest correlation with OSD (with
a correlation coefficient of 0.998) and X_{4} has the weakest correlation
with OSD (with a correlation coefficient of 0.273) among the independent variables.
The significance of each correlation coefficient is also displayed in the correlation
table.
Table 3: 
The collected data for statistical analysis from Iran coal
mines 

Table 4: 
Parameters included in the analysis and descriptive statistics 

*X_{4}, *X_{5}, *X_{6} and *X_{9}
are string variables 
Table 5: 
String variables and its imported value labels in statistical
analysis 

The significance (or p value) represents the low degree of a certain result.
A significance less than 0.05 (p<0.05) means that there is less than a 5%
chance that this relationship occurred by chance. If the significance level
is very small (less than 0.05) then the correlation is significant and the two
variables are linearly related. If the significance level is relatively
large (for example, 0.50) then the correlation is not significant and the two
variables are not linearly related.
Table 6: 
Correlations and significant between parameters 

**Correlation is significant at the 0.01 level (2tailed);
*Correlation is significant at the 0.05 level (2tailed) 
Table 7: 
Multiple parameter regression coefficients 

The strength of the correlations for the analyzed independent variables to
the dependent variable (OSD) are sequenced from strongest to the weakest as:
The unstandardized coefficients in Table 3 are the coefficients
β_{i} for Eq. 16. The independent variables in
Table 6 are often measured in different units. It is difficult
to compare the unstandardized coefficients (β’s) to each other. The
standardized coefficients or betas are an attempt to make the regression coefficients
more comparable. The tstatistic helps determine the relative importance of
each variable in the model. The larger values are the more important
the parameters in the model. The tstatistics in Table
7 show that X_{7}, X_{3}, X_{5} and X_{1}
are the most important influence factors for OSD, compared to the other contributing
factors. Type of contract X_{9} has the smallest tvalue compared to
the other factors listed. This means that type of contract is the least
important influence factor among the independent variables. The tstatistic
and its significance value are used to test the null hypothesis that the regression
coefficient is zero. With regard to the multiple parameter regression results,
the relationship between independent variables and OSD can be established as:

Fig. 8: 
Histogram of regression standardized residual 
Table 8: 
Actual and predicted OSD resulted from the proposed model
for Parvadeh coal mine (in Tabas) 

As defined in Eq. 12, ε is a random variable and usually
is referred to as the random deviation or random error term. When ε is
normally distributed, the ε term vanishes. This can be tested by plotting
a histogram of the data with a normal curve superimposed to see if the data
appear to be normally distributed. Figure 8 shows the histogram
of regression standardized residual. It shows a reasonable fit to a normal distribution,
so Eq. 18 becomes:
The statistical significance and validity of the presently derived model was
checked by comparison of actual and predicted OSD. For this comparison, field
data were collected from Parvadeh (in Tabas) coal mine as shown in Table
8. In Table 8, there is insignificant discrepancy between
the actual and predicted OSD. Therefore, the model presented can be adopted
to develop mine specific design tools for the prediction of OSD associated with
a proposed mine design.
DISCUSSION
The assessment of earlier methods shows that the OSD have only been determined by the sampling and essaying from the coal layer and mined coal in longwall mining method. Since, these methods do not adequately or specifically consider factors affecting on OSD, prediction errors may be expected when using them. Therefore, in this study, parametric statistical studies were undertaken to examine the impact of a variety of factors on OSD in the propfree front of the longwall face. Based on the collection and analysis of a large number of case histories from fieldcollected data, a relationship between OSD and contributing factors was derived from the statistical analysis. The statistical analysis results showed that each parameter included in the analysis had a certain contribution to OSD. Hence, this method is a powerful tool for OSD estimation and prediction, without any sampling and essaying process, compared to the previous methods.
CONCLUSION
The research presents the results of a study of the factors causing OSD or dilution in longwall coal mines. The main sources and factors influencing OSD for each source with a detailed description have been presented to quantify OSD. A statistical analysis was conducted to evaluate the relationship between OSD and some of its effective parameters such as variation in seam thickness, seam thickness, dip of seam, cutting methods, roof quality, floor quality and depth of seam, hydraulic radius and type of contract. This analysis shows that depth of seam, dip of seam, roof quality and variation in seam thickness are the most important influence factors and type of contract is the least important influence factor for OSD. The validity of the presented model was assessed by comparison of actual and predicted OSD in Parvadeh coal mine and may be utilized for similar mines. The results clearly show that the OSD prediction error for this coal mine data assessed using the presented model is very low.
ACKNOWLEDGMENTS
Author would like to thank the Tabas Mines and Kerman Mines who allowed me to collect data and provided the with valuable assistance for the study. Special thanks go to Mr. Moqadam for their assistance with my field work.