Reference no: EM133776461

Underground Mining - Pillar Supported Mining Methods

Question: The following table is the summary of a coal basin pillar data in Australia, corresponding to the 27 cases of pillar collapse in the original pillar strength study.

Table 1 - Database for failed pillars

wb (m)    h(m)    Pillar Load, Ld(MPa)       
3.4    2.6    6.4       
3.7    3.0    7.2       
4.0    4.6    5.0       
5.2    5.5    6.1       
3.7    2.1    6.8       
6.1    4.9    5.6       
4.6    2.4    6.5       
6.1    5.5    5.7       
4.6    3.7    5.4       
5.2    3.7    6.6       
6.1    2.4    7.9       
3.4    1.5    10.7       
7.2    4.9    8.1       
5.2    3.7    7.2       
12.8    5.5    7.5       
12.2    4.9    8.5       
4.7    3.5    9.1       
15.8    5.5    8.7       
15.8    5.5    8.3       
4.9    1.4    9.6       
6.1    4.6    6.1       
6.1    3.0    7.7       
6.1    4.0    7.3       
4.3    3.0    6.4       
9.8    3.7    7.8       
15.8    5.5    7.6       
6.1    2.0    8.7

The aim of this assignment is to provide an opportunity to gain an insight into development of a model for the prediction of pillar strength.

The original database contains information regarding both un-failed and failed pillared areas. For simplicity, only the failed or collapsed cases are considered in this assignment (Refer to Table 1). While the omission of the stable cases reduced the reliability of the obtained model, the principles of the derivation do not change.

It will be assumed that the pillar strength is describable by the following formula:

σ_p = K.(R+(1-R).w_P/h)

Where K and R are the strength of a unit cube of coal (MP_a) and a dimensionless parameter, respectively. Moreover, wb and h denote pillar width (m) and working height (m).

The tributary area load over uniform pillar arrays will be defined by:

σ_load = γ.H.(w_P+wr/w_p)²

γ → the unit rock pressure wr → the room width (m) wp → the pillar width (m)
H → the depth of cover (m)

Then the safety factor (SF) is defined as...

SF =  Pillar_Strength/Pillar_Load = σ_p/σ_load

Drive the non-linear equations to solve the numerical values of the parameters K, R, and σ, based on the class discussion on "Pillar supported Mining Methods".

Define the range for K values where the solution is located. Then compute the numerical value of parameter K from the equation in part "a" based on the database of failed cases by considering when R=0.64 and σ = 0.25...You must use Excel for this part. You are not allowed to use Goal Seek function. Otherwise, your answer will not be accepted.

Calculate the safety factor for all failed cases with the new pillar strength equation.

Construct and plot histogram of the values for safety factors from part c within the range of 0-2 with increment of 0.1 as bins.

published unit outlines.

Note 2 - You are not allowed work together for this assignment. Any similarities between submissions may result in further evaluation.
Note 3 - You must also submit your Excel file that contains your solution addition to PDF submission.