Engineering Rock Mechanics

164 Anisotropy and inhomogeneity

together with the appropriate theoretical relation, are given below.
The first row in each table is the load measured in the new test.
The second row in each table is the tensile strength of the rock as
measured by a standard method.
Classify each configuration in terms of accuracy and precision,
and hence recommend which configuration(s) should be retained
for further development.
Configuration I: strength = 0.049 x load
Load (N) 67.3 76.8 83.9 104.8 153.7 168.9 191.2 194.7 237.5 258.3
Strength(MPa) 4.2 4.8 5.2 6.5 9.6 10.6 11.7 12.2 14.6 16.1
Configuration 2 strength = 0.066 x load
Load (N)
Strength(MPa) 4.7 2.4 3.3 7.4 6.7 10.9 6.3 7.8 8.2 7.6
Configuration 3: strength = 0.074 x load
Load (N) 83.5 95.0 111.7 151.6 170.0 189.5 190.2 193.9 201.1 205.3
Strength(MPa) 6.1 7.1 8.3 11.4 12.7 13.8 14.3 14.3 14.9 15.3
Configuration 4 strength = 0.094 x load
Load (N) 68.9 105.3 106.2 120.1 148.5 164.8 197.4 220.5 232.8 236.9
Strength (MPa) 5.5 10.1 10.5 11.6 14.4 12.3 20.1 22.9 20.9 21.8

68.9 105.3 106.2 120.1 148.5 164.8 197.4 220.5 232.8 236.9

A10.4 In each of the test configurations, we should take tensile strength

(as listed in the second row of each table) as the independent variable,

because the load is being measured in the index test and we fit a line

of the form 'load = m x strength' to the data. If the fitted curve has a

different gradient to the theoretical relation, then the test is inaccurate:

there is bias in the results. If the fitted curve has a low coefficient of

determination, r2, there will be considerable spread about the fitted

curve, and so the test is imprecise. Thus, to classify each configuration a

straight line is fitted to the data, the slope of the line is compared to the

theoretical relation to determine the accuracy and the spread of results is

studied to determine the precision.

The test results are shown graphically below. In these plots the dots

represent the test results and the lines represent the theoretical relations.

Conjiguration 1: strength = 0.049 x load, or load = 20.41 x strength.

The best fit gives Ioad = 16.10 x strength and r2 = 0.999. The significant

difference between the gradients indicates that the test is inaccurate

whereas the large value of r2 indicates that it is precise.

The best fit gives load = 23.37 x strength and r2 = 0.221. The test is

inaccurate and imprecise.

The best fit gives loud = 13.47 x strength and r2 = 0.999. The test is

accurate and precise.

The best fit gives load = 10.54 x strength and r2 = 0.930. The test is

accurate but not very precise.

Configuration 3 is the best because it is accurate and precise. Configura-

tion 1 is precise, but its inaccuracy means that an adjustment will have to

Configuration 2: strength = 0.066 x load, or load = 15.15 x strength.

CoEfiguration 3: strength = 0.074 x load, or load = 23.51 x sfrength.

Configuration 4: strength = 0.094 x load, or load = 10.64 x strength.