
I calculate a value of mi to be around 100 yet RocData limits mi to be between 1 and 50. Why?
Your values of mi of around 100 are almost certainly associated with too small a range of confining stresses in your triaxial testing. This is a problem that I come across very frequently. The original definition of mi is based on triaxial tests up to one half of the uniaxial compressive strength of the intact material. The following quote is from Hoek and Brown, 1997, "Practical estimates of rock mass strength" published in the Int. J. Rock. Mech. Min Sci.
"Note that the range of minor principal stress (sig3) values over which these tests are carried out is critical in determining reliable values for the two constants. In deriving the original values of sigci and mi, Hoek and Brown used a range of 0 < sig3 < 0.5*sigci and, in order to be consistent, it is essential that the same range be used in any laboratory triaxial tests on intact rock specimens."
For example, if you analyze the following data set for Carrara marble using RocData (with Linear Regression curve fitting) you obtain sigci = 82.28 and mi = 8.68.
1.72
3.45
5.17
6.9
6.9
10.34
10.34
13.79
13.79
17.24
17.24
20.69
27.59
34.48
34.48
78.61
89.33
99.81
123.79
125.23
125.65
138.37
137.38
146.6
150.77
160.76
173.79
187.9
205.99
213.58
Note that the maximum value of sig3 is too low in this case  it should be about 40 MPa but this is a real data set and it is all that I have.
On the other hand, if I analyze only the first 5 data points, up to sig3 = 6.9 MPa, I obtain sigci = 48.92 and mi = 32.13. If this data set was for hard rock I could easily get mi values of over 100 by limiting the range of sig3 values.
All the values quoted in the various HoekBrown papers are derived from triaxial test data with the correct range of sig3 values  this was one of the criteria that we set in determining whether or not the data were acceptable. The typical range of mi values is from about 5, for soft ductile rocks, to 35 for very hard brittle rocks. Hence we set the range of 1 < mi < 50 in RocData to cover this range.

RocLab (and RocData versions 3 and 4) uses the LevenbergMarquardt method, a robust algorithm that has become the standard for nonlinear regression. The method is very reliable in practice, and has the ability to converge promptly from a wider range of initial guesses than other typical methods.
RocLab Versions 1.000 to 1.005 used a linearized form of the HoekBrown equation that had the effect of reducing the LevenbergMarquardt method to linear regression. This was modified in Version 1.006 in order to take full advantage of the power of the LevenbergMarquardt method.
We looked closely at the varying results provided by different regression algorithms. We judged the quality of the results using the "Sum Square of Errors" (SSE) – the sum of the square of the vertical distances of the given data points from the fitted curve. (In RocLab Version 1.006 and up this quantity is referred to as “Residuals”; in some statistical literature it is known as the sumofsquares.) The analysis indicated the following:
i. The linear regression results (sigci=50.7 MPa and mi=17.8) given by RocData Version 2, the published spreadsheet of Hoek and Brown, and RocLab Versions 1.000 to 1.005, gave an SSE value of 1490.98
ii. The simplex method in RocData 2.0 that gave sigci=20.47 MPa and mi=55.46 had an SSE of 663.539
iii. RocLab Version 1.007 results (sigci=20.998 MPa and mi=49.9) had an SSE of 702.858
These SSEs tell us that RocData 2.0 and RocLab 1.007 found curves that better fit the data than the linear regression approaches. It may seem that RocLab 1.007 gave slightly worse results than the simplex method in RocData 2.0, but this is not so.
RocLab 1.007 allows mi only to range between 1 and 50. When we remove the upper limit, the program gives sigci=20.487, mi=55.44 and SSE=663.539, nearly identical to the results of the simplex method.
RocLab 1.007 caps the maximum value of mi at 50 because, according to Dr. Evert Hoek, mi values higher than this threshold indicate too small a range of confining stresses in triaxial testing. The following quote is from the paper “Practical Estimates of Rock Mass Strength” by Hoek and Brown (International Journal of Rock Mechanics and Mining Sciences, Vol. 34, No. 8, pp. 11651186, 1997):
"Note that the range of minor principal stress (sig3) values over which these tests are carried out is critical in determining reliable values for the two constants. In deriving the original values of sigci and mi, Hoek and Brown used a range of 0 < sig3 < 0.5*sigci and, in order to be consistent, it is essential that the same range be used in any laboratory triaxial tests on intact rock specimens."