UDEC Modeling of an Underground Opening in Rock Masses of Varying Quality 

Tye J. Lasich, Undergraduate Student 

Mary M. MacLaughlin, Associate Professor 

Department of Geological Engineering, Montana Tech of The University of Montana, Butte, MT

Thomas M. Brady, NIOSH Spokane Research Laboratory, Spokane, WA 

Abstract 

This project involved modeling rock masses with varying Rock Mass Rating (RMR) values to 

determine the degree of instability that develops around an underground opening as a function of 

RMR. The modeling was performed using Itasca’s UDEC distinct element software, which 

allows explicit modeling of blocks of rock and how they interact with each other. The analyses 

included three different orientations of the joint sets, four different joint spacings and three 

different values of joint strength, which combine for a total of 36 different combinations of 

model parameters. Two different modes of behavior were observed: local failure of area 

immediately surrounding the roof and sides of the opening, and deep-seated failure extending a 

large distance beyond the opening. Quantification of the size of the unstable area that developed 

provides numerical validation of empirical guidelines used in design of ground support and 

instrumented monitoring systems. 

Introduction 

The development of the discrete element methods of numerical modeling have greatly increased 

our ability to model the behavior of discontinuous materials like blocky rock. One way to use 

these tools is to perform parametric studies to facilitate growth of our understanding of the 

behavior of rock masses. Another use is to provide validation for empirical design guidelines. 

This study made use of one particular discrete element method, the distinct element method in 

the form of Itasca’s UDEC software (Itasca 2000), for both of these purposes. 

An underground opening in a shallow rock mass was modeled to determine the difference in 

behavior expected when the Rock Mass Rating (RMR) classification of the rock mass varies. 

Rock mass classifications such as the RMR (Bieniawski, 1974) were developed to facilitate fast 

and inexpensive characterization of rock masses. The RMR system provides a rating that 

generally ranges from close to 0 for the worst possible situations, to 100 for perfect rock. Design 

of ground support in underground mines is often based on RMR ratings of the rock. 

The two thrusts of this study were to 1) document qualitative correlation between RMR ratings 

and behavior of the rock mass, and 2) investigate the dimensions of the unstable zone that 

develops around the excavation. Researchers at the University of British Columbia are 

performing similar studies to investigate these issues, as well. 
Model Description 

Dimensions and Loads 

The model was specified using a homogenous material with dimensions 126 m long by 84 m tall. 

All of the boundaries were fixed, and since the model was intended to simulate an excavation at 

shallow depth, only gravity load was applied rather than a combination of gravity and in situ 

stress. In order to minimize computer run time, the blocks within the model were specified to be 

rigid rather than deformable. The excavated drift was rectangular in shape, with length 6 m and 

height 4 m. 

Parameters Investigated 

There were three parameters of interest in this investigation: friction angle, joint spacing, and 

joint orientation. Table 1 shows parameter values that were varied in the suite of models. 

Table 1. Model parameters varied for parametric study. 

Friction Angle, Orientation, Joint Spacing, 

Degrees Degrees from Horizontal Meters 

40 -30,30 1 

25 -60,30 0.6 

10 -60,60 0.4 

 0.2

RMR Range 

The target RMR range for the project was between 30 and 50, indicating “fair” to “good” rock. 

The RMR ratings were calculated by determining the point totals for Rock Quality Designation 

(RQD), joint condition, joint spacing, intact rock strength, and groundwater, as well as the joint 

orientation modifier (Waltham, 2003). 

RQD values were calculated using the joint spacing parameters using the relationship RQD = 

115 – 3.3Jv (Hoek et al, 1997), where Jv is the number of joints per representative cubic meter of 

the rock mass. The joint spacings were used to calculate the number of joints per meter for each 

set, and then added together. 

Assigned friction angle values was used to simulate different fracture conditions. A friction 

angle of 40 was assumed to correspond to “rough, tight” joints with a score of 30, while a 

friction angle of 25 would be “weathered” with a score of 20, and a friction angle of 10 would be 

“gouge > 5 mm” with a score of 0. 

Joint spacing values shown in the above table were assigned to bracket a range of categories. 

The 1.0 m spacing is within the 15 point range. The 0.6 m spacing is on the border between the 

15 and 10 point ranges. The 0.4 m spacing is in the middle of the 10 point range, and the 0.2 m 

spacing is on the border between the 10 and 8 point ranges. A smaller joint spacing of 0.06 m 

was attempted, but we did not have sufficiently powerful computers to run the models. 
Several of the parameters included in the RMR calculation were not incorporated into the UDEC 

models, and were assumed to have one specific value. Intact rock unconfined compressive 

strength (UCS) was assumed to be within the middle range of “50-100 MPa” corresponding to a 

value of 7 points. Ground water was assumed to be wet, corresponding to a value of 7 and 

fracture orientation was given a value of -15 for “unfavorable.” This combination essentially 

cancels out the effects of these three parameters on the total RMR values. 

Example UDEC File 

Table 3 shows the commands used in a typical UDEC analysis file. The first 8 lines define the 

corner rounding, the model block external dimensions, and the cracks used to create the 

excavation boundaries. The save files are used throughout the code to facilitate rerunning the 

analyses without having to start over from the beginning, which saves a lot of time in some 

models. Next are lines that define the rock material and joint properties followed by the fixed 

boundaries section. Gravity is set to -10 [m/s2

] and a title is added to the computation. After all 

of the data is input an initialization solve is performed to make sure that all of the blocks are in 

equilibrium before the main part of the analysis is started. After the initial solve is done the 

excavation is removed and a second solve is initiated to allow the blocks to move, if necessary, 

to attempt to reach equilibrium. The final state of the model is then saved. 

Table 3. Commands used in a typical UDEC analysis file. 

ro 0.01 

block 0,0 0,84 126,84 126,0 

jset -30,0 160,0 0,0 0.02,0 

jset 30,0 160,0 0,0 0.02,0 

crack 60,40 66,40 

crack 66,40 66,44 

crack 66,44 60,44 

crack 60,44 60,40 

save 3030sp20.sav 

prop mat=1 dens 2000 

prop jmat=1 jkn 5e8 jks 1e8 jfric 40 

fix range 0,126 0,3 

fix range 123,126 0,84 

fix range 0,3 0,84 

fix range 81,84 0,126 

grav 0,-10 

title 

 Roof shape with -30/30 joints, fric. ang.=40, spacing=0.02 

his unbal 

damp local 

solve 

save 3030sp20f40equil.sav 

del range 62 66 40 44 

save 3030sp20f40excavated.sav 

solve 

save 3030sp20f40final.sav 
At this point more code was required to observe what actually happened during the analysis. 

The objective was to determine the configuration of the excavation after equilibrium is reached, 

or after a substantial number of timesteps have been run. To get a picture of the model the code 

contained in Table 4 needed to be typed in. 

Table 4. UDEC commands used to observe and record behavior. 

plot block nc disp red 

set plot jpg 

set output 3030sp20f40.jpg 

copy 

Plotting the block configuration is done by using the “plot block” command. The “nc” helps the 

plot function work faster because it doesn’t show the rounding of the corners of the blocks in the 

file (rounded corners take longer to draw on the screen). The “disp red” shows red arrows that 

display the displacement vectors of blocks indicating the direction and magnitude of movement. 

Setting the plot to “jpg” creates a jpeg image file. “Set output” allows the user to name the file 

and, if necessary, specify the file location. “Copy” sends the previous screen plot to the jpeg 

output file. 

Results, Discussion and Conclusions 

In all, there were 36 models that were run to collect data of the excavations failure type. Figure 

1 shows one of the UDEC models that was run, with close-up views of the excavation with the 

three joint orientation combinations. Table 5 contains a summary of the RMR values for each 

model, with the corresponding contributions from each component, and a qualitative indication 

of the mode of failure of the model. Two types of behavior were observed: local failure of area 

immediately surrounding the roof and sides of the opening, and deep-seated failure extending a 

large distance beyond the opening. Figure 2 shows models that display the two different failure 

modes. Although there is some scatter in the lower RMR values, the general trend is that higher 

RMR values correspond with “local wedge failure” behavior; of the 21 models with RMR 47 or 

higher, only 1 displayed the deep-seated failure mode. The 15 models with RMR < 47 were very 

evenly split between the two failure modes. 

During the modeling it was found that the models that collapse completely take much more time 

to run than the models that only drop the roof and sides of the excavation. The smaller the joint 

spacing, the longer the models took just because there are more blocks moving so it takes many 

more calculations to run the model. There were patterns observed in some of the models that 

were a result of the orientation. In the -30,30 models, there were diamonds around the 

excavation that showed up often in those models. In the -60,30 models it was common to find a 

chimney that stretched from the excavation to the top of the model. The -60,60 models seemed 

to settle very well and no common pattern was visible. 

Observations of the extent of the failed zone around the opening indicate that the joint 

orientations have a large influence on the results. The failed zone extends about 1⁄4 of the span 

for the 30,30 joints, about 1/3 span for the 60,30 configuration, and 1 full span for the 60,60 

joints. It should be noted, however, that the models assume that both sets of joints are perfectly 

persistent, which is not very common in nature. 
 (a) (b) 

 (c) (d) 

Figure 1. a) full model, b) 30,30 close-up, c) 60,30 close-up, d) 60,60 close-up; all 1 m spacing. 

(a) (b) 

Figure 2. a) local failure, b) deep-seated failure. 
Table 5. Failure mode as a function of RMR value. 

 Fric. UCS Water Orentation Frac Fracture RMR 

J set angles Spacing Angle 50-100MP Wet Unfavorable Spac. Cond. RQD Value Behavior

ang-30/30 0.6 40 7 7 -15 15 30 20 64 Local 

ang-60/30 0.6 40 7 7 -15 15 30 20 64 Local 

ang-60/60 0.6 40 7 7 -15 15 30 20 64 Local 

ang-30/30 1 40 7 7 -15 15 30 20 64 Local 

ang-60/30 1 40 7 7 -15 15 30 20 64 Local 

ang-60/60 1 40 7 7 -15 15 30 20 64 Local 

ang-60/30 0.2 40 7 7 -15 8 30 20 57 Local 

ang-60/60 0.2 40 7 7 -15 8 30 20 57 Local 

ang-30/30 0.2 40 7 7 -15 8 30 20 57 Local 

ang-30/30 0.4 40 7 7 -15 10 30 17 56 Local 

ang-60/30 0.4 40 7 7 -15 10 30 17 56 Local 

ang-60/60 0.4 40 7 7 -15 10 30 17 56 Local 

ang-30/30 0.6 25 7 7 -15 15 20 20 54 Local 

ang-60/30 0.6 25 7 7 -15 15 20 20 54 Local 

ang-60/60 0.6 25 7 7 -15 15 20 20 54 Deep 

ang-30/30 1 25 7 7 -15 15 20 20 54 Local 

ang-60/30 1 25 7 7 -15 15 20 20 54 Local 

ang-60/60 1 25 7 7 -15 15 20 20 54 Local 

ang-60/30 0.2 25 7 7 -15 8 20 20 47 Local 

ang-60/60 0.2 25 7 7 -15 8 20 20 47 Local 

ang-30/30 0.2 25 7 7 -15 8 20 20 47 Local 

ang-30/30 0.4 25 7 7 -15 10 20 17 46 Deep 

ang-60/30 0.4 25 7 7 -15 10 20 17 46 Local 

ang-60/60 0.4 25 7 7 -15 10 20 17 46 Deep 

ang-30/30 0.6 10 7 7 -15 15 10 20 44 Local 

ang-60/30 0.6 10 7 7 -15 15 10 20 44 Local 

ang-60/60 0.6 10 7 7 -15 15 10 20 44 Deep 

ang-30/30 1 10 7 7 -15 15 10 20 44 Deep 

ang-60/30 1 10 7 7 -15 15 10 20 44 Local 

ang-60/60 1 10 7 7 -15 15 10 20 44 Deep 

ang-60/30 0.2 10 7 7 -15 8 10 20 37 Local 

ang-60/60 0.2 10 7 7 -15 8 10 20 37 Deep 

ang-30/30 0.2 10 7 7 -15 8 10 20 37 Local 

ang-30/30 0.4 10 7 7 -15 10 10 17 36 Deep 

ang-60/30 0.4 10 7 7 -15 10 10 17 36 Local 

ang-60/60 0.4 10 7 7 -15 10 10 17 36 Deep 

References 

Bieniawski, Z.T. (1974). Geomechanics Classification of Rock Masses and the Application is 

Tunneling. Proc. Third Intl. Congress on Rock Mechanics, ISRM, Denver, Vol 11A, pp. 27-32. 

Hoek, E., P.K. Kaiser, and W.F. Bawden (1987). Support of Underground Excavations in Hard 

Rock, Rotterdam:Balkema, 215 pp. 

Itasca (2000). UDEC User’s Guide (Version 3.1). Minneapolis:Itasca Consulting Group Inc. 

Waltham, A.C. (2002). Foundations of Engineering Geology, 2nd Ed., Spon Publishing, 90 pp.