ABSTRACT

Stress analysis programs such as MULSIM/NL, LAMODEL,

MinSim 2000, and EXAMINETAB are used in the mining industry 

to analyze stresses and displacements in coal mines, platinum 

mines, gold reefs, and tabular-type deposits. These relatively 

simple numerical models can efficiently simulate yielding and

failure of a rock mass near a mine opening and subsequent stress 

transfer. The main input parameters for these models are a family 

of nonlinear stress-strain curves for the in-seam material. For many 

applications of these models, such as in coal mining, extensive field 

measurements and observations exist from which to estimate these 

stress-strain curves and calibrate the numerical models; however, 

such measurements are lacking for other types of mines.

A three-step method is presented to determine nonlinear stressstrain curves for boundary-element (BE) programs used in many 

mining applications. The method requires a suite of laboratoryscale strength tests at various confining pressures. Note that this 

analysis uses laboratory -measured strength and modulus properties 

of alluvium. The dependency of the mechanical properties of

alluvium on scale has not been established, although more tests are 

being planned. However, it is believed that the relative 

comparisons performed are valuable regardless of scale effects. 

First, the FLAC2D computer program is used to model the

laboratory tests and determine cohesion (c) and friction angle (φ) 

for a Mohr-Coulomb material model. Second, another FLAC2D 

model uses the c and φ values to calculate vertical stress and strain 

around a single opening in the rock mass. This model calculates 

the stress-strain path of points at various distances from the

opening boundary. Finally, based on these stress-strain paths, the 

stress-strain curves needed for a BE analysis are derived.

This three-step method was demonstrated in a large, flat-lying 

underground test facility in very weak rock. The BE analyses 

agreed well with observations of failure at the test facility and 

provided a basis for evaluating the behavior of alternative layouts.

INTRODUCTION

Background

The U1a complex is an underground physics laboratory at the 

Nevada Test Site (1). Figure 1 shows the general layout of the 

complex as of October 2001. The main features of the complex are 

the U1a shaft at the southern end, the new U1h shaft at the northern 

end, and the north-south U1a.01 drift that connects the two shafts.

Main features of the facility are the vent drift and user's alcove east 

of the U1a.01 drift. Numerous alcoves used for physics

experiments are located off the major drifts.

The facility is mined in a weakly cemented alluvium at a depth 

of 960 ft below the surface, where vertical stress is expected to be 

about 800 psi. Unfortunately, the unconfined compressive strength 

of the alluvium measured on 2-in-diam by 4-in-long specimens is 

only about 150 psi, which is roughly one-fifth of the vertical stress.

Therein is the source of the facility's stability problems. When new 

drifts are mined close to existing drifts, the ground yields and 

induces excessive deformation around existing drifts. Yielding and 

excessive deformation results in deterioration of the support

system, which consists of rock bolts, wire mesh, and shotcrete. The 

alcoves used for the physics experiments house expensive data 

collection systems. Any deterioration of the opening is

unacceptable, and several areas in the facility have required

rehabilitation.

The most serious damage resulted from mining crosscut D and

the U1a.05 drifts off the U1a.02 drift and the U1a.102 drifts off the 

U1a.100 drift. Mining these drifts caused excessive deformation of 

the U1a.01 main drift, the U1a.02 drift, and the vent drift areas.

Limited convergence and extensometer data are available from 

instruments installed in these areas. Unfortunately, these

instruments were installed after most of the deformation had

occurred, and they only recorded a limited amount of data.

Alternative Layouts

Keeping in mind these ground control problems, site managers 

considered two options for further facility development (figure 1). 

Option 1 locates the U1a.200 drift south of the U1h shaft, whereas 

option 2 locates it north of the shaft. The latter option

NUMERICAL MODELING OF THE U1A COMPLEX AT THE NEVADA TEST SITE: MODEL 

DEVELOPMENT AND COMPARISON OF DIFFERENT DRIFT MINING OPTIONS

R. Karl Zipf, Jr., Mining Engineer

National Institute for Occupational Safety and Health

Pittsburgh Research Laboratory

Pittsburgh, Pennsylvania USA

Francois E. Heuze, Head Geotechnical Program

Lawrence Livermore National Laboratory

Livermore, CA
 

Figure 1.General layout of U1a complex.

spreads mine development over a wider area and decreases the risk 

of geomechanical problems due to ground yielding and stress

transfer. However, option 2 also requires several hundred feet of 

additional mining at a cost of millions of dollars. Option 1 may 

carry some risk of geomechanical stability problems; however, the 

cost is substantially less. 

This case study assessed potential ground yielding and stress 

transfer associated with the alternate locations for the U1a.200 

drift. Any development option must ensure satisfactory stability of 

the new U1h shaft area and the nearby user’s alcove and vent drift. 

MULSIM/NL (2, 3), which is a pseudo-three-dimensional, 

boundary-element (BE) program, was used to examine the two 

options. 

Objectives

This paper shows how to develop nonlinear stress-strain models 

used as input parameters for BE programs such as MULSIM/NL 

from a suite of laboratory-scale strength tests at various confining 

pressures. In brief, FLAC2D (4) is used to model the laboratory

tests and determine cohesion (c) and friction angle (φ) for a MohrCoulomb material model. Next, another FLAC2D model of a 

single opening uses these material parameters to calculate the 

stress-strain path of points at various distances from the opening 

boundary. Finally, these calculated stress-strain paths become the 

required stress-strains curves for the BE analysis. Note that this 

analysis uses laboratory -measured strength and modulus properties

of alluvium. The dependency of the mechanical properties of 

alluvium on scale has not been established, although more tests are 

being planned. However, it is believed that the relative comparisons 

performed are valuable regardless of scale effects. The three-step 

method presented here, in which laboratory strength data are used 

as required input parameters for BE analysis, should also be 

applicable to a variety of other mines, such as coal, gold, platinum, 

and other commodities where input parameters are poorly known.

REQUIRED INPUT PARAMETERS FOR 3 -D BE MODELS

Stress analysis programs such as MULSIM/NL (2, 3), 

LAMODEL (5, 6), MinSim 2000 (7), and EXAMINETAB (8) are 

used in the mining industry to analyze stresses, displacements, 

yielding, and stress transfer around tabular bodies such as coal and 

gold-bearing reefs. MULSIM/NL uses the BE approach to

calculate stresses and displacements around coal seams or, in the

case reviewed here, the flat-lying U1a complex. The key

abstraction underlying BE modeling is to analyze a tabular deposit 

as a thin crack or discontinuity in an otherwise homogeneous, 

isotropic, linear, elastic rock mass. Figure 2A shows this crack or 

seam plane in the surrounding rock mass. The top and bottom 

surfaces of the crack form the problem boundary (i.e., the roof and 

floor in coal mining or the hanging wall and footwall in metal 

mining). The next critical step is to divide the crack or seam plane 

into numerous square boundary elements. Figure 2B shows an 

actual mine plan (in this case, a plan view of coal mine gateroad 

entries) and a grid showing an approximation of the model. 

Individual elements are then assigned material properties to

approximate mine geometry. Many of the stress analysis programs 

mentioned above feature stress-strain models for the in-seam 

material (figure 2C) that include (1) linear elastic for coal or rock, 

(2) strain-softening, (3) elastic-plastic, (4) bilinear-hardening, (5) 

strain-hardening, and (6) linear elastic gob or broken rock. The 

first three models are typically used for the unmined in-seam coal 

or rock material, while the last three are used for the broken rock or 

gob material left in the wake of full-extraction mining.
A

B

C

Figure 2. A, Boundary-element seam plane in surrounding rock mass; 

B, actual mine plan in-seam plane and grid of modeling approximation; 

C, six different stress-strain models available in MULSIM/NL.

In constructing a BE model similar to that shown in figure 2B, 

elements adjacent to an opening are assigned low strength

properties. Progressively stronger properties are assigned to

elements farther away from the opening to reflect increasing

confinement. However, the elements do not truly confine each 

other. BE models of this type require knowledge of the nonlinear

stress-strain behavior of the in-seam material. The stress path, and 

hence the failure path that a nonlinear in-seam material element 

will follow, is known a priori by virtue of the assigned material 

properties and through model construction. In other words,

something is known about the stress and failure distribution away 

from the opening edges before the model is run. For coal mining, 

extensive field measurements of stress distributions and the stress 

path inside coal pillars are available. These observations have 

provided estimates of the nonlinear stress-strain relations required 

as input for the in-seam material elements of coal mine models. 

However, for the alluvium comprising the U1a complex,

comparable observations and experience are unavailable.

The MULSIM/NL model of the U1a complex uses an elasticplastic model for the in-seam material. In this material model, 

yield strength increases for elements farther from an opening. The 

next section describes development of these requisite stress-strain

curves.

INPUT PARAMETER DEVELOPMENT–THREE-STEP 

METHOD

In the absence of extensive field measurements of deformation 

and stresses around the chambers, a method is described for using 

laboratory strength data and FLAC2D to develop MULSIM/NL

input parameters. In the first step, an axisymmetric FLAC2D 

model with a simple Mohr-Coulomb failure criterion is used to 

approximate laboratory data. This FLAC2D model calculates the 

complete stress-strain curve for laboratory specimens at various 

confining pressures as measured with a stiff testing system. This 

model provides reliable estimates of the Mohr-Coulomb parameters 

cohesion (c) and friction angle (φ). 

The second step uses these same Mohr-Coulomb parameters in 

another FLAC2D model of a tunnel in the alluvium at the U1a 

complex. By loading this tunnel model to stresses exceeding those 

expected in the field, information is obtained on the stress-strain 

response of the alluvium at various distances into the tunnel wall. 

In the third step , these calculated stress-strain responses become the 

basis for estimating the required stress-strain curves needed as 

input parameters to MULSIM/NL. This three-step procedure

provides input parameters to MULSIM/NL that lead to the analyses 

of the U1a complex.

Friction Angle and Cohesion Estimates from Laboratory Data

Figure 3A shows all 21 complete stress-strain curves at various 

confining pressures as measured by TerraTek, Inc. (9). The

laboratory data show the following general characteristics:

• Eight tests at 0 psi confinement exhibit strain-softening behavior 

with peak strength around 150 psi and residual strength of 100 psi 

or less at 2% strain.

• Three tests at 50 psi confinement also exhibit some strainsoftening behavior; however, peak strength has increased to about 

500 psi with a residual strength of about 300 psi.

• Four tests at 250 psi confinement are almost elastic-perfectlyplastic with a yield strength of about 1,000 psi.

• Five tests at 500 p si confinement show strain-hardening behavior 

with a yield strength of about 1,200 psi.

• One test at 750 psi confinement also shows strain-hardening 

behavior with a yield strength of about 1,100 psi.

Peak and residual strength data are extracted from these curves. 

Fitting a simple linear Mohr-Coulomb model to the data provided 
 

 

Figure 3. A, Complete stress-strain curves from laboratory tests at 

various confining pressures on U1a alluvium; B, stress-strain curves 

from FLAC2D models with friction angle of 22° and cohesion of 35 

psi; C, measured versus computed yield strength.

Peak friction angle φp = 18.9° ≈ 19°.

Peak cohesion = 93.3 ≈ 90 psi.

Residual friction angle φr = 20.4° ≈ 20°. (The residual range is 

defined as post-yield.)

Residual cohesion = 64.3 ≈ 60 psi.

Correlation coefficients (R2) for these curve-fitting exercises 

exceeded 0.8, which is good for geotechnical data. Note that the 

post-peak behavior of this alluvium is not typical of brittle rock.

Step 1 – Friction Angle and Cohesion Estimates from FLAC2D 

Model

An axisymmetric FLAC2D (4) model was developed using the 

laboratory data. Boundary conditions on the model are as follows:

• The left side is the line of axisymmetry. 

• The right side is subject to the desired normal confinement 

pressure. 

• The bottom edge is fixed in the vertical direction and free in the 

horizontal direction. 

• The grid points along the top edge move downward with

constant velocity of 4 × 10-6 in/sec. This downward velocity 

applies strain to the model at the rate of 10-6 strains per second. 

Thus, the FLAC2D model simulates testing in a perfectly stiff test

frame.

Models were run at confining pressures of 0, 50, 250, 500, and 

750 psi. Each FLAC2D model produced an elastic-perfectlyplastic stress-strain curve in which yield stress increased with

confining pressure. In the numerical studies, friction angle and 

cohesion were varied systematically until the family of elasticperfectly-plastic stress-strain curves approximated the laboratory 

data. Increasing cohesion tended to shift the family of curves 

upward as a group, whereas increasing friction angle tended to 

spread the curves apart.

The best fit of the laboratory data occurs with a friction angle of 

22° and cohesion of 35 psi. This estimate compares favorably with 

the residual strength estimate for a friction angle of 20° and

cohesion of 60 psi. Figure 3B shows this family of computed 

stress-strain curves. Computed yield strengths at confining 

pressures of 0, 50, 250, 500, and 750 psi were 100, 210, 650, 1,200,

and 1,550 psi, respectively.

For the various confining pressures indicated, figure 3C

compares the approximate average residual strength as determined 

from figure 3A to the computed yield strength as shown in figure 

3B. The simple Mohr-Coulomb failure model used by FLAC2D 

reproduced the laboratory data at an acceptable level.

Step 2 - Stress-Strain Behavior of Tunnel Wall with FLAC2D 

Model

Excavation of an underground opening redistributes stresses in 

the rock around the opening. In a linear elastic material, the 

redistributed stresses are highest at the opening boundary and 

decrease further into the rock mass. The stress concentration at the 

excavation boundary typically exceeds the in situ stress by a factor 

of 2 to 3. The stress typically returns to the in situ condition about 

three excavation widths into the rock.

Depending on conditions, most rocks will fail or yield near the 

excavation boundary. At this facility, stress concentration into the 

tunnel wall deviated considerably from the ideal linear elastic case. 

Rock failure at the excavation boundary caused the stress

concentration there to fall to zero. The vertical stress concentration 

then rose and reached a maximum some distance away from the 

excavation boundary before declining to the in situ value far into 

the rock mass. For nonlinear elastic rock that is failing, maximum 

stress concentration is normally less than the elastic case; however, 
 

the region of elevated stress concentration always extends much 

farther into the rock mass. That distance may exceed five or more 

opening widths. Such rock failure and the ensuing stress

redistribution explains the so-called “load transfer” away from

underground openings.

Use of MULSIM/NL and other similar stress analysis programs 

requires knowledge of the nonlinear elastic behavior of the failing 

rock mass surrounding an underground opening. Using the same 

material model as used in the laboratory data simulations,

additional FLAC2D models examined the stress-strain behavior of 

a single tunnel in the alluvium at the U1a complex. The model 

consists of a 70- by 100- (or 7,000-) element array containing a 

tunnel 25 ft wide by 17 ft high, which is a typical size for many of 

the larger excavations at the U1a complex. Boundary conditions 

were as follows: 

• Along the bottom edge, displacements were fixed in the ydirection. 

• The left edge was a symmetry plane where displacements in the 

x-direction were fixed. 

• The right edge was considered a remote boundary, and the x 

displacements were fixed there as well. 

• The top edge of the model was subject to a constant downward 

displacement or velocity to load the model. 

• Each element was a linear elastic material subject to a simple 

Mohr-Coulomb failure criterion.

• The tunnel models used a friction angle of 22° and cohesion of 

35 psi as determined from prior FLAC2D models of the laboratory 

tests.

A constant downward velocity along the top edge loaded the 

model and provided a picture of the evolving stress and strain away 

from the tunnel wall. Figure 4 shows the vertical stress distribution 

in the vicinity of the tunnel at a stage when the applied vertical 

stress was over 1200 psi, which was much larger than the expected 

vertical stress. Vertical stress increased from zero and reached a 

maximum value of 1,800 psi about 80 ft (960 in) into the tunnel 

wall. Horizontal stress also increased from zero and reached a 

maximum of 750 psi about 100 ft (1,200 in) into the wall. Vertical 

stress and therefore yield strength of the alluvium increased nearly 

linearly at a rate of about 20 psi/ft into the tunnel wall for an 

opening 25 ft wide by 17 ft high.

The FLAC2D model of a single tunnel recorded average stress 

and strain within elements 0 to 5, 5 to 10, etc., up to 40 to 50 ft into 

the tunnel wall as the model was subjected to a constant downward 

displacement along the top edge. Figure 5 shows the computed 

stress-strain response of these 10 selected points. For a 25- by 17-ft

opening, material at the tunnel edge yielded at about 125 psi and 

material 45 to 50 ft from the rib yielded at 1,100 psi.

Step 3 - Stress-Strain Curves for MULSIM/NL Input

The computed stress-strain responses shown in figure 5 are the 

basis for the stress-strain curves in figure 6, which were used as 

input to MULSIM/NL. Note that for materials A and B, the 

MULSIM/NL stress-strain curves are adjusted somewhat to better 

reflect the laboratory data, which exhibit strain-hardening at high 

confining pressure. In creating a MULSIM/NL model of the U1a 

complex, elements adjacent to an excavation boundary will follow 

stress-strain curve J, elements 5 to 10 ft from an excavation 

boundary will follow curve I, and so forth, to elements more than 

45 ft from an excavation boundary, which will follow curve A.

Figure 4. Vertical stress distribution in vicinity of tunnel 25 ft wide by 

17 ft high when applied vertical stress equals 1200 psi.

Figure 5.Computed stress-strain response into wall of 25- by 17-ft 

opening.
 

Figure 6.Ten nonlinear elastic-plastic stress-strain models for inseam material used in MULSIM/NL models of U1a complex

CASE HISTORY - U1a COMPLEX MODEL CALIBRATION 

AND RESULTS

Ten-Step Model Up to Present

Table 1 summarizes the major input parameters used in the 

MULSIM/NL model of the U1a complex. The model uses a 5-ft 

element width and is centered along the U1a.01 drift near the vent 

drift. The fine mesh extends 240 elements north-south and 250 

elements east-west, which is an area 1,200 by 1,250 ft. This finemesh grid adequately covers all the existing and proposed U1a 

complex drifts from south along U1a.01 to north beyond the

proposed U1a.50 and U1a.200 drifts, and from west well beyond 

the U1a.03 drift and alcoves to east well beyond the U1a.104 drift 

and alcoves.

Table 1.Input parameter summary for MULSIM/NL model of U1a 

complex 

Element w idth 5 ft

Model size 70-by-68 coarse mesh blocks

250-by-240 fine-mesh elements

Seam thickness 16 ft

Rock mass moduli E = 200,000 psi, ν = 0.25

Vertical stress on-seam 800 psi

Number of in-seam materials 10 (A through J)

The first analysis involved 10 mining steps and simulated

development of the U1a complex to its present state. Figure 7 (top)

shows computed vertical stress and convergence as they evolved

during mining. Note that the vertical stress scale always ranges 

from 0 to 1,500 psi and the convergence scale always ranges from 3 

to 18 in. Calculated convergence includes a pre-excavation in situ 

component of about 1 in induced by an in situ stress of 800 psi.

The calculations shown in figure 7 (top) agree well with visually 

observed damage to the U1a workings. Ground control problems 

in the U1a.01, U1a.02, U1a.100, and vent drifts began to develop 

with excavation of the U1a.03 D crosscut, the U1a.105 drift, and 

the U1a.102 drift. The MULSIM/NL calculations showed that the 

new large excavations induced an additional 2 to 4 in of

convergence on the existing support system, resulting in flaking of 

alluvium, cracking of shotcrete, and bagging of wire mesh. 

Elevated stresses developed in the pillars between the U1a.01 and 

U1a.05 drifts and the U1a.01 and U1a.102 drifts. However, 

elevated stresses in the interiors of pillars were not the cause of 

ground control problems at the U1a complex. More likely is that 

induced convergence on the support system in existing workings 

was caused by additional excavation nearby.

The MULSIM/NL models showed that 1 in of additional

convergence correlated with the onset of visually observed damage 

to nearby drifts at the U1a facility. Most of the convergence 

occurred shortly after initial development and before the

application of shotcrete. When a MULSIM/NL model predicts 

more than 1 in of additional convergence due to nearby mining, 

that area is likely to experience flaking ground and spalling

shotcrete. In this case study, model areas with less than 1 in of 

additional convergence are not likely to have significant ground 

control problems.

Pressure cells installed in the tunnel wall along U1a.01 prior to 

mining the connection to the U1h shaft provided some information 

that supported the validity of the calculated stresses from

MULSIM/NL and the model’s input parameters. As shown in 

figure 8, MULSIM/NL predicted a maximum pressure increase of 

about 380 psi about 50 ft into the tunnel wall. Measurements 

indicated a maximum pressure increase of about 260 psi at a

distance of 35 ft into the tunnel wall. Thus, the pressure cell data 

provided some confirmation of the stresses and pressure changes 

calculated by MULSIM/NL and the model’s input parameters. The 

depth of the measured maximum pressure increase is less than that 

predicted by MULSIM/NL; therefore, the model is conservative in 

that it may predict load transfer over distances greater than what 

may actually be the case.

In summary, value of the MULSIM/NL model of the U1a 

complex was established by three considerations:

1. Good correlation between calculated additional convergence 

and visual observation of tunnel distress;

2. Similarity between the pressure arch resulting from

minethrough of the U1a.01 drift as estimated by MULSIM/NL 

and as measured by hydraulic pressure cells, both of which are 

consistent with theory ; and

3. Careful definition of input parameters.

Thus, the MULSIM/NL models can be used as a basis to 

compare the relative merits of alternate mine plans. Evaluation of 

alternative mine plans will use the additional convergence

threshold criterion of 1 in.

Options Analysis for U1a.200 Drift

The calibrated MULSIM/NL model enabled analyses of two

options for the U1a complex.

1. U1a.200 drift located south of the U1h shaft, and 

2. U1a.200 drift located north of the U1h shaft.

In both options, the U1a.200 drift will extend east about 500 ft

where it will join the U1a.104 drift. The analyses provided

comparative stress and convergence data for a critical area of the
 

Figure 7.Comparison of computed vertical stress and convergence.
 

Figure 8.Comparison of measured pressure changes to predicted 

pressure changes with MULSIM/NL along U1a.01.

U1a complex that is near the user’s alcove and vent drift area east 

of the U1a.01 drift. The critical question is whether constructing 

the U1a.200 drift south of the U1h shaft will have a significant 

adverse impact on the user’s alcove, vent drift, or U1h shaft area.

Figure 7 (middle and bottom) shows computed stress and

convergence for option 1 (south of the U1h shaft) and option 2 

(north of the U1h shaft). Close examination of stresses in the 

vicinity of the user’s alcove, vent drift, and U1h shaft areas shows 

that no appreciable differences exist between the two options.

Slightly higher values are seen in the vent drift area, but no 

differences are discernable elsewhere.

For closer examination of the differences, figure 9A and 9B

shows stress and convergence profiles looking east along a northsouth section just east of the U1a.01 drift and passing through the 

pillar between the east and west user’s alcoves. Figure 9A shows 

slightly higher stress (50 to 100 psi) for option 1 between the user’s 

alcove and the U1a.200 drift. Stresses under both options are the 

same elsewhere, such as in the user’s alcove pillar and between the 

vent drift and the U1a.100 drift. More importantly, figure 9B

shows no appreciable difference in convergence. With option 1, 

convergence is greater than with option 2 by about 0.5 in. in the 

user’s alcove, by about 0.3 in. in the user’s alcove pillar, and by 

about 0.2 in. in the vent drift. The additional convergence above 

the base case associated with option 1 is less than 1 in (remember 

that the convergence threshold criterion is 1 in). In summary, the 

MULSIM/NL analysis shows that locating the U1a.200 drift south 

of the U1h shaft will not induce significant additional convergence 

and associated ground control problems in the user’s alcove and 

vent drift area.

CONCLUSIONS

MULSIM/NL (2, 3) and related stress analysis programs such as 

LAMODEL (5, 6), MinSim 2000 (7), and EXAMINETAB (8) have 

become standard tools in the mining industry for analyzing stresses 

and displacement in coal mines, platinum mines, gold reefs, and 

tabular-type deposits. Early versions of these programs had linear 

elastic capability only. Zipf (2, 3) introduced a suite of six

nonlinear material models that enabled realistic simulation of coal 

mines. MULSIM/NL and LAMODEL have been applied to a wide 

variety of longwall coal mines, room-and-pillar coal mines, trona 

mines, and underground stone mines.

These relatively simple numerical models can efficiently

simulate yielding and failure of a rock mass near mine openings 

and subsequent stress transfer. The main input parameters for these 

models are nonlinear stress-strain curves for in-seam materials. 

Extensive field measurements and observations from many types of 

mines allow stress-strain curves to be calculated and numerical 

models to be calibrated. However, for many mines, such 

measurements are lacking. 

A three-step method is presented to determine the nonlinear

stress-strain curves for quasi-three-dimensional BE programs. The 

method requires a suite of laboratory -scale strength tests at various 

confining pressures. In the first step, FLAC2D is used to model the 

laboratory tests and determine cohesion (c) and friction angle (φ) 

for a Mohr-Coulomb material model. In the second step, another 

FLAC2D model uses the c and φ values to calculate vertical stress 

and strain around a single opening in the rock mass. This model 

calculates the stress-strain path of points at various distances from 

the opening boundary. In the third step, the stress-strain curves 

needed for a BE stress analysis are derived.

A case study demonstrated the practicality of this three-step 

method for determining input parameters for BE programs. The 

BE analyses shown in figure 7 (top) agreed well with failure 

observations at a test facility. The MULSIM/NL model showed

clearly that extension of the U1a.03 D crosscut and development of 

the U1a.05 drift would lead to additional induced convergence of 1 

in or more along the U1a.01 and U1a.02 drifts and the user’s alcove 

and the vent drift areas. Unacceptable ground conditions at the 

U1a complex have occurred at these locations.

Subsequent analyses predicted the behavior of alternative

layouts. From a geomechanics viewpoint, locating the U1a.200 

drift south of the U1h shaft (option 1) is feasible. This location 

results in additional induced convergence of 0.9 inch in the user’s 

alcove and vent drift area, which is less than the threshold of an 

acceptable additional induced convergence of 1 in. Option 2 results 

in additional induced convergence of about 0.5 in. in these critical 

areas. However, the expense that would be incurred with the 

additional excavation footage required for option 2 is not justified 

from a ground control perspective.

REFERENCES

1. Nevada Test Site U1a Experimental Facility.

(http://www.nv.doe.gov/nts/facilities/u1a.htm)

2. Zipf, R.K., Jr. MULSIM/NL–Application and Practitioner’s 

Manual. U.S. Bureau of Mines Information Circular 9322. 1992, 

48 pp.

3. Zipf, R.K., Jr. MULSIM/NL–Theoretical and Programmer’s 

Manual. U.S. Bureau of Mines Information Circular 9321. 1992,

52 pp.
 

Figure 9.(A) Stress and (B) convergence profile parallel to U1a.01 drift and through user’s alcove.
2

 

4. Itasca Consulting Group, Inc., Minneapolis, MN. FLAC2D: 

Fast Lagrangian Analysis of Continua. 2003.

5. Heasley, K.A. Numerical Modeling of Coal Mines with a 

Laminated Displacement-Discontinuity Code. Ph.D. dissertation, 

Department of Mining and Earth Systems Engineering, Colorado 

School of Mines, Golden, CO. 1998, 187 pp.

6. Heasley, K.A., and G. Chekan. Practical Stress Modeling 

for Mine Planning. Proceedings, 17th International Conference 

on Ground Control in Mining, ed. by Syd S. Peng (Univ. of WV, 

Morgantown, WV, Aug. 4-6, 1998). 1998, pp. 129-137.

7. Council for Scientific and Industrial Research (CSIR), 

Johannesburg, South Africa. MinSim 2000. 2000. 

(http://www.minemodel.co.za/minsim.asp), 

8. Roc Science, Inc. EXAMINETAB. 2003.

(http://www.rocscience.com/products/ExamineTab.asp)

9. TerraTek, Inc. Mechanical Testing of Alluvium Samples for 

U1A Complex. Report TR99-43 from TerraTek, Salt Lake City,

UT, to Bechtel Nevada, May 1999.