Abstract: This paper presents a fully coupled thermal-hydrological-mechanical analysis of FEBEX-a large underground heater test conducted in a bentonite and fractured rock system. System responses predicted by the numerical analysis-including temperature, moisture content, and bentonite-swelling stress-were compared to field measurements at sensors located in the bentonite. An overall good agreement between predicted and measured system responses shows that coupled thermal-hydrological-mechanical processes in a bentonite barrier are well represented by the numerical model. The most challenging aspect of this particular analysis was modeling of the bentonite&apos;s mechanical behavior, which at FEBEX turned out to be affected by gaps between prefabricated bentonite blocks. At FEBEX, the swelling pressure did not develop until a few months into the experiment when moisture swelling of bentonite blocks had closed the gaps completely. Moreover, the wetting of the bentonite took place uniformly from the rock and was not impacted by the permeability difference between the Lamprophyres dykes and surrounding rock

C.-F Tsang

J Rutqvist

CiteSeerX

A FULLY COUPLED THREE-DIMENSIONAL THM ANALYSIS OF THE 
FEBEX IN SITU TEST WITH THE ROCMAS CODE: PREDICTION OF THM 
BEHAVIOR IN A BENTONITE BARRIER 
J. Rutqvist and C.-F. Tsang 
Earnest Orlando Lawrence Berkeley National Laboratory (Berkeley Lab) 
Earth Sciences Division, Berkeley, CA 947 2, USA 
 
 
Abstract: This paper presents a fully coupled thermal-hydrological-mechanical analysis of FEBEX—a 
large underground heater test conducted in a bentonite and fractured rock system. System responses 
predicted by the numerical analysis—including temperature, moisture content, and bentonite-swelling 
stress—were compared to field measurements at sensors located in the bentonite. An overall good agreement 
between predicted and measured system responses shows that coupled thermal-hydrological-mechanical 
processes in a bentonite barrier are well represented by the numerical model. The most challenging aspect of 
this particular analysis was modeling of the bentonite’s mechanical behavior, which at FEBEX turned out to 
be affected by gaps between prefabricated bentonite blocks. At FEBEX, the swelling pressure did not 
develop until a few months into the experiment when moisture swelling of bentonite blocks had closed the 
gaps completely. Moreover, the wetting of the bentonite took place uniformly from the rock and was not 
impacted by the permeability difference between the Lamprophyres dykes and surrounding rock.  
 
 
 
1 INTRODUCTION  
    As part of the DECOVALEX III project, 
several independent research teams have used 
various numerical models to analyze a full-scale 
engineered barrier experiment (FEBEX), currently 
conducted at the Grimsel Test Site in Switzerland. 
This paper presents the analysis conduced by the 
Berkeley Lab research team, using the fully 
coupled thermal-hydrological-mechanical (THM) 
numerical model ROCMAS. Specifically, the 
paper presents model predictions of coupled THM 
responses at FEBEX that are compared to field 
measurements. 
 
 
2 FEBEX IN SITU TEST 
    The FEBEX in situ test has been conducted as a 
multi-national project coordinated by the Spanish 
organization ENRESA. In essence, the experiment 
involves the installation of two cylindrical heaters 
(4.54 m long and 0.97 m in diameter) centered in a 
tunnel (diameter 2.27 m) and surrounded by a 
barrier (thickness 0.64 m) made of highly 
compacted unsaturated blocks of bentonite (Figure 
1). The tunnel is located in a mountainous area of 
massive saturated granite about 420 m below 
ground surface.  
    The FEBEX in situ test started in 1995 with 
rock-mass characterization and tunnel excavation. 
After the installation of heaters, the bentonite 
barrier, and monitoring equipment, the heating 
began on February 27, 1997. The heater power 
was first increased stepwise to reach a targeted 
maximum heater temperature of 100°C. After 53 
days, the system was switched to a constant-
temperature mode, keeping the maximum 
temperature at 100°C for the next several years. 
System responses—including temperature, 
moisture content, fluid pressure, stress and 
displacements—were monitored by several 
hundred sensors located in both the buffer and 
surrounding rock mass.  
 
Heater (diameter 0.97)
Bentonite blocks
Steel liner
Granite
Heaters Bentonite
Concrete
Plug
4.54
1.0
4.54 4.34
17.4 2.7
(m)
Access tunnel
Granite
2.27
 
Figure 1. The set up of the FEBEX in situ test 
located at the Grimsel Test Site about 
420 m below the ground surface.    
3 ROCMAS 
    ROCMAS is a finite-element code for analysis 
of coupled THM processes in partially saturated 
geological media (Noorishad and Tsang, 1996, 
Rutqvist et al., 2001). In ROCMAS, the Biot 
(1941) formulation is extended to partially 
saturated media through Philip and de Vries’ 
(1957) theory for heat- and moisture-flow in soil. 
This results in a comprehensive coupled THM 
formulation for partially saturated geological 
media that includes the coupled processes shown 
in Figure 2.  
    In ROCMAS, solid, liquid, and gas phases are 
considered. However, it is assumed that the gas 
pressure Pg is constant and equal to atmospheric 
pressure throughout the porous medium. As a 
consequence, vapor transport occurs only through 
molecular diffusion driven by a gradient in vapor 
concentration. The heat transfer may take place 
through conduction over all phases and by 
advection with water in both liquid and gas 
phases. 
    For the analysis of the FEBEX in situ test, a soil 
mechanics state-surface model was implemented. 
This state-surface approach provides a better 
representation of bentonite behavior under 
partially saturated conditions than a single 
effective stress approach. The logarithmic state 
surface model proposed by Lloret and Alonso 
(1985) was adopted in this analysis. In their 
model, void ratio (e) is a function of both net mean 
stress, (σm′′ = σm – pg, where σm = total mean 
stress and pg is gas pressure) and suction (s = pg – 
pl, where pg and pl is gas and liquid pressures, 
repectively).  
 
M
Stress and strain
H
Fluid flow and pressure
T
Heat flux and temperature
Fluid  density
Fluid viscosity
Heat convection
Thermal conductivity
Specific heat
“E
ffe
cti
ve
 st
res
s”
M
ois
tur
e s
we
llin
g
Po
ros
ity
Pe
rm
ea
bil
ity
Thermal
expansion
 
 
Figure 2. Coupled THM processes in 
unsaturated geological media 
simulated by the ROCMAS code   
4 FEBEX MODEL  
A three-dimensional fully coupled THM analysis 
of the FEBEX in situ test was carried out for the 
first 1,000 days of heating. Model geometry and 
material properties are presented in the next two 
subsections.  
4.1 Geometry 
    A half-symmetrical three-dimensional model 
was discretized as shown in Figure 3a. The model 
includes two highly permeable lamprophyre dykes 
that intersect the FEBEX tunnel (Figure 3). These 
zones are included in the model because wetting 
rate of the bentonite might depend on the local 
permeability of the surrounding rock. The 
engineered materials included in the model are a 
concrete plug, the bentonite barrier, a steel liner 
(around the heaters), and the heater canisters 
(Figure 3b).   
 
 
66 m
56 m
Rock
Lamprophyre dikes
FEBEX tunnel
Rock
 
(a) Entire model of FEBEX 
 
X
Y
Z
Concrete Plug
Bentonite
Heater #1
Heater #2
 
(b) Detailed view of the near field materials 
 
Figure 3. Finite element model of FEBEX 
4.2 Material properties  
    The material properties were obtained from 
various field and laboratory tests that were 
performed before the emplacement of the buffer 
and heaters. For example, the inflow into the open 
drift was utilized to calibrate the in situ hydraulic 
properties of the rock mass and Lamprophyre 
dykes. Moreover, several laboratory tests were 
utilized for numerical back-analyses of coupled 
THM properties of the bentonite. The properties of 
the bentonite and rock are listed in Tables 1 and 2.  
    Some of the material properties listed in Table 1 
are given in the form of functions. The water- 
retention curve of the bentonite is described by a 
modified van Genuchten (1980) function as:  
 
( ) ( )[ ] [ ] 5.130.043.1 4000/135/199.0
01.0
ss
S
−+
+=
−        (1) 
 
where S is liquid saturation and s is suction.  
   The thermal conductivity is a function of 
saturation according to: 
 
( ) 1.065.01
71.028.1 −+
−= Sm e
λ        (2) 
 
and specific heat is a function of temperature 
according to: 
 
5.73238.1 += Tcs        (3) 
 
  The state surface model for this particular 
bentonite’s mechanical behavior is defined as: 
 
ss
e
m
m
loglog23.0log17.0
log49.003.1
σ
σ
′′+
−′′−=
       (4) 
  
    As shown in Table 2, the properties of the 
Lamprophyre properties and the surrounding rock 
are the same except for permeability and thermal 
conductivity. The mechanical rock-mass 
properties are obtained from the geological 
description of the Grimsel Test Site (Kneussen et 
al., 1989). Significantly, the Young’s modulus of 
the rock mass was reduced to 70% of its value for 
intact rock.   
 
 
 
 
Table 1. Material properties of the bentonite barrier 
used in modeling the FEBEX heater test   
Parameter Value 
Dry density, [kg/m3] 1.6⋅103  
Porosity, [-] 0.41 
Saturated permeability, [m2] 2.0⋅10-21 
Relative permeability, krl krl = S3 
Water retention Equation (1) 
State surface  Equation (4) 
Poisson ratio, [-] 0.35 
Thermal expan. coeff., [1/°C] 1.0⋅10-5  
Dry specific heat, [J/kg⋅°C] Equation (3) 
Thermal cond.,  [W/m⋅°C] Equation (2) 
Flow times tortousity factor 0.8 
Thermal diffusion factor 2.0 
 
 
Table 2. Material properties of the rock mass used 
in modeling the FEBEX heater test 
Parameter Value 
Density, [kg/m3] 2700  
Porosity, [-] 0.01 
Biot’s constant, α [-] 1.0 
Young’s Modulus, [GPa] 35 
Poissons ratio, [-] 0.3 
Specific heat, [J/kg⋅°C] 800  
Thermal conductivity, [W/m⋅°C] 3.6  
Thermal expan, coefficient [1/°C] 8.21⋅10-6  
Vertical permeability, [m2] 5×10-18  
Horizontal permeability, [m2] 5×10-19  
Van-Genuchten’s parameter, P0 [MPa] 1.47  
Van Genuchten’s parameter, β 2.47 
Lamprophyre permeability, [m2] 1.1×10-17 
Lamprophyre thermal cond. [W/m°C] 2.45  
 
 
 
 
 
 
 
 
5 SIMULATION RESULTS  
    The simulation of the FEBEX in situ test 
included both pre-heating and heating periods, as 
shown in Figure 4. The simulation began eight 
months before heating to take into account the 
wetting of the benonite during the experimental 
setup. After the initiation of heating, the heater 
power was increased step-wise during the first 53 
days. Then the power of each heater was 
individually controlled by a constant heater 
temperature of 100°C. The simulated heater power 
shown in Figure 4 is slightly lower than the 
measured one.  
   In the following subsections, simulated and 
measured system responses are compared at 
selected monitoring points within the bentonite 
barrier.   
 
 
TIME (day)
H
E
A
TE
R
P
O
W
E
R
(W
)
0 500 1000
0
500
1000
1500
2000
2500
3000
1200 W
2000 W
Constant temperature
power control mode
Pre-heating Heating
 
 
Figure 4. Simulated heater power as a function 
of time for each heater. A constant 
temperature mode is implemented after 
53 days  
5.1 Results of temperature 
    Figure 5 presents simulated temperature in the 
bentonite barrier after 1,000 days. The figure 
shows the location of the hottest point on the 
heater surface, which is kept at a constant 
temperature of 100oC. At the drift wall the 
temperature reaches a maximum of about 40–
50oC, giving rise to a thermal gradient of about 80 
to 90oC/m.  
    In Figure 6, simulated and measured 
temperature evolutions are compared at 
monitoring point D1G, located near the drift wall. 
The good agreement between simulated and 
measured temperature shown in Figure 6 is 
typical. This confirms that temperature can be 
very well predicted by numerical analysis in this 
type of environment.  
 
50°C contour line
Max temperature 100 °C
at heater surface
25°C contour line
Point D1G at
side wall of drift
 
 
Figure 5. Simulated temperature contour after  
1,000 days of heating  
 
 
Point D1G
TIME (Days)
TE
M
P
E
R
A
TU
R
E
(o
C
)
0 500 10000
10
20
30
40
MEASURED
SIMULATED
 
 
Figure 6. Simulated and measured temperature 
evolution in point D1G located at the 
drift wall 
5.2 Results of moisture content 
    Figure 7 shows simulated liquid saturation after 
1,000 days of heating. The dark contours in Figure 
7 indicate zones where wetting of the bentonite 
have taken place. The simulated wetting has begun 
already before heating through water infiltration 
from the fully saturated rock. The light contours in 
Figure 7 indicate that the drying zone has taken 
place near each of the heaters. This drying is 
caused by evaporation and transport of vapor 
along the thermal gradient away from the heaters. 
Another observation in Figure 7 is that the wetting 
of the bentonite progresses uniformly all around 
the drift without any visible effects from the high 
permeability Lamprophyres.   
    Figure 8 presents simulated and measured 
evolutions of the moisture content (relative 
humidity) at three points located along a vertical 
monitoring section between the two heaters (HG, 
HC and HH in Figure 7). Figure 8 shows that the 
wetting of the bentonite starts at the drift wall 
(Point HG located a few centimeters from the rock 
surface) as soon as the bentonite is installed in that 
section. At this monitoring point, the relative 
humidity has increased to about 80–90% at heater 
turn-on (time = 0 in Figure 8).  
    At point HH, condensation of vapor caused a 
slight wetting during the first 100 days. For the 
period between 100 to 300 days, the water content 
decreased slightly because of drying induced by 
the heat. After 300 days, the relative humidity 
increased again as a result of capillary driven 
liquid flow from the outer regions of the bentonite. 
    At point HC—located halfway between the 
heater and the drift wall—the moisture content 
increased gradually as a result of infiltration from 
the fully saturated rock. 
   Figure 8 indicates that the evolution of relative 
humidity was reasonable well predicted by the 
numerical analysis.  
 
 
 
Point HG at r = 1.08 m
Point HC at r = 0.81 m
Point HH at r = 0.52 mDrying near heater
Wetting from the
fully saturated rock
 
 
 
Figure 7. Simulated contour of liquid saturation 
in the bentonite buffer after 1,000 days 
of heating: Dark and light contours 
indicate wetting and drying, 
respectively 
 
 
 
TIME (Days)
R
E
LA
TI
V
E
H
U
M
ID
IT
Y
(%
)
0 500 1000
0
10
20
30
40
50
60
70
80
90
100
SIMULATED
MEASURED
Point HC
Point HH
Point HG
 
 
Figure 8. Simulated and measured evolution of 
relative humidity at points HG, HC and 
HH with locations shown in Figure7 
 
5.3 Results of stress 
    Figure 9 presents simulated contours of 
intermediate compressive-principal-stress at 1,000 
days. The figure shows that compressive stress 
caused by swelling pressure has developed at the 
drift wall, especially at the front end of the tunnel, 
where the bentonite blocks were first installed.  
    Figure 10 presents simulated and measured 
evolution of stress normal to the drift wall at two 
locations (E2G2 and B2G in Figure 9). The 
simulated stress began to develop as soon as the 
wetting commenced and increased to about 2 to 
2.5 MPa at 1,000 days. The measured stress 
indicates that the swelling stress might not have 
begun to develop until several months after heater 
turn-on. This delay in the development of swelling 
stress was a common observation at many 
monitoring points in the bentonite barrier at 
FEBEX.  
 
 
 
Point B2G
at drift wall
Point E2G2 at
side wall of drift
 
 
 
Figure 9. Simulated contour of intermediate 
principal stress in the bentonite buffer 
after 1,000 days of heating: dark 
contour indicates the highest 
compressive stress  (2 to 3 MPa), 
whereas light contour indicates the 
lowest compressive stress (0 to 1 MPa)  
 
 
 
TIME (Days)
S
TR
E
S
S
(M
P
a)
0 500 1000
0
0.5
1
1.5
2
2.5
3
MEASURED
SIMULATED
Point E2G2
Point B2G
 
  
Figure 10.  Simulated and measure evolution of 
radial stress at points E2G2 and B2G, 
with locations shown in Figure 9  
6 DISCUSSION 
    The general agreement between simulated and 
measured THM responses at FEBEX indicates that 
coupled THM processes are well represented in 
the ROCMAS code.  
   The good agreement between simulated and 
measured temperature indicates that thermal 
responses can be predicted with high confidence. 
This is a consequence of heat conduction being the 
dominant mode of heat transport. If the thermal 
conductivity and specific heat are accurately 
represented in the model, the temperature 
responses should be well predicted.  
   The evolution of the moisture content was 
reasonably well predicted both in trends and 
magnitudes. Moreover, results from the modeling 
and field measurements at FEBEX indicate that 
the presence of highly permeable Lamprohyres  
(Figure 3a) did not have a significant impact on 
the wetting of the buffer. This shows that the 
wetting of buffer was controlled by the hydraulic 
properties of the bentonite barrier with 
unrestricted water supply from the surrounding 
rock mass.  
   The evolution of swelling pressure in the buffer 
was generally underestimated during the first 
several hundred days. The measured delay in the 
swelling stress at FEBEX was probably caused by 
the existence of gaps between the bentonite 
blocks. It appears that the swelling stress in the 
buffer begun to develop after a few months when 
the gaps had closed. These gaps were not 
considered in our numerical model, and 
consequently the simulated swelling stress 
developed much earlier.  
 
 
7 CONCLUSIONS 
The numerical model ROCMAS was applied to 
predict coupled THM processes in a bentonite 
barrier at the FEBEX in situ test. The results 
indicate that numerical modeling can provide 
highly reliable predictions for temperature 
distribution, and reasonably reliable predictions 
for moisture flow and stress in a bentonite barrier. 
Moreover, field observations and modeling shows 
that resaturation of the buffer was controlled by 
the properties of the bentonite barrier whereas the 
permeability of the rock was sufficiently high to 
act as an unrestriced water source. Therefore, the 
wetting of the bentonite took place uniformly from 
the rock and was not impacted by the permeability 
difference between the Lamprophyres dykes and 
surrounding rock.   
    The evolution of stress in the bentonite barrier 
at FEBEX was affected by the existence of gaps 
between the pre-fabricated bentonite blocks. The 
swelling pressure did not develop until moisture 
swelling of the bentoninte blocks had closed the 
gaps completely.    
 
 
ACKNOWLEDGEMENTS 
   Reviews and comments by Hui-Hai Lui and Dan 
Hawkes, Lawrence Berkeley National Laboratory 
are much appreciated. Financial support was 
provided by a grant from the Swedish Nuclear 
Power Inspectorate (SKI).     
 
 
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Lloret A. & Alonso E.E. 1985. State surfaces for 
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Noorishad, J. & Tsang, C.-F. 1996. ROCMAS 
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A fully coupled three-dimensional THM analysis of the FEBEX in situ test with the ROCMAS code: prediction of THM behavior in a bentonite barrier

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A fully coupled three-dimensional THM analysis of the FEBEX in situ test with the ROCMAS code: prediction of THM behavior in a bentonite barrier

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