Fracture step structure: geometrical characterization and effects … · 2019. 1. 15. · 1995;...

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Engineering Geology 75 (2004) 107–127

Fracture step structure: geometrical characterization and effects

on fluid flow and breakthrough curve

N.D. Khanga,*, K. Watanabea, H. Saegusab

aGeosphere Research Institute, Saitama University, 255 Shimo-okubo, Saitama, Saitama-ken, 338-8570, JapanbTono Geoscience Centre, Japan Nuclear Cycle Development Institute, 1-64, Yamanouchi, Akeyo-cho, Mizunami, Gifu-ken, 509-6132, Japan

Received 16 June 2003; accepted 12 May 2004

Available online

Abstract

Groundwater flow and solute transport through fractured rock is highly responsive to the hydraulic anisotropy and

heterogeneity that are specific to every major fracture. A major fracture is modeled as the combination of some primal master

fractures and several splay fractures that branch out from primal master fractures: step structures (or jog parts). Step structures

are commonly observed along a major fracture on various scales. Master fractures were formed and developed by shear

movement while some splay fractures were formed by extension normal to their wall. This difference in fracturing process may

lead to a permeability difference between master fractures and splay fractures which seems to be one of the major factors

controlling flow and solute transport through the fracture networks due to its hydraulic anisotropic and heterogeneous features.

This study is composed of two major components: (1) identification and characterization of a step structure from borehole data;

(2) evaluation of effect of some idealized step structures on breakthrough curve by numerical simulations. The fracture data of

four 1000-m boreholes were used to make clear fracture patterns in the Tono area of Japan. Some major fractures were

identified using stereographic projection technique. On the basis of these results, several idealized models of a major fracture

having a step was constructed for the numerical study. The obtained results from numerical simulations clearly imply that

geometry of step structure plays an important role in flow and transport through the fracture networks.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Fractured rock; Step structure; Borehole, stereographic projection, dipole test; Numerical analysis

1. Introduction wastes. Since the 1960s, several research programs

Fluid flow and solute transport in a fractured rock

mass have been an important subject in civil engineer-

ing such as tunneling, dam construction, exploitation

of oil and gas reservoirs. In recent years, it has also

received increasing attention in the field of geological

disposal of hazardous waste such as radioactive

0013-7952/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.enggeo.2004.05.004

* Corresponding author. Fax: +81-48-855-1378.

E-mail address: [email protected] (N.D. Khang).

have been devoted to investigate the hydrogeological

conditions in the deep underground of basement rocks

in many countries in the world directed towards this

end. In Japan, the geological, hydrological, and me-

chanical conditions have been mainly studied in the

Tono area, and the Kaimashi mine by the Japan

Nuclear Cycle Development Institute (JNC) to reveal

the relation between geological conditions and ground

water flow (JNC, 1999). Fractures are known to be the

most important geological structures since they pro-

N.D. Khang et al. / Engineering Geology 75 (2004) 107–127108

vide pathways for fluid flow, and control the disper-

sion of pollutants into and through the subsurface. In

sparsely crystalline rock masses, it is thought that

groundwater flow system is mainly controlled by a

limited number of major fractures (Smellie et al., 1995;

Watanabe et al., 1997; Yoshida et al., 2000). The

investigations on the features of major fractures have

confirmed that there exist several step structures (jog

parts, fault zones), which formed by the combination

of master faults and secondary splay fractures, in a

major fracture (Nicolas, 1984; Mazurek et al., 1996;

Watanabe and Takahashi, 1995). Obviously, these step

structures are important to the groundwater flow

controlling behavior of the major fractures and the

fracture networks as well. There have been a number

of research works related to modeling fluid flow and

transport through a fracture network considering the

major fractures and fracture zones as the primary flow

pathways (Moreno and Neretnieks, 1993; Watanabe et

al., 1997; Molinero et al., 2002). However the general

geometry and the role of step structures in controlling

flow and transport is still in question because geolog-

ical modeling of the step structure has not been well

established.

In this paper, we present a technique to identify and

characterize/model major fractures having step struc-

tures using fracture orientation data, which has been

collected from four 1000-m boreholes in the Tono

area using the Borehole Television (BTV) technique.

Once the directions and sizes of a typical major

fracture are estimated, some idealized geometry mod-

els of a step structures are proposed basing on the

features of that major fracture. These geometry mod-

els are then used to study the effect of a step structure

on groundwater flow. Flow and transport of a conser-

vative non-sorbing tracer in a dipole test model are

simulated using a numerical model.

2. Modeling of step structures

Fig. 1 schematically illustrates fracture networks

on three different scales around a tunnel as described

by Mazurek et al. (1996) and Bossart et al. (2001). As

illustrated in Fig. 1b and c, a major fracture may

include some step structures in which fracture density

is very high in comparison with the surroundings. The

length and the width definitions of step structure used

in this study are also shown in Fig. 1c. The step

structure is the junction connecting two master frac-

tures. This part is also called as jog in the field of

geophysics (Scholz, 1990; Mcgrath and Davison,

1995; Sibson, 1996). Mazurek et al. (1996) and

Watanabe and Takahashi (1995) studied the fracture

system in the Äspö area of Sweden, and the Hinachi

and the Tono areas of Japan, and concluded that such

step structures are commonly found at various scales,

especially at the tunnel scale (scale of several meters

to several 10-m).

The step structures might be created and developed

by shear movement along pre-existing faults/joints.

The increasing displacement along a fault results in not

only the growth of the fault trace but also the linkage of

adjacent faults via splay fractures to form larger fault

zones, a process called segment linkage (Cartwright et

al., 1996). Martel and Pollard (1989) have studied in

detail the mechanics of development of such struc-

tures. In case of the slip along a single joint, which is

reactivated by shear movement, they point out that the

slip causes an antisymmetric pattern of compressive

stress fields at the fault end, and the splay cracks grow

antisymmetrically forward the decreased stress direc-

tion. In an idealized case of slip along a pair of faults,

they found that slip on a fault induces slip on the other

fault due to progressive changes in the normal and

shear stresses in the vicinity of the fault end. Because

the antisymmetric compressive stress is created at the

fault end, the splay cracks converge antisymmetrically

towards the corresponding fractures. As a result, a step

structure is created connecting the adjacent master

fractures.

In the field cases, the inhomogeneous and aniso-

tropic rock body yields a much more complex fracture

patterns than in idealized cases of slip along a single

fault or a pair of faults. Furthermore, slip does not

only occur along a single or a pair of faults but rather

than along an array of discontinuities of different

orientations, lengths and densities. Even though in

the complicated fracture system, Mazurek et al. (1996)

reported that the step structures can clearly be ob-

served. Martel (1990) reported several examples of

faults development in granitic rock of the Sierra

Neveda in California, where pre-existing discontinu-

ities are represented by a set of parallel faults.

A step fracture includes some different types of

splay fractures such as open fractures (i.e. tension

Fig. 1. Conceptual models of fracture geometries at three different scales: (a) regional scale; (b) meso-scopic scale; (c) block scale.

N.D. Khang et al. / Engineering Geology 75 (2004) 107–127 109

fractures), fractures filled with clay by long-term

water rock interaction or hydro-thermal alteration

(closed fractures), and fractures that are filled with

small rock fragments (fault-gauges). Groundwater

mainly migrates through the open fractures and the

fault-gauges, while fractures that are filled with clay

are more likely to act as a water barrier. These

characteristics contribute to the complicated features

of groundwater flow through step structure and frac-

ture network. However, their features have not been

clarified yet. For example, the proportion of open

fractures in a step structure, the relation among

orientations of open fractures, fault gauge filled frac-

tures, and closed fractures have not been well studied.

The direct observation of step structures appearing

in a borehole can be effective for to study the

geometry in detail. The Borehole Television (BTV)

appears to be the most direct and effective method for

getting information on geometry, including the size,

density, and orientation of fractures in the boreholes.

The geometry of fractures observed along four 1000-

m boreholes were described in detail in the Tono area

of Japan. The data was examined to investigate the

geometry of step structures developing in this area.

Then the influence of step structures on groundwater

flow in some idealized step structures was studied.

3. Geological conditions in the Tono area

3.1. Site description and borehole TV data

In order to investigate the geological, hydrogeo-

logical and chemical features in the deep under-

ground, JNC has drilled four 1000-m-deep vertical

boreholes (AN-1, MIU-1, MIU-2, MIU-3), one 400-

m-deep borehole (AN-3), and one 800-m-deep in-

clined borehole (MIU-4) in the MIU site of the Tono

area. The inclined borehole MIU-4 was drilled to

check the orientation of vertical structures. Fracture


data from boreholes excluding MIU-4 and AN-3 were

used in this study. Fig. 2 shows the location of those

boreholes.

Fig. 3 shows a schematic geological cross-section

of the Tono area (Saegusa and Suyama, 2000). The

basement of this area is composed of Cretaceous

crystalline rock (Toki granite) overlain unconformably

by Tertiary sedimentary rock (Mizunami Group). The

Mizunami Group is stratigraphically divided into the

Toki lignite bearing formation and the Akeyo forma-

tion in ascending order. The Toki granite is divided

lithologically into two facies: biotite granite and felsic

Fig. 2. Location of MIU site and

granite. The weathered zone at the top of granite was

formed before the deposition of tertiary sedimentary

rock. The area is intersected by the Tsukiyoshi fault

having an EW strike and dipping 80j toward thesouth. The area is characterized as hill type topogra-

phy with forest covering. Saegusa et al. (1997) inves-

tigated the regional groundwater system in a area of

approximately 30� 30 km including the MIU site asshown in Fig. 2b. The results indicate that the ground-

water flow in the area is roughly from north to south.

JNC has monitored pore water pressure fluctuation

since 1990 in several boreholes including the 1000-m-

boreholes, Tono area, Japan.

Fig. 3. Schematic geological cross-section of the Tono area.


deep boreholes. In addition to the pore water pressure

measurements, meteorological data, river discharge,

soil moisture, etc., have been continuously measured.

Fracture geometry on every 1000-m borehole wall

was investigated using Borehole Television. As men-

tioned in Section 2, fractures are basically classified

into three types: open fractures, fault-gauges, and

clay-filled fractures. However, due to the high-pres-

sure circulation of drilling fluid, fault-gauge is usually

washed out. As the results, it is difficult to distinguish

an open fracture from fault-gauges using borehole

data. For this reason, fractures are classified into

two types: open fractures and closed/filled fractures.

In the other words, the fault-gauges are identified with

the open fractures.

Several hydraulic tests have been conducted to

determine the permeability of the rock basement along

the four boreholes by JNC. The test intervals are not

the same, but are approximately 2.5 m for the tests in

borehole AN-1, 6.5 m in boreholes MIU-1 and MIU-

2, and 25 m in borehole MIU-3, respectively. The data

from these hydraulic tests together with the fracture

geometry data observed along the boreholes can be

used to study the potential relation between the

geologic structure and hydrological properties. Fig.

4 displays the distribution of the measured hydraulic

conductivity versus the number of all fractures (Fig.

4a, d, g, and j), versus the number of open fractures

(Fig. 4b, e, h, and k), and versus the total apertures of

the open fractures (Fig. 4c, f, i, and l) in the

corresponding test interval at four boreholes. All

plotted data are taken from the tests conducted in

granitic rocks. However, the test intervals are not

identical even in a borehole, so that only the data of

tests with similar intervals are compared together in

the analysis.

Qualitatively, it is expected that there might be a

weak correlation between fracture density and hydrau-

lic conductivity. As shown in Fig. 4i and l, the data

from the tests in boreholes MIU-2 and MIU-3 sug-

gests two weak correlations between hydraulic con-

ductivity and the number of total fractures as

expected, where the common trending is that the

hydraulic conductivity is proportional to the number

of total fractures (i.e. fracture density). But there is no

clear correlation that can be found for the data in AN-

1 and MIU-1 (Fig. 4a and e). It is also expected that

the hydraulic conductivity can be proportional to the

number of open fractures as well as the total apertures

of open fractures in a test interval. However, the data

plotted in Fig. 4b, c, f, g, l, and m suggests no such

expected correlation. There may be several reasons:

some of the counted open fractures are created due to

the drilling work and just existing in the vicinity of the

boreholes; some of the open fractures are just ‘‘open’’

locally near the borehole wall but mainly sealed at the

other locations; some open fractures are local fractures

only as they does not connect to the major conducting

Fig. 4. Relation between hydraulic conductivity and number of open fractures (a, d, g, and j), total fractures of all types (b, e, h, and k), and total

open fracture apertures in each hydraulic test interval (2.5 and 6.5 m interval in AN-1 and MIU-3 boreholes, respectively, and 25 m interval in

MIU-1 and MIU-2 boreholes) (c, f, i, and l).



feature network; or some ‘‘open’’ fractures are actu-

ally fault-gauges. Furthermore, it should be recog-

nized that the permeability of open fractures is much

dependent on their apertures: a larger aperture results

in a higher permeability. Thus in some intervals, the

number of open fractures is not many but the perme-

ability measured at those location is still high due to

the larger apertures (e.g., intervals at 78.9 and 266.5 m

depths of the borehole AN-1 as shown in Fig. 5), and

vice versa. It may be interpreted that the aperture of a

fracture observed at the boreholes does not represent

the average feature of the whole fracture, but local

feature. This implies the complication in observing/

determining the fracture aperture in the field.

3.2. Geometry and orientation of fractures

The stereographic projection technique is a power-

ful tool to represent the fracture orientation, where a

Fig. 5. Hydraulic conductivity distribution along borehole AN-1 (a), th

distribution (c).

fracture orientation is represented by its pole. (Billings,

1972; Price and Cosgrove, 1991). The equal-area

lower-hemisphere projection is adopted in this study.

As the fracture distribution is influenced by the orien-

tation of the borehole, the correction must be per-

formed considering the angle between fracture

direction and borehole direction.

In a step structure, the splay fractures are tend to

develop in the direction normal to shear movement (as

shown in Fig. 12b), thus the poles of fractures in the

step structure may be identical and arranging on a

great circle in the stereographic projection. By exam-

ining carefully the distribution pattern of fracture

orientations displayed on stereographic projections,

step structures and then major fractures, can be

identified.

Fig. 6 shows the orientation of all fractures ob-

served in the four boreholes. These orientation dis-

tributions were corrected considering the borehole

e corresponding open fracture distribution (b) and total fracture

Fig. 6. Fracture orientations at MIU site, Tono area: equal area lower hemisphere projections of poles to fracture planes (a) Borehole AN-1, (b)

Borehole MIU-1, (c) Borehole MIU-2, and (d) Borehole MIU-3.


directions. The total number of fractures (open frac-

tures and closed fractures) of boreholes AN-1, MIU-1,

MIU-2, and MIU-3 are 1364, 1530, 1801, and 2350,

respectively. The high-density spots and the great-

circle-type distributions on the stereographs indicate a

regularity of the fracture system developing in this

area. The projection plots above, however, are com-

posed of poles of several major fractures, splay

fractures in some step structures as illustrated in Fig.

7. It is impossible to identify individual step structures

and major fractures in such plots. Therefore stereo-

graphic projections in smaller sections, in which

fracture steps can be well observed, were studied.

In order to identify step structures appearing along

a borehole, three types of stereographic analysis were

Fig. 7. Illustration of possible patterns of major fractures.

performed as shown in Fig. 8. First, stereographic

projections of consecutive 5 m lengths along the

boreholes were made for a rough interpretation of

fracture orientation distribution patterns. Because

fracture density of a fracture step is much higher than

surroundings, only projections containing more than

10 fractures were selected. Next, projections of 5 m

section sliding 1 m were used to make clear the

gradual changes in the fracture orientation distribution

patterns. As illustrated in Fig. 9, a potential step

structure pattern can be identified at 303–310 m

section of the borehole MIU-1 as shown by the great

circles. Finally, stereographs of 1 m sections were

made, which were then used to estimate the major

fracture width as defined in Fig. 1c. In the example of

the 1-m section projections shown in Fig. 10, the fault

step may exist from 154 to164 m below ground

surface from the similar pattern in projections, and

10 m in length along the borehole.

Several fracture orientation distribution patterns, or

in the other words, several potential step structures

were observed in the boreholes from the stereographic

projection analysis above. Fig. 11 shows some typical

observed patterns, in which the patterns in Fig. 11a–d

are of individual fracture zones (clear patterns) while

those in Fig. 11e–h are though as the fracture inter-

sections (composite patterns). Table 1 presents the

obtained fracture zone widths of the step structures

having the same pattern as shown in Fig. 11b (in the

following, this pattern is named as pattern A) at the

different sections. Obviously we can only determine

the fracture zone width in the vertical direction using

Fig. 8. Procedure for major fracture selection.


the stereographic projection. In order to determine the

real fracture zone width (see Fig. 1c for definition), it

is necessary to know the general direction of the major

Fig. 9. Example of checking the gradual changes in orientation distribution

of the borehole MIU-1.

fracture, which is difficult to determine using borehole

data only, and thus needs further information from

field investigations. It can be assumed that when the

using sliding-sections projections for fractures at section 302–311 m

Fig. 11. Examples of fracture orientation distribution patterns: (a, b, c, and d) clear patterns; (e, f, g, and h) patterns of fracture intersections.

Fig. 10. Example of 1-m section projections for fractures at section 154–164 m of the borehole MIU-1.


Table 1

Fracture zone width and fracture density of the pattern A in the boreholes

Borehole No. Section location Length Dip Width Number of Fracture

Top

(mbgl)

Bottom

(mbgl)

(m) (degree) (m) fractures in

section

density

(m� 1)

(1) (2) (3) (4) (5) (6) (7) (8) (9)

AN-1 1 61 66 5 75 1.29 10 2.0

2 263 272 9 75 2.33 15 1.7

3 411 419 8 75 2.07 15 1.9

MIU-1 4 90 102 12 75 3.11 24 2.0

5 137 148 11 75 2.85 20 1.8

6 154 165 11 75 2.85 28 2.5

7 276 280 4 75 1.04 11 2.8

8 303 310 7 75 1.81 21 3.0

9 316 325 9 75 2.33 21 2.3

10 592 598 6 75 1.55 15 2.5

11 649 658 9 75 2.33 22 2.4

12 879 890 11 75 2.85 35 3.2

13 935 942 7 75 1.81 26 3.7

14 979 982 3 75 0.78 8 2.7

MIU-2 15 208 213 5 75 1.29 14 2.8

16 319 323 4 75 1.04 12 3.0

17 929 935 6 75 1.55 14 2.3

18 937 945 8 75 2.07 23 2.9

MIU-3 19 136 140 4 75 1.04 9 2.3

20 144 148 4 75 1.04 15 3.8

21 187 194 7 75 1.81 16 2.3

22 299 304 5 75 1.29 9 1.8

23 571 576 5 75 1.29 10 2.0

24 605 610 5 75 1.29 16 3.2

25 641 649 8 75 2.07 20 2.5

26 676 681 5 75 1.29 13 2.6

27 779 783 4 75 1.04 14 3.5

28 809 819 10 75 2.59 21 2.1

29 823 846 23 75 5.95 53 2.3

30 870 880 10 75 2.59 72 7.2

31 921 926 5 75 1.29 29 5.8

32 953 965 12 75 3.11 28 2.3

Average 1.96 2.79


same orientation pattern as in the field is found in the

stereographs of fractures in borehole, the direction of

the major fracture is the same as the one that observed

in the field investigation.

Fig. 12a illustrates an example of a step structure

of about 30 cm wide observed at an outcrop in the

Tono area. Many fractures orienting in different

directions exist, where the master fractures strike

nearly E–W. The general view of geometry of that

step structure and mechanism can be idealized as

shown in Fig. 12b. The stereographic projection in

Fig. 12c shows the orientation distribution of those

fractures, where it can be seen that the poles of the

fractures roughly arrange on a great circle. In this

case, most of the fractures dip vertically so that the

great circle is close to the circumference. The pattern

A as mentioned above is thought be similar to this

pattern, although the dips of fractures are not verti-

cal. From the study on lineament distribution and

surface inspection in this area, Saegusa et al. (sub-

mitted for publication) was confirmed that the dip of

such E–W sub-vertical fractures are in range of 70–

80j. Finally, the pattern A is roughly considered tobe the fracture orientation distribution of step struc-

Fig. 12. Outcrop in Tono area: (a) the sketch of the outcrop; (b) schematic view; (c) orientation of fractures in the outcrop.


tures in a EW75N major fracture. As a result, the

real fracture zone width of such pattern now is now

able to be estimated for every section as shown in

column 7 of Table 1, where the averaged width is

about 2 m over 32 different sections. The fracture

density at every section was also estimated (columns

8 and 9), in which only the fractures arranging on

each great circle were counted. The overall averaged

fracture density as shown, is approximately 3 m� 1.

It is worth noting that the direction of the fracture

pattern A is almost the same as the Tsukiyoshi fault,

which is the largest fault in the Tono area. In the

other words, the pattern A seems to be the most

fracture pattern of fracture system developing in the

area.

Hypothetically, the master fracture directions of

the other pattern also can be determined in similar

way as above. Unfortunately, as the Tono area is

sedimentary and forest covered, not so many out-

crops of those patterns are available for observation.

In the following, since the fracture pattern A

appears to be the clearest observed pattern, its

features are used in modeling some idealized geom-

etry models for study the effects of step structures

on groundwater flow as shown in the following

section.

The stereographic projection also can be used to

study the relation between open fractures and closed

fractures in a fracture step, as well as the orientation

distribution of open fractures since open fractures are

important to groundwater flow controlling behavior of

the step structure. Such information is useful to have a

rough understanding about the heterogeneity and the

anisotropy of a step structure. A comparison between

orientations of all fracture directions and open fracture

directions suggests that step structures can be divided

into several patterns as schematically displayed in Fig.

13, which can be further classified into two main

categories: (1) step structure with open fractures, and

(2) step structure without any open fracture.

3.3. Idealization of step structure

It is obviously that the reality of a step structure is

possibly very complicated. In order to investigate the

effect of such structure to flow and transport using a

numerical model, simplifications are needed in order

to reduce the natural complexity and variability. In

this paper, simplifications and assumptions relate to

the geometry, and to heterogeneity and anisotropy of

step structures. Since hydrothermal alteration has

suffered fractures in rock masses in Japan (JNC,

Fig. 13. Example of typical distributions of closed and open fractures in step structures in MIU site (all step structures illustrated here are

belonged to the fracture pattern A).


2000a), a fracture is idealized as a plane which have a

width and a conductivity (see Fig. 15b). In the other

words, a fracture is considered as a continuum porous

medium itself.

Fig. 14 shows two-dimensional view of three

geometry models of the step structure (model 1,

model 2, and model 3) proposed for numerical anal-

Fig. 14. The cross-sections of the idealize

ysis of flow. As mentioned in Section 3.2, the geo-

metric parameters of these models were assigned

using the averaged parameters of the fracture pattern

A. As the result, the fracture zone width of 2 m was

adopted, while the spacing of the splay fractures was

assumed to be 3 m� 1 as same as the averaged fracture

density of the pattern A. However, the length of the

d models of fracture step geometry.


step was difficult to determine. In this study, a length

of 4 m (two times of the fracture zone width) was

assumed. In addition to the master fractures and

connecting splays as described in the previous sec-

tions, some minor fractures parallel to master fractures

(parallel fractures) are assumed to exist. All fracture

planes (master fracture, splay fracture, parallel frac-

ture) were assumed to have the same width of 0.02 m

based on the most frequently observed width of

altered zone at the Kamaishi mine (JNC, 2000a).

The geometry models 2 and 3 were used together

with model 1 to investigate the role of fracture step

geometry in controlling flow and tracer movement.

Although there remain some uncertainties in modeling

process, it is thought that the general effect of a step

structure on flow and tracer movement can be studied

by these idealized geometry models.

4. Numerical simulation of flow and tracer

transport

4.1. Numerical model

A 3-D numerical model was used to investigate

the fluid flow and tracer transport through the

fracture step structure. The model was developed

in decoupled manner in which the flow solution are

obtained first and then used as input parameters for

transport calculation. The model is able to simulate

flow and solute transport in a heterogeneous and

anisotropic environment. For completeness, the gov-

erning equations used in the model are listed in this

section.

According to JNC (2000b), the groundwater table in

Japan is generally near the surface, which implies that

flow in the rock mass is predominantly saturated.

Therefore it was assumed that flows in the all simula-

tion cases are saturated. The saturated flow equation

written with total head (h) as the independent variable

is:

B

BxiKij

Bh

Bxj

� �¼ C Bh

Btþ S ð1Þ

whereKij is the saturated hydraulic conductivity tensor,

C is the storage coefficient, S is a sink/source term.

The governing equation for solute transport,

known as the advection–dispersion equation, can be

written as:

B

BxiDij

Bc

Bxj

� �� vi

Bc

Bxi� kcRd þ

CVS

ne¼ Rd

Bc

Btð2Þ

where c is concentration and CV is the known sourceconcentration, Dij is dispersion coefficient component,

vi is flow pore velocity in xi direction, Rd is retardation

factor, k is the first-order decay coefficient, and ne iseffective porosity. The dispersion coefficient is calcu-

lated from

Dij ¼ aijmnvmvn

v

� �þ Dm ð3Þ

where all components of aijmn are zero, except foraiiii = aL, aiijj = aijji = (aL� aT)/2 for i p j; aL and,aTare longitudinal and transverse dispersivities, respec-tively; Dm is the fluid molecular diffusion coefficient.

The model was developed based on the finite

element method using a hexahedral grid. The grid

divisions of step structure models will be discussed

later in detail. The flow equation was discretized by

the classic Galerkin scheme while the Streamline

Streamline Upwind Petrov–Galerkin (SUPG) (Zien-

kiewicz and Taylor, 1998; DeBlois, 1995) scheme was

applied for advection–dispersion equation in order to

prevent the numerical solution from oscillating in case

of dominant advection. In the SUPG formulation used

herein, the Brooks and Hughes (1982) type weighting

function can be written as:

WI ¼ NI þ s viBNI

Bxi

� �¼ NI þ NV ð4Þ

where s is defined (Christie et al., 1976) as

s ¼ 12

cothðaÞ � 1a

� �l

NvN

� �ð5Þ

where V is the global velocity scale, NvN is the localvelocity scale, h is the global length scale, l is the

local length scale, and D is the dispersion coefficient.

The coefficient matrices of the system of linear

algebraic equations resulting from discretization of the

flow equation and the transport equation are symmet-

ric and asymmetric, respectively. A preconditioned

conjugate gradient solver (Behie and Vinsome, 1982)

Fig. 15. Hydraulic nature of a step structure: (a) nomenclature;

(b) idealization of a fracture.


is used for the flow equation while the transport

equation is solved by ORTHOMIN (preconditioned

conjugate gradient square) solver with the use of

incomplete lower/upper preconditioning (Behie and

Forsyth, 1984). The model was verify by comparison

the calculation results to analytical solutions for

several special test cases of porous medium geometry,

properties, and boundary conditions, such as the

analytical solution achieved by Leij et al. (1991) for

solute transport in three-dimensional semi-infinite

porous media with rectangular source. Due to the

limitation of space, the discussion on the verification

and validation work is not presented in this paper.

4.2. Model parameters

4.2.1. Hydraulic conductivity

JNC (2000b) has made a comprehensive report on

hydraulic conductivity in deep underground rock

masses in Japan based on literature data and measure-

ments in the Tono area and Kamaishi mine. According

to their results, the hydraulic conductivity of a fault

filled with clay (closed/filled fracture) is generally in

the order of 10� 8 to 10� 5 m s� 1, whereas that of a

fault-gauge filled fracture/open fracture is typically in

the order of 10� 6 to 10� 3 ms� 1. The hydraulic

conductivities of step structures in this study are

assigned by these values.

The hydraulic nature of a step structure is defined

(see Fig. 15). The ‘‘direction of the step structure’’ is

the direction normal to shear movement. The anisot-

ropy of a fracture is presented by an orthotropic

conductivity tensor with conductivities along the

principal directions x1, x2, and x3 are k1, k2, and k ,

respectively. For a fracture, x1- and x2-directions are

parallel to the fracture plane while x3-direction is

normal to the fracture plane. For all fractures, x1 is

the direction of the step structure.

The possible relationship between three prin-

cipal components can be k1 = k2 = k3, k1 = k2 > k3, or

k1 > k2 > k3. The average hydraulic conductivity of

master fractures, splays, and minor fractures parallel

to master fractures (average over ki, ki, and k3 for a

given fracture) are represented by symbols km, ksp,

and kp, respectively. The concept of heterogeneity in

this paper implies a difference in the permeabilities

of master fractures (km), splays (ksp) and parallel

fractures (kp). By changing the combination of k1, k2,

k3, km, ksp, and kp values, all most types of step

structures can be presented. In this study, some

examples of analyses were performed to check the

effect of those values.

4.2.2. Macroscopic dispersion length

Numerous studies have been conducted on disper-

sion length in heterogeneous rock masses. Most of the

results from those studies have led to the conclusion

that the dispersion length increases with travel distance.

The apparent increase in dispersion length can be

caused by channeling and by various interaction me-

chanics with the rock, e.g., matrix diffusion (Bear et al.,

1993). It was reported by JNC (2000a) that the longi-

tudinal dispersion length for travel distances of 10–

1000 m was assumed to be 1/10 of the travel distance,

based onmeasurements in fractured rock by Neretnieks

(1985) and Gelhar (1987). Fig. 16 shows the relation-

ship between longitudinal dispersion length (aL) andtravel distance (L) obtained byGelhar et al. (1992) from

the review of the measurement data for 59 sites.

According to this figure, highly reliable longitudinal

dispersion lengths are distributed around 1/10 and

range between 1/100 and 1/1 of the evaluated distance.

The line aL= 0.017� L1.5 represents the linear regres-sive relationship obtained by Neuman (1995) from

field and laboratory measurements with travel distance

Fig. 16. Relationship between longitudinal dispersivity aL and scaleL, after Gelhar et al. (1992), Neretnieks et al. (1982), and Cliffe et

al. (1993) (JNC, 2000b).


in between 10 cm to 3.5 km. It is worth noting that the

macroscopic dispersion lengths derived from this equa-

tion are in the order of 1/10 of the evaluated distances in

the range 10–100 m (JNC, 2000a). Based on these

observations, the longitudinal dispersivity used in this

study is chosen as 1/10 of the travel distance. The

transverse dispersion length is usually much smaller

than longitudinal one, and is assumed to be 1/100 of the

longitudinal dispersivity for simplicity.

4.3. Numerical simulation: effects on breakthrough

curve in dipole test problem

To investigate the effects of the step structure on

flow and tracer transport, numerical analyses have been

conducted for the well-known dipole test problem (see

Fig. 17) which is a method commonly used to study the

nature of flow paths in geological media. In the model

domain, the injection well is located on one side of the

step structure, and the pumping well is located on the

other side. The distance between the two wells is set as

10 m considering actual in situ test data (Mark and

Kemakta, 1999). It was assumed that the hydraulic

head at some distance, roughly 20–25 m, from the

‘‘assumed experiment site’’ was unaffected by the

pumping. The assumption was used as a criterion to

decide the dimensions of the model domain.

Table 2

Numerical simulation cases

Running casea Hydraulic conductivity (� 10�5 m/s)Master fractures (km) Splay fracture

k1 k2 k3 k1 k2

I (km= ksp = kp) 1.0 1.0 1.0 1.0 1.0

II (km< kpV ksp) 1 1.0 1.0 1.0 10+1 10+

2 10+1 1.0 1.0 10+2 10+

3 10+1 10+1 1.0 10+2 10+

III (kp < ksp < km) 1 10+1 10+1 10+1 1.0 1.0

2 10+2 10+1 10+1 10+1 1.0

3 10+2 10+1 10+1 10+1 10+

IV-a (km= kp = ksp) 1 10+1 10+1 10+1 10+1 10+

2 10+1 10+1 10+1 10+1 10+

3 10+1 10+1 10+1 10+1 10+

IV-b (km< kp < ksp) 1 10+1 1.0 1.0 10+2 10+

2 10+1 1.0 1.0 10+2 10+

3 10+1 1.0 1.0 10+2 10+

V (km< kp < ksp) 1 10+1 1.0 1.0 10+2 10+

2 10+1 1.0 1.0 10+2 10+

a Cases I, II, III, and IV use the same boundary conditions of no flow

Based on the geometry and hydrological models

illustrated in Figs. 14 and 15, several simulation cases

using different sets of hydrogeological properties of

fractures were performed (see Table 2) to successively

make clear the role of permeability heterogeneity,

Notes

s (ksp) Parallel fractures (kp)

k3 k1 k2 k3

1.0 1.0 1.0 1.0 –1 10+1 10+1 10+1 10+1 geo. model 11 10+1 10+2 10+1 10+1 –1 10+1 10+2 10+1 10+1 –

1.0 1.0 1.0 1.0 –

1.0 10+1 1.0 1.0 –1 1.0 10+1 10+1 1.0 –1 10+1 10+1 10+1 10+1 geo. model 11 10+1 10+1 10+1 10+1 geo. model 21 10+1 10+1 10+1 10+1 geo. model 31 10+1 10+2 10+1 10+1 geo. model 11 10+1 10+2 10+1 10+1 geo. model 21 10+1 10+2 10+1 10+1 geo. model 31 10+1 10+2 10+1 10+1 no flow boundary1 10+1 10+2 10+1 10+1 fixed head

at boundaries.

Fig. 17. An example of dipole test calculation around an ‘‘assumed experiment site’’: piezometric head contours and flow pattern (no flow

boundary).


fracture geometry, and boundary condition to flow

and tracer transport. Two types of boundary condi-

tions were employed: a no flow boundary and a fixed

head boundary. The no flow boundary means the

hydraulic gradient at the boundary is assumed equal

to zero while in the fixed head boundary assumption,

head values at the boundary are kept constant. The

injection rate in all cases was equal to the pumping

rate of 50 ml/min. The tracer injection was assumed to

be a pulse function Co= 10e� t, where Co is the solute

concentration (ppm), t is the time (day) (see Fig. 18).

As the injection rate was equal to the pumping rate,

and there was no additional source/sink, flow was

considered steady, and only transport is transient. In

Fig. 18. Tracer pulse injection in dipole test models.

other words, after the flow calculation reached a

steady-state, the tracer transport calculation (tracer

injection) was started. Due to these conditions, the

effect of storage of fractures and source/sink term on

breakthrough curves was not discussed in this study.

The zero gradient condition of concentration was

applied to tracer transport at boundaries. The numer-

ical analysis was conducted for a conservative non-

adsorbing tracer. Matrix diffusion was not considered

in the analysis process.

As mentioned, the numerical simulations were per-

formed using the hexahedral grids for all geometry

models. The grids were generated in the manner that

they are finer near the ‘‘ assumed experiment site’’ and

coarser near the boundaries (Fig. 17). Each fracture was

divided into only one element for its thickness dimen-

sion. This means that the flow in a fracture is locally

two-dimensional in general, and fully three-dimension-

al only at the fracture intersections.

4.3.1. Effect of permeability heterogeneity

As mentioned in Section 4.2.1, permeability het-

erogeneity describes the hydraulic conductivity differ-

ences among km, kp, and ksp. As shown in Table 2,

three general cases I (km= ksp = kp), II (km< kpV ksp),and III (kp < ksp < km) are used to study the effects of

permeability heterogeneity using the same geometry

model 1.


In case II, the simulations was performed for the

case that the master fractures have lower permeabil-

ities than the step part for all sub-cases (II-1, II-2, and

II-3). Each fracture is homogeneous and isotropic

(k1 = k2 = k3) in sub-case II-1, where the permeability

of the splay and the parallel fractures is one order

higher than master fractures. The permeability in the

direction of step structure (k1) in sub-case II-2 is one

order higher than in sub-case I-1 for all fractures. In

sub-case II-3, the permeability of splay and parallel

fractures are the same as in sub-case II-2 while the

Fig. 19. Effects of heterogeneity and anisotropy on breakthrough

curves.

permeability in shear direction (k2) of master fractures

is one order higher. The breakthrough curves of tracer

at the pumping well obtained from three simulation

cases are shown in Fig. 19a. The tracer reached the

pumping well earliest in sub-case II-1 and latest in

sub-case II-2. The order of concentration peak reach-

ing time is the same. The peak is highest in sub-case

II-1 and lowest in sub-case II-2. The transit time of the

tracer is thus shortest in sub-case II-1 and longest in

sub-case II-2. In other words, the overall diffusion

effects in sub-cases II-1 and II-3 are much greater than

in sub-case II-2. This results can be explained as

follows: the increase of k1 components in sub-case

II-2 results in the more tracer spreading in direction of

the step structure toward boundaries before converg-

ing to the pumping well. This leads to the later arrival

time, the longer transit time, and the lower concen-

tration peak. Contrarily, the increase of k2 component

of the master fractures makes the tracer from the

injection well move faster toward the step structure

and then to the pumping well, thus results in the

earlier arrival time, the higher peak, and the shorter

transit time.

In the inverse case (case III), the permeabilities of

the master fractures are higher than the splay and

parallel fractures (kp < ksp < km). Similar to sub-case II-

1, each fracture in sub-case III-1 was considered

homogeneous and isotropic, but the permeability of

the master fractures is one order higher than the splay

and parallel fractures. The k1-components in sub-case

III-2 are one order greater than in sub-case III-1 for all

fractures. The k2-components of the splay and parallel

fractures in sub-case III-3 are one order greater than in

sub-case III-2 while the permeabilities of the master

fractures are the same. The results shown in Fig. 19b

indicate that, similar to case II, the increase of k1-

components in sub-case III-2 results in a later arrival

time, a lower concentration peak, and a longer transit

time. The higher permeability in the shear direction of

the splay and parallel fractures also make the tracer

move more quickly from the injection well through

the step structure to the pumping well. This indicates

the strong effects of the step structure part on the

spreading pattern of tracer. Fig. 19c, in which the

breakthrough curves of three cases km < kpV ksp (lineI-1), km= kp= ksp (line II-1) and kp < ksp < km (line III-

1) are compared, shows the effects of the fracture step

part on breakthrough curves more clearly.

Fig. 21. Effects of boundary condition to solute transport solution.


4.3.2. Effect of geometry

To access the effect of the step structure geometry

on breakthrough curve, the numerical simulations

were conducted for three geometry models (Fig. 14)

using the same hydrogeological properties and trans-

port parameters. As shown in Fig. 20a, in the case of

homogeneous and isotropic filled materials (km =

kp = ksp), the reduction in the number of the splay

fractures in sub-case IVa-2 leads to faster arrival time

and obviously reduces the transit time of tracer in

comparison with sub-case IVa-1. A similar result was

obtained for sub-case IVa-3 with the additional re-

moval of the parallel fractures. This indicates that the

more complicated geometry will result in greater

macroscopic dispersion. This result is one more time

indicated in sub-case IV-b (Fig. 20b) in which the

heterogeneity was introduced into calculation

(km< kpV ksp). This agrees with the results obtainedby Khang and Watanabe (2002) from the two-dimen-

sional scale analysis. It can be concluded that geom-

etry is one of the most important factor in controlling

flow and transport through the fracture network.

Fig. 20. Effects of step structure geometry on breakthrough curves.

4.3.3. Effect of boundary conditions

To study the effect of boundary condition, the

results of numerical solutions with the same geometry,

hydrogeological and transport properties, but with

different boundary conditions were compared. As

shown in Fig. 21, the concentration of tracer in the

case of fixed hydraulic head at the boundary (V-2) is

relatively less than in the case of the no flow boundary

(V-1). The reason is that some part of the tracer mass

was transported out the model domain at some

boundary parts near the injection well. At the same

time, the tracer is diluted by the flow from outside of

the model domain at some boundary parts near the

pumping well. However, the difference between the

breakthrough curves in the two cases is not much.

This means that the boundaries of the proposed

models are far enough from the ‘‘assumed experimen-

tal site’’ so that their effect to numerical solutions is

ignorable.

5. Conclusions

A methodology for identifying step structures

based on the analysis of the borehole image process-

ing orientation data using stereographic projection

technique has been proposed. The methodology has

been applied to the fractured rock in the Tono area

where several 1000-m-deep boreholes were drilled.

The orientation of major fractures having step struc-

tures was determined by fieldwork and stereographic

projection analysis. The average size of a common

type of step structure was also estimated, e.g. the

width of 2 m for several major fractures of which


direction is almost same as the biggest fault in the

area. On the basis of the geological study, three

idealized models of step structure for the analysis

of flow and transport were proposed. Numerical

modeling was then used to carry out the role of step

structure in controlling groundwater flow and trans-

port. For this purpose, a three-dimensional numerical

model has been developed and then applied to

idealized models of fracture containing a step struc-

ture. Flow and transport of a conservative non-

sorbing tracer in a dipole test problem was simulated

in which tracer was injected at an injection well and

the breakthrough curves were calculated at the

pumping well. The calculation was conducted for

several cases of different sets of hydrogeological

properties in order to investigate the effects of

permeability heterogeneity and anisotropy. It was

found that the permeability heterogeneity is an

important controlling factor in flow and transport

behaviors. The anisotropy of master fractures and

splays also plays a key role. To study the effects of

step structure geometry on breakthrough curves, the

calculation was also performed for three geometry

models using the same initial and boundary condi-

tions. The results indicated that the step geometry

significantly influences on groundwater flow and

tracer movement; it is an important factor for esti-

mating the overall diffusion effects. Based on the

results above, it is concluded that the role of step

structure in controlling flow and transport is very

important and should not be ignored. However, there

remain many open questions for future research such

as the anisotropy characteristics of a fracture, rela-

tionship between characteristics and shear move-

ment. These unknowns must be studied by in-situ

tests.

Acknowledgements

The authors are grateful to Japan Nuclear Cycle

Development Institute for providing and permission

for publishing their data. Many thanks are given to

Mr. Morita of the Saitama Package-D, Japan for his

suggestions and providing the software used to

analyze stereographic projection. We would like to

express our sincere thanks to Dr. Christine Doughty

and an anonymous reviewer for their constructive

comments and suggestions for the enhancement of the

original manuscript.

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Fracture step structure: geometrical characterization and effects on fluid flow and breakthrough curveIntroductionModeling of step structuresGeological conditions in the Tono areaSite description and borehole TV dataGeometry and orientation of fracturesIdealization of step structure

Numerical simulation of flow and tracer transportNumerical modelModel parametersHydraulic conductivityMacroscopic dispersion length

Numerical simulation: effects on breakthrough curve in dipole test problemEffect of permeability heterogeneityEffect of geometryEffect of boundary conditions

ConclusionsAcknowledgementsReferences

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