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CHARACTERISTICS OF WATER FLOW IN JOINTED ROCK MASS
V.N.Zhilenkov
The B.E.Vedeneev All-Russian Research Institute of
Hydraulic Engineering
21 Gzhatskaya St., St.Petersburg 195220, Russia
Phone: (812) 535-88-85, Fax.: (812) 535-67-20,
E-mail: uu gidro @ gidro, odusz elektro.ru
Abstract
The
paper discusses the methods applied to and the results obtained from
experimental investigations performed in laboratory to study basic
regularities associated with the steady
flow of water (or any Newtonian fluid) in fissures and cracks with walls of
roughness characteristic for rock.
The
method of determining morphological parameters of roughness and the
experimental facility used are described. The experiments enabled the initial
data on water flow through cracks of various openings to be got in the form of
gradient-velocity curves. These data analyzed and generalized made it possible
to establish the following hydraulic characteristics of both laminar and
turbulent fluid flows in jointed rock: flow velocities, head gradients,
Reynolds numbers, as well as their critical values corresponding to the regimes
transition. The effect of wall roughness on the hydraulic resistance of cracks
is estimated quantitatively, this effect being particularly marked for small
(of a fraction of a millimeter) openings, when the water permeability of rock
can vary directly with the fourth degree of crack opening. In this
connection approximate calculation of water permeability of jointed rock under
an external compressive load is given
as an example of investigations important for practical purposes.
Keywords:
Geohydraulics, rock permeability, joint
morphology, flow simulation, flow parameters
1. Initial morphological
parameters of cracks in rock
Practically all the kinds of rock of both magmatic and
sedimentary formations are characterized by the presence of cracks which
represent discontinuities rupturing a brittle body ( a rock monolith originally
in this case) into separate rock blocks.
Depending
on the causes of rock disturbances there exist tectonic cracks , bedding
joints, joints separating individual rock blocks, gravity fissures etc. Cracks
can be closed and open ones. Some of them are completely filled with a stiff or
loose material ( a filler ) of various mineralogical composition.
The
crack walls are most commonly irregular and rough, so the hydraulic resistance
of a crack to a water flow moving along it may be much higher than that of a
slot with smooth walls. More than half a century ago G.M.Lomise ( Lomise, 1951)
was the first to quantitatively estimate the effect of artificial roughness of
walls on the hydraulic resistance of cracks. Lomise's experiments are
methodologically close to the classical experiments performed on pipes by
Nikuradze.
At
the same time the hydraulic resistance in large cross-section pipes, e.g. water
pipelines, at the laminar fluid motion is known to be virtually unaffected by
the wall roughness as all the irregularities and asperities are gently washed
with a flow. In contrast, at the turbulent fluid motion roughness of pipe walls
always add hydraulic losses due to vortices formed and intensively developed on
the roughness elements. Proceeding from the experience of practice and
calculations in the field of rock mechanics it is established that crack wall
roughness can be referred do either the first or second kind, depending on the
thickness of the laminar boundary layer of a flow being more or less than the height of roughness
elements, respectively. Besides, the thickness of the boundary layer are quite
close to crack opening not exceeding 1 or 2 mm, as a rule. In this connection
the following questions arise: what asperities on crack walls are to be
considered as typical ones? is it possible to involve a value of relative
roughness (here it is the typical asperity height related to crack opening)
into estimates of the hydraulic resistance of cracks?
As
a results of investigations performed under the direction of the author it is
concluded that «effective» values of hydraulic parameters of crack wall
roughness can be found through the coefficient of wall surface development N2
equal to the relationship between the total area (with all the asperities taken
into account) of a wall under consideration and the area of its projection on
the parallel plane. It can also be shown that
N2 = N12,
where N1 is the coefficient
of the development of a rough surface profile, which equals to the relation
between this surface profilogram length and the length of a section within
which the profilogram is plotted.
We
have chosen a simple and rather exact method of dissecting a rough surface with
a thin flat beam of light, the so-called «light knife», directed at 450
to a rough surface under study. The light profilogram of the surface is
photographed, pictures being magnified several times and processed, i.e. the
profilogram length is measured and the N1 and N2
coefficients are calculated.
2. EXPERIMENTAL PROCEDURE
Regularities associated with a water flow in a jointed rock mass were studied in laboratory on the specially designed experimental facility shown as Fig 1. A controllable water flow was created in a crack between the two parts of a specimen made as a rock or concrete parallelepiped and splitted longitudinally in a press. Crack opening could be varied over a wide range, as well as crack shapes, including a wedge-like one, but of most importance was the fact that the facility enabled a crack with walls of «natural» roughness to be simulated. This roughness parameters were previously found by the method mentioned above. The maximum length of the cracks tested in the course of experiments was 100 cm and opening between 0.25 and 10 mm. The crack side surfaces were sealed hermetically and water moved in the longitudinal direction from the entrance- to exit-section.
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Fig.1. Scheme of the ²Fitron² experimental facility. The upper movable portion of a specimen and the
crack are designated with figures 13 and 4, respectively.
The
experiments were aimed at the search of regularities in head losses varied with
the mean velocity of a water flow in a crack characterized by fixed opening d, head losses being determined from readings of pipe piezometers, which
controlled the test section of the crack taken at a distance of 20 to 30 d from its entrance-section.
3. EXPERIMENTAL RESULTS
Experimental
results published by the author (Zhilenkov, 1971) were presented as the
gradient-velocity curves (Fig.2), plotted at different openings of the crack
with the morphological parameter N2 of wall roughness predetermined
(crack opening was monitored with the help of dial gauges to an accuracy of
0.01mm). Subsequent analysis of experimental data showed that crack wall
roughness could be taken into consideration with tolerable accuracy by the
inclusion into design relationships of the ²hydraulic² parameters of roughness at laminar (1) and turbulent
(2) fluid flows:
A
= 5(N2 - 1), cm (1)
and
B = 170(N2 - 1)2, cm (2)
Numerical
values of these parameters calculated for various cracks see in Table 1.
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Fig.2. The gradient-velocity
curves of a water flow through a crack with rough walls
(at A = 1.1 cm; B = 8.5 cm
and t
= 200C).
Table 1
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Crack category |
Character of crack walls |
Morphological parameter of roughness |
Hydraulic parameters of roughness |
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A2 |
A, cm |
B, сm |
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I |
Practically smooth |
< 1.004 |
< 0.02 |
< 0.003 |
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II |
Low-roughness |
1.004 - 1.02 |
0.02 - 0.1 |
0.003 - 0.068 |
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III |
Lowered-roughness |
1.02 - 1.05 |
0.1 - 0.25 |
0.068 - 0.42 |
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IV |
Medium-roughness |
1.05 - 1.1 |
0.25 - 0.5 |
0.42 - 1.7 |
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V |
Higher-roughness |
1.1 - 1.2 |
0.5 - 1.0 |
1.7 - 6.8 |
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VI |
High-roughness |
> 1.2 |
> 10 |
> 6.8 |
In particular, cracks in sandstone and concrete are characterized by A = 0.5 cm, B = 1.8 cm and A = 1.1 cm, B = 8.5 cm, respectively. Accordingly mean velocities of water motion in cracks are established as
(3)
and 
(4)
at
laminar and turbulent regimes,
respectively. Here g is the acceleration of gravity; i is the head gradient; v is the kinematic coefficient of viscosity
of fluid moving through a crack.
As
seen from the above, effects of wall roughness on the resistance of crack walls
to water motion is introduced into equations (3) and (4) as simplexes 
and 
.
The
all-important specific feature of water percolation through cracks is the
ability of a flow to a fast transition
from the laminar to turbulent regime when head gradient exceeds its so-called
critical value (Fig.2). As a result, with the flow characteristics equal at the
transition point we get the equation for the critical head gradient
(5)
and the equation for the critical velocity of a water
flow in a crack
(6)
Then critical Reynolds number is
(7)
It
follows from equation (5) that with the increase in opening of a fine fissure
characterized by A and B much less than d, the critical gradient decreases rapidly almost inversely the 4th
degree of fissure opening.
As
an example, Fig.3 presents curves of hydraulic resistance coefficient 
of cracks with A = 0.5 cm and B = 1.8 cm varying as a
function of Reynolds number.
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Fig.3. Hydraulic resistance coefficient vs Reynolds number curves plotted for a crack characterized by A = 0.5 cm and B = 1.8 cm.
It
should be noted that when crack opening d is known, the parameter A can
be determined from the section of a gradient-velocity curve as related to the
laminar flow regime by
(8)
and
B from its section as related to the turbulent flow regime by
(9)
The method of the in-situ determination of parameters
of crack and fissure wall roughness is protected by the USSR Patent No. 1048411
Then the gradient-velocity curves for water motion in
jointed rock mass can be approximated by the well-known two-termed relationship
(10)
In our case it acquires the following form
(11)
By solving equation (11) in respect to u we get
(12)
From this the conclusion of practical significance can
be drawn. When developing a geopercolation model of slightly pervious and
fissured rock (e.g. clay shale) foundation it should be remembered that the
permeability of such rock can markedly decrease (sometimes by several orders )
with the increase in external pressure.
To previously judge on probable decrease in water
permeability of rock mass under compression d0, use can
be made of the following equation
(13)
where Em
is the modulus of deformation of a rock monolith, Ec is the same of rock mass and
is the water permeability of cracks.
The value of the initial opening of a crack d0 in a rock
mass can be obtained by the method of successive approximations from the equation
(14)
in which k0
is the permeability coefficient of a rock mass with no external pressure.
Inasmuch as the specific water rate through a hole drilled in a jointed rock
mass characterized by the prevalence of cracks of opening d0 is equal to
(15)
considerable decrease in water permeability of the
rock mass due to the effects of a structure dead weight and other loads or
seepage forces is to be expected at
q<0.001 l/min×sq.m.
REFERENCES
1. Lomise G.M. Seepage in jointed rock. - Gosenergoizdat, Moscow, USSR,
1951.
2. Zhilenkov V.N. On regularities of water percolation in cracks of concrete structures. - Trudy Koordinatsionnykh Soveshchanij po Gidrotekhnike. VNIIG im. B.E.Vedeneeva, - 1971.- Vyp.68.
