2-1

2 Fluid tightness - Transport mechanisms through concrete

2.1 Introduction In Chapter 1 it already was mentioned that concrete is a porous material which is not entirely liquid tight. The challenge in this respect is to discover the structural possibilities of reinforced and prestressed concrete. A liquid of gas can penetrate the concrete by capillary suction or under influence of hydro-static pressure, respectively pressure differences. Other driving forces behind the transport mechanisms are concentration differences, temperature differences and the draining of pores by chemical shrinkage. By the effect of pressure differences a medium shall be able to flow through the porous concrete. As a result of concentration differences across a reservoir wall, diffusion will take place. When cracks, joints and seams are present, the transport driven by pressure will generally be much larger than the transport driven by diffusion. However, for an uncracked casing, molecular diffusion will be an important cause of - a relatively small - transport of fluid.

2.2 Porosity and permeability of uncracked concrete 2.2.1 Porosity of hardened cement paste and concrete Porosity of the hydration product ( = gel) The reaction of cement with water creates the product cement paste, which is also called gel. For the full hydration of cement a wcr (water cement ratio = mass/mass) is required of about 0.4. So, for the hydration of 100 kg cement 40 kg water is needed. Of this amount, 25 kg will be chemically bound and 15 kg will be physically bound. The physically bound water is absorbed at the surface of the gel parti-cles and fills up the so-called gel pores. These gel pores have a diameter of 20 to 40 (1 =10-10 m). The volume of the formed gel, including the physically bound water, is smaller than the initial volume of the cement and the water. This volume reduction is called the chemical shrinkage. The magnitude of the chemical shrinkage is about 25% of the volume of the chemically bound water. In the above sketched example 25 kg of chemically bound water is present, which corresponds with a volume of 25 litres. The volume reduction of the gel therefore becomes 0.2525 = 6.25 litres. Assuming a density of the cement of 3.15 kg/lce = , the initial volume of the cement and the water be-comes:

100 3.15 40 1.0 71.75 lce w ce ce w wV G G + = + = + = Of these 71.75 l, an amount of 15 l is occupied by the physically bound water in the gel pores and 6.25 l is present as capillary pores. The total porosity of the formed gel is equal to:

15 6.25 100% 29.6%71.75gel

P + = =

In this case, the pores resulting from the chemical shrinkage are included in the gel porosity.

Porosity of hardened cement paste and concrete A concrete mixture is considered with a cement content of 3320 kg/mC = and a 0.6wcr = . The den-sity of the cement is 3.15 kg/lce = . The initial air content is 31 1% 10 l/mV = = . For the total volume of the cement paste per cubic metre of concrete it then holds:

, 1 1320 0.6 320 10 102 192 10 304 l3.15paste ce w o ce

CV V V V wcr C V= + + = + + = + + = + + =

The porosity of the cement paste in unhardened state reads:

,192 10 100% 66%

304paste oP + = =

2-2

Suppose that after some time a hydration degree is reached of 0.7h = , in 1 m3 of concrete an amount of capillary water ,w capV is left of :

( ) ( ), , 0.4 192 0.7 0.4 320 102 lw cap w o hV V C= = = For the determination of the porosity of the hardened cement paste, this capillary volume ,w capV has to be increased by the initial air entrapment 1 10 lV = and the extra capillary pore volume generated by the chemical shrinkage. This last volume is indicated by ,ch shrV and is equal to 25% of the chemically bound water:

( ) ( ), 0.25 0.25 0.25 0.25 0.7 320 14 lch shr hV C= = = Now, the total capillary volume of the hardened cement paste becomes:

, , 1 102 14 10 126 lcap w cap ch shrV V V V= + + = + + = The capillary porosities of the hardened cement paste ,paste hrdP and of the concrete cP with a degree of hydration of 0.7h = can now be obtained:

,

126100% 100% 41.6%304

126100% 100% 12.6%1000

cappaste hrd

paste

capc

c

VP

V

VP

V

= = = = = =

In most cases, the capillary porosity of concrete varies between 10% and 15%. The volume of gel pores is normally not included in the capillary pore volume.

2.2.2 Permeability Permeability of a material is the property that defines the ease of fluid transport through that material. The material concrete, with a porosity of 10% to 15%, does not necessarily need to be permeable for liquids. This depends on the manner how the porosity manifests itself. Several possibilities are shown in Fig. 2.1.

The determining factor is the degree of connectivity of the pores. For concrete, this connectivity is a function of the wcr and the degree of hydration. Fig. 2.2 displays how large the degree of hydration for a certain wcr needs to be, to be certain of a closed pore system. Additionally, it is indicated which de-gree of hydration can be achieved under practical circumstances. From the figure it immediately can be concluded that for a wcr smaller than 0.5, the degree of hydration may reach values to guarantee a closed capillary pore system. For a wcr larger than 0.5 a closed capillary pore system cannot be achieved not even on the long term.

high porosity porous low permeability permeable porous low porosity not permeable high permeability

Fig. 2.1: Characteristic examples of different manifestations of pores in a material [1].

2-3

2.2.3 Permeability parameters Basically, the permeability of a material is given by the so-called intrinsic permeability 2 [m ] . It is used to define the permeability [m/s]k according to:

gk = (2.1) where:

= density of the penetrating fluid [kg/m3] g = gravitational acceleration [m/s2] = dynamic viscosity (Table 2.1) [Pa.s = N.s/m2 = kg/(m.s)]

Often the permeability k of concrete is determined for the liquid water. It should be clear that the per-meability k is NOT a material constant. It indicates the permeability for a specific substance x. From (2.1) it can be concluded that the dynamic viscosity plays an important role. For a number of fluids, the dynamic viscosity can be obtained from Table 2.1; the variety in values is quite large. From the above it should be clear that:

Water tightness is NOT the same as fluid tightness!

Contrary to the permeability k , the intrinsic permeability would be a real material parameter. How-ever, one should be aware that in practice some dependence on the penetrating fluid will be present [2].

dynamic viscosity [10-3 Pa.s] product gas liquid

ammonia n-butane carbon dioxide ethylene hydrogen methane nitrogen oxygen propane water oil sodium chloride

0.009 0.008 0.014 0.010 0.008 0.010 0.017 0.019 0.008

0.174 0.241 0.138 0.125 0.012 0.142 0.141 0.166 0.216

1.0 3.2 1.0

Table 2.1: Dynamic viscosity of several liquids and gases [3].

,maxh

,closed pore systemh

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8wcr

degr

ee o

f hyd

ratio

n [%

] 100

80

60

40

20

0

Fig. 2.2: Maximum achievable degree of hydration and required degree of hydration for the realisation of a closed capillary pore system.

2-4

The permeability of concrete is depending on the permeability of the aggregates, the cement paste and the boundary layer between the cement paste matrix and aggregates. Although the aggregates constitute about 70|% of the concrete and their permeability demonstrates considerable variations (Table 2.2), still the permeability of concrete will mainly be determined by the cement paste and the mentioned bound-ary layer between cement paste and aggregates.

Factors influencing the permeability of cement paste are: wcr ; degree of hydration; micro-crack formation; fabrication of the concrete (in relation to its purpose); curing of the concrete. Because of the many factors that influence the permeability, the values for are very different for the several classes of concrete. The intrinsic permeability for concrete varies between 10-14 and 10-19 m2. For hardened normal gravel concrete with a wcr from 0.4 to 0.5, often a permeability k is chosen of 10-11 up to 10-12 m/s. Application of blast furnace cement (CEM III) in combination with a low wcr may lead to permeabilities that are a factor 100 less. Addition of fly ash to the cement delivers a lower permeability as well. Very tight concrete is obtained by the suppletion of silica fume. This material is a required additive for the production of high-strength concrete. The permeability of concrete produced with light, slightly water absorbing aggregates, does not need to be larger than that of normal gravel concrete, in some cases it even may be a factor 1000 lower. This is caused by the very dense boundary layer between the aggregates and matrix. As a result of the relatively porous boundary layer between the dense aggregates and the cement paste matrix, the permeability of concrete generally will be larger that that of the hardened cement paste. A rough estimate for the difference is a factor 10. However, slightly absorbing aggregates may produce a very dense boundary layer leading to a permeability that does not need to be larger than that of the ce-ment paste itself.

2.2.4 Permeability as a function of water-cement ratio and degree of hydration Fig 2.3 shows the permeability of cement paste for water as a function of the capillary pore volume. In its turn, this pore volume can determined as a function of the wcr and the degree of hydration from the lower part of the diagram in Fig. 2.3.

Example 1 A cement paste is being produced with a wcr of 0.4 and a degree of hydration of 60%h = . According to Fig. 2.3 this delivers a capillary pore volume of the cement paste of about 26% with a corresponding permeability of

138.5 10 m/sk = . Application of a wcr less than 0.45 to 0.5 leads to concrete that is practically water tight. A condition for water tight concrete is that the pore system is closed. For higher values of wcr , the degree of hydration has to be higher as well for the realisation of a closed pore system. Fig. 2.2 already showed that for values of wcr larger than ca 0.5, generally an open pore system will be created, which results into a severe increase of the permeability k .

type of aggregate permeability k [m/s]sandstone limestone, dolomite granite diorite-porphyry quartz

10-6 10-10 10-8 10-15 10-10 10-15 10-10 10-13 10-13 10-15

Table 2.2: Permeability of aggregates (after [4]).

2-5

2.3 Penetration depth into uncracked concrete 2.3.1 The numerical determination of the penetration depth For the penetration depth x resulting from the capillary suction it holds:

2

r tx = (2.2)

where:

x = penetration depth [m] r = pore diameter [m] = surface tension [N/m] t = time [s] = dynamic viscosity [Pa.s] The penetration depth x of a gas or a liquid driven by a (hydrostatic) pressure can be computed with the formula ([5], also see Fig. 2.4):

2

cap

r g htxP = (2.3)

where:

= density of the fluid [kg/m3] g = gravitational acceleration [m/s2]

Fig. 2.3: Permeability k [m/s] for water of hardened cement paste [Powers].

0 10 20 30 40

100

90

80

70

60

50

40

30

20

10

100

80

60

40

amount of capillary pores [vol. %]

degr

ee o

f hyd

ratio

n [%

]

p

erm

eabi

lity

[10-

13 m

/s]

0.2

0.3 0.40.5

0.60.7wcr

2-6

h = pressure head (m water column) [m] capP = capillary porosity [m

3/m3]

From a number of liquids and gases that are stored in tanks, the dynamic viscosity is listed in Table 2.1. For several other liquids, in Germany classified as reference liquids used for classification of envi-ronmentally damaging liquids, the dynamic viscosity is given in Table 2.3. The practical use the formulae (2.2) and (2.3) is limited, because the determination of the representative pore diameter r is quite a challenge. Capillary pores vary in diameter between 10-9 and 10-4 m. To avoid this problem, with the formula of Valenta ([6], [7]) a reasonable approximation can be obtained:

2cap

k htxP= (2.4)

where:

k = permeability [m/s]

x

h

d

ip

ep

cQ

h

d

Fig. 2.4: Penetration depth (left) and flow (right) through uncracked concrete.

no.

main chemical group

possible hazardous

action

reference liquid

dynamic viscosity

[Pa.s]

surface tension

[N/m2]

density

[kg/m3] 1 aliphatic

hydrocarbons loss of

strength n-heptane 0.041 20.3 686.8

2 aromatic hydrocarbons

loss of strength

toluene 0.582 28.5 866.9

3 alcohols dissolving attack

n-butane alcohol

2.928 33.5 809.4

4 esters dissolving attack

ethyl acetate 0.450 23.9 925

5 aldehydes, ketones

dissolving attack

methyl ethyl ketone

0.4 24.6 803

6 aliphatic amines

n-butyl amine 0.5 23.0 740

7 halogenated aliphatic hydrocarbons

production of chlorides

methyl chloride

0.440 26.5 1325.5

8 organic acids

dissolving attack

acetic acid (20% solution)

1.10 47.7 1026.1

9 halogenated aromatic hydrocarbons

production of chlorine

chloro benzene

0.810 33.5 1106.4

Table 2.3: Physical properties of several reference liquids [6].

2-7

Above formulae for the calculation of the penetration depth are based on the assumption that during the penetration process the permeability remains unchanged. However, when the penetrating fluids are able to react with the cement paste, the assumption of a constant permeability is no longer correct. In the pore system reaction products may be deposited, leading to a reduction in permeability (also see Section 2.3.3). When the reaction products are soluble, a process of leaching out may occur, which even can in-crease the permeability. Further, the extrapolation of short-term permeability tests to the long-term be-haviour of structures is a challenging but difficult task.

Example 2 Question Give an indication of the penetration depth of lightly aggressive waste water under a pressure head of 1 m in hard-ened concrete after 3 and 28 days, followed by 1 and 5 years. Data Cement type: blast-furnace cement (coarse) CEM III 42.5; A wcr of 0.45 and 0.55, respectively; The concrete with 0.55wcr = appeared to be poorly compacted and poorly cured; The waste water can be considered to be water with the following properties: Dynamic viscosity: 310 Pa.s = Density: 31000 kg/m = Maximum pressure head: 1 mh = Intrinsic permeability It is assumed that the concrete reaches a degree of hydration of 60% and 70% for a wcr of 0.45 and 0.55, respec-tively. With the aid of Fig. 2.3, the permeability k and the capillary porosity capP of the hardened cement paste can be found, the obtained values are listed in the table below under the headings mixture A and mixture B. Because of the relatively poor curing of mixture B, a permeability factor for the concrete is selected, which is a factor 10 higher that that of the hardened cement paste. Penetration depth x The penetration depth is determined with the formula of Valenta (2.4). The table below shows the results.

time theoretical penetration depth x [m]

exposure time days or years

exposure time

seconds

mixture A

13

13

cap

0.4517 10 m/s

17 10 m/sP 0.30

con

wcfk

k k

== = =

mixture B

13

12

cap

0.5545 10 m/s

10 45 10 m/sP 0.35

con

wcfk

k k

==

= =

3 days 28 days 1year

5 years

3260 10 62.4 10

631 10 6157 10

0.002 0.005 0.019 0.042

0.008 0.025 0.089 0.201

Discussion The calculated values clearly show the effect of the wcr on the penetration depth. For a wcr of 0.45, after 5

years of penetration, the waste water will just have reached the reinforcement (assume a concrete cover of 30 mm). Notice that transport of ions by diffusion is not taken into account and may lead to an extra contribution to the flow.

Penetration by capillary suction into the outer centimetres of concrete is often much larger than the penetration driven by fluid pressure.

Next to the wcr , the way and carefulness of the fabrication and curing of the concrete are determining factors for the actual permeability. In many cases, these factors are even more important than the choice of the wcr However, it should be clear that in the opposite case of a concrete with a superb fabrication and curing but with a high value for the wcr , it is not possible to produce a concrete with a high tightness.

2-8

2.3.2 Experimental determination of the penetration depth The prediction of the penetration depth by numerical models is possible, but is nevertheless not very ac-curate. The reason for this is that it is very hard to estimate the permeability of concrete with sufficient accuracy, without testing. That is why the engineering practice often relies on experimental determina-tion of the penetration depth. For this purpose, the standardised ISO/DIS 7031 test and the capillary ab-sorption test can be utilised. Both test methods have been intensively investigated by the Dutch CUR/ CROW/PBV research commission D29. The results have been published in CUR aanbeveling 63.

ISI/DIS 7031 test With the ISI/DIS 7031 test, liquid is forced to penetrate into the concrete by an excess pressure of 1, 3 and 7 bars in consecutive periods of 48, 24 and 24 hours. After the test the penetration depth is deter-mined from a split face. For a brief discussion of the ISI/DIS 7031 test, it is referred to [19].

Capillary absorption test In the capillary absorption test, an excess pressure of 400 mm is used to penetrate the concrete. The penetration depth is obtained from split faces. Fig. 2.5 shows a test setup.

plug

burette with calibration

connection tube

glass funnel

liquid

400 mm

100 mm

1 mm

second layer of coating aluminium adhesive foil first layer of coating

Fig. 2.5: Setup for capillary absorption test [8].

2-9

In [8] a comparison has been made between the results of the ISI/DIS 7031 test and the capillary ab-sorption test. In this research the penetration depth has been studied of water as well as diesel and pet-rol. No unambiguous relation could be established between the penetration depth according to the ISO/DIS 7031 test and the capillary absorption test. For an extensive elaboration it is referred to [8, 9].

2.3.3 Autogenous healing (self healing) According to equation (2.2), capillary suction is a process that proceeds according to a t relation. For a number of fluids such behaviour as a function of time was observed over a period of several months. However, water displays a deviating tendency. In Fig. 2.7 the results are displayed of absorption tests,

3% relative humidity

50

80

mm

plastic cap

dehydratingagent

seal of epoxy resin

75

mm

5

-70

mm

dehydrating zone

capillary zone

inside, dry

100 mm

Fig. 2.6: Schematic of test setup for the determination of moisture transport through concrete.

water emissionmoisture from specimen only

capillary water absorption

change moisture content of concrete

height of specimen [mm]

wat

er a

bsor

ptio

n or

em

issi

on a

fter 2

90 d

ays [

l/m2 ]

12

10

8

6

4

2

0

-2

-4 0 100 200 300 400 500 600 700 800

Fig. 2.7: Absorption and emission of water after 290 days as function of the specimen height [12].

2-10

at which a concrete specimen sucks up water from a shallow basin and releases moisture at the top in a confined space with a constant humidity of 3% (Fig. 2.6). Because of the constant difference in relative humidity one would expect that a steady-state situation would develop, in which a constant flow of wa-ter would be absorbed at the bottom and released again at the top of the specimen. However it was ob-served that for the larger specimen the absorption of water stagnated. No water was sucked up anymore and (nearly) no moisture released at the top. This phenomenon is caused by a reaction between the ce-ment paste and the water. Lime crystals in the pore system dissolve and generate a concentration gradi-ent, which creates a diffusion process that prohibits further capillary intrusion of the water [10]. It should be remarked that chemical interactions between the penetrating fluid and the cement paste may occur that influence the penetration rate as well (for example the dynamic viscosity may be re-duced).

2.4 Determination of the leakage flow through uncracked concrete For the determination of the flow of a liquid or gas through uncracked concrete driven by a pressure gradient, Darcys law can be used (see [13] and Fig. 2.4b), i.e.:

cA pQ

d

= (2.5)

Where:

= intrinsic permeability [m2] cQ = flow through the concrete [m

3/s] A = cross-sectional area of wall [m2] p = pressure difference over the wall or slab thickness [Pa] = dynamic viscosity of the fluid [Pa.s] d = wall thickness [m]

A worked out example can be found below.

Example 3 Question Determine the flow of water through an uncracked concrete panel. Data Concrete on bases of CEM I Wall thickness: 0.25 md = Pressure difference across the wall: 44 10 Pap = Wall area considered: 21 mA = Intrinsic permeability: 20 218 10 m = Dynamic viscosity: 310 Pa.s = Solution With Darcys formula it directly follows:

4

20 12 33

1 4 10 18 10 28.8 10 m /s 0.0025 l/day10 0.25c

A pQd

= = = =

2.5 Transport of fluids through cracked concrete A number of factors are decisive in the determination of fluid transport through cracked concrete. Dis-tinction has to be made between factors at structural level and at crack level.

A. Structural level At structural level attention is paid to the existing crack pattern. The following characteristic aspects can be distinguished:

2-11

1) Crack width; 2) Number of cracks; 3) Type of cracks;

a) Separation cracks; b) Flexural cracks;

4) Crack characteristics; a) Stability (for example not stable due to settlement and continuous shrinkage); b) Cyclic crack width (cyclic loading).

On the one side the crack pattern is determined by the relevant loading scenarios and on the other side by the design and dimensioning of the structure.

B. Crack level For the calculation of the transport of a fluid through a crack, the following parameters are important: 1) Crack width; 2) Crack length, i.e. the thickness of the concrete element; 3) Morphology of the crack face;

which is influence by: a) Type of aggregates; b) Water cement ratio wcr ;

4) Pressure drop across the crack; 5) Type of fluid (viscosity); 6) Autogenous healing capability. Both the crack patterns and the transport of a fluid through a single crack are governed by factors that display a large amount of scatter. These conditions invite to address transport problems of fluids through cracks with probabilistic considerations respectively probabilistic computations. However in the next section, a deterministic approach will be followed for the analysis of the transport problem.

2.5.1 Transport calculation Separation cracks For the calculation of fluid transport through cracks normally the formula of Poiseuille is used:

3

crackw pQ l

d

= [m3/s] (2.6)

where:

w = crack width [m] p = pressure difference [Pa] l = crack length [m] = dynamic viscosity [Pa.s] d = thickness of concrete element [m] = coefficient, depending on roughness of the crack face [-] The factor depends on the morphology of the crack surface, the type of aggregates and the wcr . For smooth surfaces it holds 1/12 = (Poiseuille). Because of the roughness of the crack surface the value of reduces with a factor 2 up to 10. The magnitude of the factor increases with increasing crack width. For many practical applications a value of 0.01 = can be selected. Separation cracks with a crack width 0.06 mmw < can be regarded as liquid tight for a period of at least 72 hours [14]. In Ger-many, these 72 hours is used as the reference period for the definition of the suitability of concrete for environmental protective structures. By the way, for very small crack widths, 0.1 mmw < , the reliabil-ity of equation (2.6) is quite limited.

2-12

When determining the factor it normally is assumed that the crack width remains constant. Altera-tions in the crack width during the fluid transport due to clogging up of the crack, due to autogenous healing or due to freezing up (cryogen applications) are not explicitly taken into consideration. Cracks may also become larger by cyclic loading. For separation cracks with a varying crack width in flow direction, the crack width w in formula (2.6) has to be replaced by the effective crack width effw given by (Fig. 2.8):

( )2

32 A B

effA B

w ww

w w= + (2.7)

Example 4 Question Calculate the flow of water through a crack of 1 m length in a 0.25 m thick wall. Vary the crack width from 0.1 to 0.2 mm. Data Wall thickness: 0.25 md = Crack width: w = 0.1, 0.15 and 0.2 mm Crack length: 1 ml = Pressure drop over wall: 44 10 Pap = (4 m water head) Dynamic viscosity: 310 Pa.s = Morphology factor: 0.01 = Solution With the formula of Poiseuille (2.6) the following relation is found:

3 3 4

6 3 334 100.01 1 1.6 10 m /s

10 0.25crackw p wQ l w

d

= = = The results for the given crack widths are shown in the table below. For reasons of comparison the results of ex-ample 2 (flow through uncracked concrete) are indicated as well.

crackQ Comparison of crackQ with cQ Crack width w [m] m3/s l/day cQ (example 2) crack cQ Q

0.00010 0.00015 0.00020

1.610-6 5.410-6

12.810-6

138 467 1106

0.0025 l/day 0.0025 l/day 0.0025 l/day

55103 187103 442103

conclusion The results of the calculations clearly show that the fluid transport through cracks can easily exceed the flow through uncracked concrete by a factor 105. Therefore, it confidently can be concluded that generally the transport of fluids through cracks will be several orders of magnitude larger than the transport through the concrete itself.

w Bw

Aw

h

d

Fig. 2.8: Schematic representation of separation cracks.

2-13

Flexural cracks In the case of the presence of flexural cracks, the flow rate will predominantly be determined by the size of the concrete compressive zone (Fig. 2.9). Relation (2.5) can be used for the determination of the flow rate, in which case the wall thickness d of the element has to be replaced by the depth of the concrete compressive zone xh . This leads to a conservative estimation of the permeability, because the flexural cracks that still have a significant flow resistance are not included in the analysis.

Crack concentrations For the control of crack widths in thick-walled structures, the reinforcement is preferably placed in the edge regions. Due to this action, the crack widths indeed remain small near the edges, but in the core of the structure may attain considerable values. The mechanism behind this is that in the core of the struc-ture many small cracks are merging into a smaller number of large cracks. A schematic representation of this crack pattern is shown in Fig. 2.10 and will be indicated by the term crack concentration. The problem is to estimate the fluid flow through a concrete element in which crack concentrations are

present. This phenomenon has been investigated by Favre e.a. [12]. The transport of air and water through cracked concrete beams, with different reinforcement fractions and reinforcement configura-tions, was determined experimentally. The used test setup has been drawn in Fig. 2.11. Fig 2.12 depicts the reinforcement configurations of the tested beams. The beams were made from high-strength con-crete (C53/65, C55/67). Fig 2.13 shows the results of the permeability tests carried out on the beams E3, E4, E5 and E6 as function of the imposed deformation. It clearly can be seen that a reduction of the crack widths near the edges, by the application of a finely distributed reinforcement has a large positive effect on the permeability. In the element E4 and E5 the reinforcement is concentrated near the edges. The cracks in the core of these elements were larger than those in the elements E3 and E6, which had a homogeneous distribution of the reinforcement. The larger crack widths in the core of the elements pro-mote the liquid transport through these cracks. The fact however that the number of large cracks in the core are limited and the fact that the crack widths at the surface of the elements E4 and E5 are smaller that those of the elements E3 and E6, results into a smaller transport through the cracks in the beams E4 and E5. A similar favourable effect, of the application of a finely distributed reinforcement in the edge regions, has been reported by Edvardsen [16].

Fig. 2.9: Fluid transport through flexural cracks.

M M

xh

h

d

w

N N

h

1w

2 1w w

tmh

tmh

Fig. 2.10: Schematic representation of a crack concentration.

2-14

at the top and bottom air and water tight coating

measurement length3000 mm

1

4

pressue reducer

2

6

flow meters

cracks

3

filter

strain gauges

temperature

5

displacement transducers

P2 pressure

P1 pressure

P0 pressure

Fig. 2.11: Setup for measurement of air and water transport through cracks in a concrete beam [12].

1

0.60%20

250 mm

sA

s

==

concrete IBAP R1 R2 R3 R4 R5 EDF E3 E4 E5 E6

reinforcement 2

0.57%16

167 mm

sA

s

==

3

0.86%16

167 mm

sA

s

==

4

0.86%16

111 mm

sA

s

==

5

1.15%16

83 mm

sA

s

==

6

1.15%16

125 mm

sA

s

==

Fig. 2.12: Reinforcement configurations in beams for permeability measurements [12].

1500

1250

1000

750

500

250

0

corr

ecte

d flo

w [l

/h]

imposed strain []0 0.05 0.10 0.15 0.20 0.25 0.30

E3

E4

E5

E6

Fig. 2.13: Liquid transport through cracked concrete as function of the imposed strain with reinforcement configurations according to Fig. 2.12 [12].

2-15

2.5.2 Leakage through poor functioning joints and through leads-through Dilatation and settlement joints These types of joints in liquid retaining structures are an undesired necessity. Practical experience has confirmed that leakage at the spot of not properly functioning joints may easily exceed the leakage through cracks by a factor 106 [15]. For this reason, the number of joints in liquid retaining structures should be restricted to the bare minimum. The design of an effective and durable properly sealing joint, which also has a high resistance against chemical attack, is often a large challenge [17]. For this reason, the dimensioning and detailing of joints should be focussed on the ability to inspect, reach, repair and replace the joints. The same design condi-tions as for joints do also hold for leads-through and the like.

Construction joints These types of in-situ created joints require special attention during the construction phase. Not care-fully carried out preparations will easily lead to leakage. The casting in of a porous tube, which is grouted after the curing is an effective way to prevent leakage or to solve a leakage problem.

Prefabricated joints For the production of liquid tight joints, prefabrication is an appealing option, because of the high con-crete quality. In order to optimise the use of the tight concrete, special attention has to be paid to the de-tailing of the joints. Not much is known about the tightness of standard prefab-joints. Depending on the type of structure prefab-joints, just like dilatation joints, have to comply with requirements regard-ing the ability for inspection, control, repair and replacement.

2.6 Tightness criteria

2.6.1 Local and global tightness For reservoirs, Bomhard [20] makes distinction between local tightness and global tightness. Local tightness occurs if nowhere any penetration of liquid can be observed (dark colouring). The evaporation speed of the penetrated liquid is higher than the discharge. In this case Bomhard also speaks of absolute tightness. A reservoir is called globally tight if the leakage is less than a prescribed threshold value. For example, a water reservoir satisfies the condition of global tightness if the leakage percentage is lower than 0.02% per day of the reservoir volume. British Standards also describes a criterion for global tightness. In [21] the condition for liquid tightness reads that the total leakage flow totQ per day should not be larger than 0.1% of the reservoir volume. According to BS (1976), a reservoir is called liquid tight if the liquid level does not fall more then 0.4 inches (about 10 mm) in seven days [22]. In the BS of 1982 this condition has been made more strin-gent because next to the condition for dropping of the liquid level, it is required that the total leakage flow totQ per week should not exceed 0.2% of the reservoir volume (see [23]).

2.6.2 Autogenous healing (self healing) The fact that liquid tightness even may occur under the presence of separation cracks has to do with the ability of filling up the cracks. This ability is called autogenous healing or self healing. Possible mecha-nisms for self healing are: continuous hydration; sedimentation of solid particles that are present in the penetrating liquid; closure of the crack by cement particles from the crack face; swelling of the cement paste. Conditions for eventual closure of the cracks are: the crack must be stable,

remark: a small crack mobility does not have to be disastrous (see Edvardsen [16]); the flow rate in the crack should not be too large;

2-16

the penetrating liquid should not have leaching properties. Schntgen [24] investigated the relation between the width of separation cracks and water tightness. The crack widths varied between 0.08 and 0.3 mm and were governed by the reinforcement present. Af-ter an initial leakage, for crack widths from 0.08 up to 0.3 mm, the rate of flow considerably reduced within 24 hours. Irrespective the pressure drop across the crack, no leakage could be observed anymore for a crack width of 0.06 mm (parallel crack faces), only drop-wise leakage at the back of the wall. According to Bomhard [20] autogenous healing is possible for crack widths 0.2 mmw < , under the condition that the flow velocity in the crack is low. On the basis of practical observations Lohmeyer [25] has constructed a simple graph, in which a critical crack width for self healing is provided as func-tion of the ratio between liquid head and wall thickness (Fig. 2.14). For crack widths larger than 0.2 mm, self healing should not be considered to be a real option.

Meischner [26] is a bit more optimistic, however it should be remarked that his curve is based on results of experiments conducted under laboratory circumstances. Recent laboratory research of Scheissl et. al. [27] even provides wider margins for the occurrence of autogenous healing. However the values of Lohmeyer, that are based on practical observations, still have preference for practical applications.

2.6.3 Water tightness criteria on basis of practical experience Generally a structure will behave water tight if no separation cracks are present. Flexural cracks are al-lowed to be present as long as the depth of the compressive zone satisfies certain conditions. When separation cracks are present, these should be smaller than a critical value critw . As long as the crack width remains below this critical value, the crack may close through autogenous healing, provided that certain requirements are met (see Section 2.6.2). On basis of practical experience Bomhard [20] has formulated an integral tightness criterion, i.e.:

,min 50 mmx xh h = (2.8) Smaller values of xh are acceptable, provided that certain crack-width conditions are satisfied. These conditions depend on the presence or absence of self healing:

95%95%

0.1 mm (without self healing)0.2 mm (with self healing)

ww

it holds: ,max max ,max max20 mm or 2x xh D h D + (2.10) In the case of separation cracks, Lohmeyer gives a guideline for the critical crack width for which auto-genous healing is still possible. This guideline is given in Table 2.4. An important parameter in this ta-ble is the ratio of the pressure head lH and the wall thickness wh or bh of the element. For a crack in the floor slab the pressure head should be measured from the bottom side of the slab.

2.7 Fibre reinforced concrete An effective method to keep the crack widths within limits is the addition of fibres to the concrete mix. This can be done for example in the form of steel fibres. The fibres have crack distributing properties. In the transport formula (2.6) the crack width appears to the third power, which means that the reduc-tion of the crack width has an immense effect on the transport rate. Fig. 2.15 gives an idea about the ef-fect of the addition of fibres on the water-permeability of cracked concrete. In this figure the leakage volume of normal cracked concrete is compared with fibre concrete that is subjected to the same im-posed deformation.

2.8 System technology When very severe conditions are imposed on the tightness of a structure, a large possibility exists that untreated concrete will not meet these conditions. Possible solutions for this kind of problems may lie in the domain of system technology. System Technology is a design method that realises structural-technological solutions, which will guarantee that environmentally hazardous fluids cannot leave the storage system. An example is the double-walled reservoir for the storage of non-processable chemical waste. The primary storage structure has to be designed such that, in the case leakage of the hazardous fluid, it is accessible from all directions for the purpose of inspection and repair. If necessary total over-haul of the structure should be possible. These measures prevent that fluids leave the system. So, at macro-level the system can be regarded to be fluid tight.

Cat. orl l

w b

H Hh h

calculated

critw [mm]

1 2.5 0.20 2 5 0.15 3 1)5> 0.10

1) an upper limit for l wH h or l bH h can be obtained from Fig. 2.14. Remark Cyclic loading is permissible as long as its effect is explicitly taken into account. This delivers such a stringent condition that preferably cyclic loading should be prevented, for example by thermal isola-tion of the structure.

Table 2.4: Permissible crack widths for separation cracks for which still water tightness can be guaranteed (after [28]); Classification of tightness criteria [2].

ground water level

ground water level

liquidhead

lH liquidhead

lH

wh

bh

crack in floorposition of largest crack

liquid head lH to be applied for wall and floor slab

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2.9 References [1] Stutech (1992): Permeabiliteit van beton, Research report No. 12, 73 p. [2] Walraven, J.C., et al (1994): Betonnen beschermingsconstructies tegen milieubelastende stof-

fen, CUR-report 94-3, 65 p. [3] Turner, F.H. (1979): Concrete and Cryogenics, Viewpoint publication, Cement and Concrete

Association. [4] Reinhardt, H.W. (1985): Beton als constructiemateriaal - Eigenschappen en duurzaamheid,

Delft University Press. [5] Deutcher Ausschluss fr Stahlbeton (1991): Beton beim Umgang mit Wassergefrdenden Stof-

fen, Vol. 416, 201 p. [6] Valenta D. (1970): Durability of concrete, from the 2nd RILEM symposium Prague, Materials

and Structures 3, No. 17, pp. 333-345. [7] Valenta D. (1979): The permeability and the durability of concrete in aggressive conditions,

10th congrs des grands Barrages, Montreal, Vol. IV, pp. 103-119. [8] CUR/CROW/PBV (1998-2): Vloeistofindringing in beton, Background report of CUR/PBV-

Recommendation 63, 51 p. [9] CUR-Recommendation 63 (1998): Bepaling van de vloeistofindringing in beton door de capil-

laire absroptieproef, CUR, Gouda, 8 p. [10] Wegen G. van der (1996): Vloeistofdichtheid van betonvloeren: De stand der kennis, INTRON

report No. 95278 (for PBV), 42 p. [11] Beddoe R. (1998): Gibt es einen Feuchtetransport durch Betonbauteile?, Proc. Seminar

Technologie und Ausfhrung anspruchsvoller Betonkonstruktionen, Mnchen. [12] Favre R. et al (1996): Cracking and tightness of reinforced concrete structures, Publication

IBAP, No. 143, pp. 3-13. [13] Breugel K. van et al (1983): Betonconstructies voor opslag van tot vloeistof gekoelde gassen,

STUVO report No. 70. [14] Imhoff C.: Tightness and permeability of pressed separation cracks and flexural cracks in rein-

forced concrete, Darmstadt Concrete, Vol. 7, pp. 49-54.

water / 7dh h =

temp. 20 0C = PVA fibres (0.8 vol. %) = steel fibres (1.0 vol. %) = PAN fibres (1.7 vol. %) = no fibres

crack width [mm]

flow

[ml/m

in.m

]

800

600

400

200

00 0.1 0.2 0.3 0.4

Fig. 2.15: Permeability for water of ordinary concrete and fibre concrete [18].

2-19

[15] Bomhard H. (1992): Concrete and Environment - An Introduction, FIP symposium, Budapest, Vol. 1, pp. 51-59.

[16] Edvardsen C. (1996): Water penetration and autogenous healing of separation cracks in con-crete, Betonwerk+Fertigteiltechnik, Vol. 11, pp. 77-85.

[17] Nordheuss H.W. (1991): Berechnungsgrundlagen und Vorschlge fr die Konstruktion und Ausbildung von Fugen in Bodenplatten aus Beton, die chemischen Angriffen ausgesetzt sind, Darmstadt.

[18] Tsukamoto M. et al: Permeability of cracked fibre reinforced concrete, Darmstadt Concrete, Vol. 6, pp. 123-136.

[19] Betoniek (1998): Voeistofdicht beton III, no. 9, October 1998. [20] Bomhard H. (1983): Wasserbehlter aus beton Anforderungs-, Entwurfs, Planungs- und Be-

messungskriterien, Mnchen, 46 p. [21] BS 5337 (1976), Code of Practice for the Structural Use of Concrete for Retaining Aqueous

Liquids, British Standards Institution, London. [22] BS 5337 (amendment 1982: see [23]) (1976), Code of Practice for the Structural Use of Con-

crete for Retaining Aqueous Liquids, British Standards Institution, London. [23] ACI-committee 350/AWWA (1993), Testing Reinforced Concrete Structures for water tight-

ness, ACI-Structural Journal, Vol. 90, No. 3, pp 324-328. [24] Schntgen B., Durchlssigkeituntersuchungen an gerissenen Betonbauteilen (mit Wasser und

wssriger Lsung), Deutscher Ausschluss fr Stahlbeton, 25, Forschungkoll., pp. 79-86. [25] Lohmeyer G., Wasserdurchlssige Betonbauwerke Gegenmassnahmen bei Durchfeugtungen,

Beton 2/84, pp 57-60. [26] Meischner H., Ueber die Selbstheilung von Trennrissen in Beton, Beton- und Stahlbetonbau,

Vol. 87 No. 4, pp95-99. [27] Schiessl P. et. al. (1993), Massgebende Einflussgrssen auf die Wasserdurchlssigkeit van ge-

rissenen Stahlbetonbauteilen, DBV Arbeitstagung, Wiesbaden, pp. 25-32. [28] Lohmeyer G. (1994), Weisse Wannen Einfach und Sicher, Beton-Verlag, Dsseldorf, p. 255.