5-1

5 Reservoirs in prefabricated and in-situ placed concrete

5.1 Reservoirs made from prefabricated concrete

5.1.1 Introduction Concrete reservoirs that have to be liquid tight can also be built with prefabricated elements. The liquid tightness and economy of the design can be positively influenced by: The conditioned circumstances during the production of the concrete, with among other things me-

chanical compaction and excellent curing capabilities; Independence of weather conditions and production under controlled temperatures; The use of steel formwork for the larger series, achieving a higher degree of accuracy; Shrinkage limitation in prefabricated elements after erection; The option of standardization for a more economic production; Shorter erection times; Major cost savings by less investment in formwork, scaffolding and wages. Especially the last aspect will be highlighted in a practical example (Section 5.1.5). Prefab elements, contrary to in-situ placed concrete elements, are able to meet the highest requirements regarding liquid tightness. An important issue is that they have to be connected, making the joints the weakest link in the total structure. Both with respect to the desired force transmission and the required liquid tightness, it is of paramount importance to dimension and construct the joints in the proper man-ner. In this course, firstly recently carried out research about the liquid tightness of construction joints in concrete, for example applied in rectangular reservoirs, will be highlighted. After that the structural possibilities will be discussed of joints in cylindrical reservoirs. This is followed by an example of a re-cently erected tank structure in prefab concrete, including a comparison of costs with a more traditional structure made out of in-situ placed concrete.

5.1.2 Permeability of construction joints

Introduction Regarding the functional aspects, the following basic types of joints can be distinguished: joints having both a sealing and structural function; joints having a sealing function but no or hardly any structural function. The choice depends on the force transmission in the structure and on the possibilities to create joints that are also capable of force transmission. In the German literature, in this respect distinction is made between kraftschlssig and nicht- kraftschlssig, i.e. capable of force transmission and not capable of force transmission, respectively. An example of a rectangular structure is shown in Fig. 5.1. It shows the erection of a drinking water res-ervoir composed out of prefab wall and floor elements. A construction joint between the elements is necessary. In many cases this joint is filled in-situ with concrete or cement mortar, whereby the steel re-inforcement bars sticking out of the prefab elements are connected by lap welds. The liquid tightness of this sort of construction joints have been investigated in Germany in relation to the research programme Sicherheit von Betonkonstruktionen technischer Aanlagen fr umweltgefrdende Stoffe (Safety of concrete structures with respect to environmentally hazardous substances). The research has been con-ducted at the University of Technology of Bochum [1]. The results will briefly be discussed.

Parameters of the construction joint The considered joint has been schematically depicted in Fig. 5.2. Two prefab elements can be distin-guished with profiled end-faces and a space between them (the joint), which will be filled up with a joint filler, for example concrete mortar. In the detailing of the joint three parameters play a crucial role:

5-2

the structural connection; the joint geometry; the joint filler. Further, a number of additional provisions can be listed, which influence the tightness of the joint but have no effect on the force transmission.

The structural connection Several options are available to realise the structural connection between the two prefab elements. They may be: a welded of screwed steel connection; a socket or sleeve connection; a lap-weld connection; a connection made by prestressing. The first two types are referred to as dry connections; the last two types are wet connections. An example of a welded steel connection is given in Fig. 5.3. Cast-in steel angle sections are connected by a V-section (also an angle section). The advantage of this construction method is that a firm connec-tion is made immediately without the necessity of long-term propping of the concrete elements. The disadvantages of this connection, which is discontinuous in nature, are: the concentrated force transmission, which increases the probability of cracking and consequently of

leaking the required high dimensional accuracy it is labour intensive

A welded connection can also be obtained by directly joining (lap weld) the protruding bars of the pre-fab elements (Fig. 5.4). However, the advantage of above sketched method is that a relatively short joint

joint

in-situ placed concrete prefab concrete

Fig. 5.2: Schematic of a construction joint in a wall (horizontal cross-section).

Fig. 5.1: Vertical joints in a rectangular drinking water reservoir in Beiroet.

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can be realised that leads to a relatively small absolute shrinkage. Apart from the danger of brittle frac-ture of the reinforcement steel, especially the large labour intensity is a disadvantage. A socket or sleeve connections are generally applied in columns and beams, but for walls and slabs they are too expensive and labour intensive. Sockets are available that can be slid over the reinforcing bars after which the structural joint can be made by grouting or welding. Also sockets for screwed connec-tions can be obtained commercially. A lap weld (Fig. 5.5) is the most common form of a structural wet prefab joint. The joint is simple and rather insensitive to dimensional variations. Disadvantages are the large joint gaps to be filled and the required curing time before the props can be removed. A reduction of the joint dimensions can be achieved by the applications of loops. When a structural joint is made by prestressing, the joint filler is subjected to compression. By this ac-tion, the joint is able to transmit loads without direct involvement of the prestressing steel. The

plan view

front view

detail

3-D view

Fig. 5.3: Joint construction with welded angle sections.

prefab concrete

zone for the in-situplaced concrete

Fig.5.4: Connection by means of welded reinforcement bars.

Fig. 5.5: Lap weld by means of loops.

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prestressing can be achieved by continuous cables of short prestressing elements at the position of the joints. On basis of previous judgements and corresponding literature surveys with respect to the several op-tions of prestressed joint design, it has to be concluded that only loop anchorages have additional value for the considered area of application. The research in [1] is based on this structural concept. A very positive influence of the prestressing on the liquid tightness can be expected. For this reason this pa-rameter is included in the research.

The joint filler The joint filler applied in a prefab joint, should have a number of important properties, such as: resistance against chemical attack of the retained medium; high compressive and tensile strength; large bonding properties with the prefab concrete; limited shrinkage and good workability A careful compaction of the joint filler is of paramount importance, just as the quality of the curing. Fast drying-out of the joint is very dangerous and should be avoided with the appropriate means. Glob-ally is can be assumed that for the production of liquid tight joints curing periods are required that are twice as long as normally applied. To achieve proper liquid tightness good bonding properties between the joint filler and the prefab con-crete are conditional. The target value of the bonding strength is that it should be equal to the tensile strength of the prefab concrete and the tensile strength of the joint filler. The bonding properties depend on both chemical and mechanical adhesion. Mechanical adhesion depends on the shape of the anchoring of the joint filler in the open pores of the prefab concrete. Roughening of the concrete surfaces by high water pressure is a very useful activity. Keeping moist of the concrete surfaces before filling prevents non-uniform shrinkage and drying-out of the filler material. However, there should not be a superfluous amount of water present to avoid that a water film is produced at the bonding zone, which may lead to failure of the joint.

The shape (contour) of the joint has a positive impact on the shear capacity of the connection. Another advantage of contouring is that the eventual transport length of the liquid next to the bond is increased considerably, leading to a better liquid tightness. The shape of the joint should be designed such that it always allows proper placement and compaction of the filler. The dimensions provided in Fig 5.6 are the minimum boundary conditions. Additional measures that may improve the tightness of (wet) joints are the application of steel cover plates or sealing sections and the application of injection with cement paste or synthetic resin. However, this type of measures falls beyond the scope of this course.

Testing of the liquid penetration Consider a prefab structure that is subjected to a unidirectional bending moment. Then an uncracked compressive zone is present, which is responsible for the liquid tightness of the joint (Fig. 5.7). The liquid tightness is guaranteed if it holds:

1.5x th e>

d 13 d

20 mm 20 mm

Fig. 5.6: Minimum dimensions for joint geometry after DIN 1045

5-5

where: xh = the depth of the compressive zone

1.5 = the factor of safety te = the characteristic penetration depth of the considered fluid after an exposure time t

All penetration tests, that have been done up to now, concerned monolithic concrete. Preliminary re-search however revealed that the condition of the boundary layer between the prefab concrete and the filler material has a large influence on the penetration depth. Therefore, extra laboratory penetration tests have been carried out on drill cores [1]. These experiments were done on three series of in total 48

test elements, each consisting of two prefab parts connected with a joint. From these test elements (Fig. 5.8) 138 drill cores with a diameter of 80 mm were extracted and tested. The cores were taken from the prefab concrete itself, from the pure filler material and from the interface area of the two materials. The faces of the prefab elements forming the construction joint underwent different types of pre-treatment. They were: T no pre-treatment; GT sandblasted; NN not properly wetted (too much water used); GNN sandblasted & not properly wetted; GN sandblasted & properly wetted; GNZ sandblasted & properly wetted & pre-treated with a cement-based bonding material; GE sandblasted & properly wetted & pre-treated with an epoxy-resin-based bonding material. Other parameters in the research were: the pouring direction of the concrete: perpendicular to the joint (slab construction) or in longitudinal

direction of the joint (wall construction); the test fluid: water, acetone, n-butane alcohol, fuel oil EL and n-hexane. The last parameter represents a wide spectrum of liquids with a certain viscosity and surface tension. All specimens were placed in a metal cylinder en tested during 72 hours under a pressure corresponding with a liquid head of 1.4 m.

Fig. 5.7: Loading in one direction with a cracking moment.

prefab placed prefabin-situ

compressive zone compressive zone

Fig. 5.8: Characteristic trend of the penetration depth, obtained by drill core testing.

prefab joint

72,Pe

72,Ie

72,Je

interface

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To obtain one mean value of the penetration depth at least three specimens were tested and averaged. Further, a factor of 1.35 was introduced to relate the mean and characteristic values of the penetration depth, i.e.:

,, 72, 72 72,; 1.35t m

t m m t m

n

i

ee e e e e

n= = = =

The penetration depths were measured in the prefab concrete ( 72,Pe ), at the position of the interface ( 72,Ie ) and in the joint filler material ( 72,Je ). Per test element this delivered a nose shaped curve as in-dicated in Fig. 5.8. The ratios 72, 72,I Pe e and 72, 72,I Je e are a measure for the relative penetration depth in the joint. For the judgement of the structure, the penetration depth in the joint filler and the interface should be investi-gated and compared (the concrete quality of the prefab is always better and has the lowest penetration depth). Therefore, the smallest ratio of penetration depth is decisive and is indicated by F , the so-called joint coefficient, it holds:

72, 72,F I Je e = Table 5.1 lists the average results. For example, looking at the measurements from series 1, it demon-strates that only for the pre-treatment variant GT (sandblasted) a result was obtained which was compa-rable with that of the in-situ concrete of the joint. In the case of no pre-treatment (T) or not properly wetted surfaces (NN or GNN), the joint coefficient was considerably higher.

A summary of the average overall results of all tests can be found in Table 5.2. It can be noticed that the pre-treatment method GNZ (sandblasted & properly wetted & cement-based bonding) leads to the best results. For the other pre-treatment methods it holds that the penetration depth varies strongly compared with that of the in-situ placed concrete. Next to GNZ, the other favourable pre-treatments are GN, GE and GT. The results of the table can be used to check the liquid tightness in practical situations, without the necessity of doing specific tests.

series 1 series 2 series 3 water water n-butane

alcohol fuel oil acetone n-hexane

mean

n Fi n Fi n Fi n Fi n Fi n Fi F T

NN GNN GN

GNZ GE GT

6 5 6 - - - 6

2.02 1.71 1.88

- - -

1.30

- - - 2 4 4 2

- - -

1.10 1.02 1.12 1.21

- - - 2 4 4 2

- - -

1.00 1.00 - 1) - 2)

- - - 2 4 4 2

- - -

1.33 1.16 1.27 1.11

- - - 3 3 3 3

- - -

1.18 1.20 1.40 1.34

- - - 3 3 3 3

- - -

- 2) - 2) - 2) - 2)

2.02 1.71 1.88 1.16 1.09 1.25 1.27

1) Failure of the bonding; 2) Exact determination of the penetration front was not possible

Table 5.1: Joint coefficients.

pre-treatment F GNZ sandblasted & properly wetted & cement based bonding layer GN sandblasted & properly wetted GE sandblasted & epoxy resin based bonding layer GT sandblasted T no pre-treatment

1.09 1.16 1.25 1.27 2.02

Table 5.2: Mean values of the joint coefficients.

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The question, whether a cement-based bonding layer should be applied is a matter of weighing the risks. Namely, the bonding layer should be applied strictly within the setting time and covered with concrete. When this time is exceeded, the danger exists that the bonding layer starts to act as a separa-tion layer instead.

Permeability research In the case of a prefab structure loaded by alternating moments, the compressive zone is not uncracked anymore but pre-damaged. The check with respect to liquid tightness as discussed in previous section is not relevant anymore. For this situation, separate tightness experiments were carried out in the re-

search programme, where prefab structures were used that were loaded before and during testing [1]. In Fig 5.9 one of the in total 16 specimens has been depicted. Each specimen consisted of two prefab ele-ments and an in-situ poured reinforced concrete joint. The most important parameters in the experi-ments were: the distinction between horizontal and vertical elements; the several pre-treatment methods NN, GNN, GN, GNZ and GE (see previous section); the effect of the prestressing; the geometry of the joint; the influence of prohibited shrinkage; different test fluids: water, n-butane alcohol and n-hexane. Prior to the permeability tests, all specimens were subjected to cyclic loading in the form of alternating bending moments. These moments induced crack formation and the process was continued until a target crack width of 0.16 mm was reached. Subsequently, permeability tests were done on the specimens in both unloaded and loaded state. The relevant conclusions of the experiments can be summarised as follows: The weak spot in the joint is always the interface between the prefab concrete and the joint filler. Al-

ready after one load cycle, two cracks were visible in all test specimens. Only an effective pre-treatment of the prefab contact surfaces resulted, after loading until cracking, in an irregular crack pattern with rough crack flanks around the interface (Fig. 5.10).

The minimum pre-treatment should at least be GN (sandblasted & properly wetted). Further im-provement can be achieved by the application of a bonding agent (GNZ or GE). Poor pre-treatment (NN or GNN) even led to separation of the interface.

Fig. 5.9: Specimen for permeability research (dimensions in mm).

2 1 2323 1

2 2323 1

20

41

10

40

500

40

41

10

20

650 30 20 20 30 6501800

2 8 6 5 12 8 2 865 12

A A

8 6 12 8 86

200

55 9

0 55

section A-A

5-8

By repetitive cyclic loading of a joint at constant load level, the crack width shall increase steadily. This effect can be counteracted by the application of a prestress with order of magnitude of 1.5 up to 2.5 N/mm2. This action leads to a smaller crack width and at the same time to a higher concrete compressive stress.

Permeability tests with water as a medium, performed on not loaded (unloaded) and properly pre-treated specimens demonstrated that all of them were watertight. Hereby autogenous healing plays a role, so that also the poorest specimens demonstrated an improvement of the tightness in due time.

The loaded, with water tested specimens, also appeared to be sufficiently watertight. For another medium than water (n-hexane), a constant liquid flow developed in the course of time, which was not reduced by self healing. The cause of this can be found in the occurred damage by the cyclic loading in the crack flanks of the concrete. The crumbled off particles are not capable to seal the crack completely, which means that leaking occurs.

The tightness of a pre-damaged structure can be restored by the application of a prestress of about 2.5 N/mm2. This decreases the crack width and increases the concrete compressive stress.

Another possibility to enhance the liquid tightness at cyclic loading is adaptation of the joint geome-try (Fig. 5.11). The horizontal slot guarantees a better tightness. But one should investigate if this joint shape could actually be applied in view of other important properties such as force transmis-sion, filling and compacting of the joint.

Experiments with respect to the shrinkage behaviour of the joint have shown that indeed micro-cracks are formed by shrinkage, but that these hardly affect the permeability of the joint. Also the way the concrete was placed in the joint (horizontal versus vertical), had no effect on the permeabil-ity.

It can be concluded that the tightness of prefab structures, depending on the type of loading, always can be guaranteed, when the proper pre-treatment and eventual other measures have been applied correctly. The flow diagram of Fig. 5.12 provides a summary of the conditions for proper tightness.

Fig. 5.10: Crack pattern for proper (left) and improper (right) pre-treatment.

Fig. 5.11: Sealing action of modified joint geometry (right).

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5.1.3 Joints in circular tanks In circular prefab reservoirs two types of joints can be distinguished: the horizontal joint between the prefab wall elements and the in-situ poured base slab; the vertical joints between the wall elements. Because of the stable shape of the cylindrical wall construction and the possibility to absorb axial-symmetrical loads with circumferential forces, a lot of freedom exists in the choice of wall-base con-nections. This topic is the source of a lot of discussion. In the literature [2, 3, 4] and in the engineering practice many solutions have been realised. Fig. 5.13 gives an overview of several solutions for the wall-base connection. In principle, this connection can be of the following type: clamped, this means that the deformation is completely prohibited; elastically clamped; hinged, for example by a concrete hinge or ridge construction elastically supported; horizontally displaceable (sliding support). When a reservoir is constructed in reinforced concrete, a monolithic wall-base connection with rigid clamping is the preferred solution. Crack formation in the wall, as a result of the prohibited deforma-tions, should be controlled by proper reinforcement. In the wall, horizontal tangential forces are gener-ated next to shear forces and flexural moments in vertical direction. For the larger diameters, the wall structure is often prestressed in horizontal direction. In practice, a horizontally displaceable wall-base connection is preferred as shown in Fig. 5.14. This means that the full load has to be carried by the circumferential forces. In vertical direction only traditional reinforce-ment will be applied. Deformations caused by shrinkage and temperature variations can freely develop. The wall-base joint requires some extra prestressing, but the costs of this action are relatively small. Special attention and experience is a prerequisite for proper construction of the joint.

72 72,t m Fe e e = = 1.35 2

poured-inproperly centric modified additionalfeaturespre-treated prestressing joint conventional(joint tape,(GNZ, GN, GE) geometry reinforcement(2.5 N/mm ) joint section)

e t

e

e

t

d ed

et

==

==

wall thicknesssafety factor forpenetration depth( 1.5)penetration depthfor exposure time

loads not leading to crack formation

tightness of forcetransmitting structures

loads leading to crack formation

cyclic loads leading to crack formation

F pre-treatment1.09 G1.16GN1.25GE1.27GT

reinforced elements

prestressed elements

if all requirements aresatisfied, the tightness

of the structure is assured

e t

e

e

t

x ex

et

==

==

depth compr. zonesafety factor forpenetration depth( 1.5)penetration depthfor exposure time

Fig. 5.12: Check on tightness of structural joint in prefabricated concrete.

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statical system volume

constructionmethod

from small to middle

large (< 5000 m3)

elastic clamp

cross-section

clamp

hinge

hindered displacement

elastic displacement

from small

to large (< 10000 m3)

from small

to large (< 10000 m3)

no

limitation

from large

to very large(> 10000 m3)

reinforced concrete

& prestressed

concrete

reinforced concrete

& prestressed

concrete

prestressed concrete

prestressed concrete

prestressed concrete

Fig. 5.13: Structural examples of wall-base connections.

prestressed wall

elastic joint section of 240 mm height

poly urethane

foam

sliding support

in-situ cast

base

cover 30 mm

Fig. 5.14: Joint detail of horizontally displaceable wall-base connection.

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A variant of the wall-base connection contains a rubber bearing strip, which is glued to the concrete (Fig. 5.15). However, this variant is sensitive to settlements and therefore only can be applied under set-tlement free conditions, for example when a piled base slab is present. Compared with an in-situ poured wall structure, the prefab wall structure differs at two important as-pects: the prefab element may be vertically prestressed; at the moment of erection, the major part of the shrinkage has occurred already. The prestressed elements can be attached to the floor with a hinged or clamped connection without any danger for crack formation. An example of a prefab structure with vertical load transmission is shown in Fig. 5.16. It concerns a basin of a waste-water purification plant of the company DSM in the Nether-lands [5]. An in-situ placed ring beam takes up the horizontal circumferential forces, so that the vertical joints in the wall does not take part in the force transmission and only have a sealing function.

The construction method whereby the prefab walls are forced together by horizontal prestressing cables is very common. During the prestressing action, the elements should be able to move freely, after that the walls can be fixed to the base slab. Fig 5.17 gives an example. A variant to this solution, whereby a sealing section has been used will be discussed in Section 5.1.4.

rubber glued to concrete

Fig. 5.15: Variant of horizontally displaceable joint with rubber strip for settlement-free conditions.

Fig. 5.16: Wall construction with ring beam of settlement basins at the DSM plant.

prefab wall element

in-situ cast concrete

in-situ cast concrete

adjustingmortar

asphalt concrete

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For the realisation of vertical joints many solutions are available. An overview is given in [3]. Require-ments imposed on joints are: ability of proper force transmission, a simple design that easily can be ap-plied, and the capacity to address tolerances in the dimensioning. The most important parameters for the selection of a joint are the choice of a wet or dry joint and whether prestressing should be utilised. This prestressing can be applied externally or internally, and it may be continuous or in the form of short ele-ments. Some examples of joints are: a loop connection as discussed in Section 5.1.2; a hinge shaped joint that will be concreted on and externally prestressed (Fig. 5.18); a mortar joint with internal prestressing (Fig. 5.19); a prestressed joint with a tongue-and-groove system (Fig. 5.20). The last joint can be real-

prefab wall element

in-situ castconcrete

Fig. 5.17: Hinged wall-base connection put in place after prestressing of the wall elements.

prefab wall-element

protective layer

A A

construction joint

tendon

temporary support

foilin-situ cast concrete base

in-situ castC28/35

tendon spacer

section A-A

Fig. 5.18: Joint construction of the ACONTANK, Sweden.

duct for tendon

1000

10151015

0 10-

Fig. 5.19: Prestressed mortar joint (dimensions in mm).

5-13

ised as a dry joint by using a rubber strip or with epoxy resin filler. A disadvantage of a dry joint is that due to dimensional inaccuracies in the production, especially for the higher tank walls, concrete-to-concrete contact may occur leading to possible splitting of the concrete.

5.1.4 Practical example: aeration circuit In this section a recent project will be discussed as an illustration of an economic solution for a waste-water reservoir, erected in prefab concrete. It concerns the construction of two tanks for the sewage pu-rification plant Goedereede in the Province South-Holland in the Netherlands. The layout of the instal-lation is depicted in Fig. 5.21, including the extension with a new aeration tank and a new resettling tank, both with a diameter of 40 m. The tanks were made from prefab concrete instead of the more tra-ditional in-situ poured concrete. The main reasons for this choice were the lower construction costs and

Fig. 5.20: prestressed joint with tongue-and-groove system.

Fig. 5.21: Lay-out of the sewage purification plant at Goedereede.

aeration tank

Fig. 5.22: High aeration tank: situation during construction.

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the shorter construction time. Fig. 5.22 gives an idea of the situation during the erection phase. In more detail the high aeration tank will be considered. It has a wall height of 6.0 m and retains a water height of 5.0 m. As can be observed from Fig. 5.22, the tank possesses several compartments combining several technological functions: the so-called selector, the anaerobe zone, the denitrification zone and the nitrification zone. Here, attention will be paid to the construction of the outer wall. On the one hand this wall experiences the largest load and on the other hand it has to comply with the highest require-ment with respect to liquid tightness. The so-called Muleby-II prefab system was applied for the construction of the tank. The system is from Danish origin and is used under licence by the Dutch firm Farmex Environmental Engineering BV. Outside the Netherlands this system is applied quite frequently, in the Netherlands however just a few years at least at this scale.

The outer wall of the tank is composed from concrete panels with a width of 2.40 m and a height of 6.00 m. The elements have a thickness over the entire height that varies from 170 mm to 200 mm. The inside of the elements is flat while the outside is convex (Fig. 5.23). The concrete class is C35/45 and the elements are prestressed in vertical direction with 25 strands of 9.3 mm diameter. The elements are connected with a tongue-and-groove system and prestressed with internal prestressing cables. Before the application of the prestress, the vertical joints were filled up with a layer of cement based self-compacting mortar. This mortar was cast in the hollow space of the joint between the two sealing strips of hard-neoprene (Fig. 5.24). The surfaces forming the joint did not receive any form of pre-treatment. The tongue-and-groove connection receives an extra seal at the inside of the wall on the basis of polyurethane.

Normally, the wall-base connection is realised according to the standard design as sketched in Fig. 5.25. The elements are firstly adjusted on steel plates and mortar and then prestressed. After prestressing the insert at both sides of the wall is filled with Spramex concrete containing elastomeric fibre cement; Spramex is a concrete with small aggregates, in present case smaller than 4 mm. At the inside of the wall a swelling seal is applied.

2400

2383

170

200

200

duct for tendon

Fig. 5.23: Cross-section of a wall element (dimensions in mm).

200 170

cement-based swellingself-compacting mortar

neopreneseal

extra seal of polyurethane

Fig. 5.24: Detail of the joint of the wall elements (dimensions in mm).

5-15

At the sewage purification plant at Goedereede, this standard design has been adapted because of the high probability of settlements of the shallow foundation of the base slab. An additional curb was placed containing a sealing section providing extra safety against leakage in the case some settlement would occur (Fig. 5.26). The hinged wall-base connection that was realised in the final situation had to keep the tensile forces in the lower part of the wall within acceptable limits. The distribution of the prestress over the height of the wall helped to achieve this goal (Fig. 5.27). In total 20 horizontal strands have been used of 15.2 mm diameter tensioned to a prestressing force of 170 kN. The minimum centre-to-centre distance of the strands was 150 mm. The total erection time of the entire wall was 10 working days.

5.1.5 Comparison of costs In this section, the costs of the prefab concrete wall as described in Section 5.1.4 (price level 1998) will be compared with the costs of the more traditionally in-situ poured prestressed wall. In Table 5.3 the cost estimations are summarised of the prefab wall, realised with the standard wall-base connection of Fig. 5.25. Indicated are the total costs of a tank wall of 6 m height, consisting of 52 ele-ments with a width of 2.4 m, and the relative costs in percentages. The total wall area is 749 m2. The mentioned costs boil down to an amount of 163.60 per m2 wall. This excludes the extra costs of the curb and the sealing section at the wall-base connection (Fig. 5.26). These extra costs are 136.40 per m joint. The total amount becomes 136.40522.40 = 17,020, or 22.70 per m2 wall. Summarising, the total costs including the extra curb but excluding VAT become:

300 200 500 300 150

330

17

0 120

20, 248R =19,598R =

adjustingmortar swelling seal finish 30 mm

bedding 50 mm

Fig. 5.25: Detailing of standard wall-base connection (dimensions in mm).

300 200 250 200 300

360

20, 631R =19,881R =

swelling sealconcreted curbsealing section

350

50

bedding 50 mm

Fig. 5.26: Detailing of wall-base connection for outer wall of aeration tank (dimensions in mm).

5-16

total amount 139,590.00 per m2 186.40 In the traditional design, the wall would have been poured in-situ having a thickness of about 250 mm and a wall-base connection according to the details of the Figs 5.14 and 5.28. The concrete class would be C28/35 and the prestressing realised with 38 strands of 12.9 mm diameter that are anchored in 4 prestressing ribs. The distribution of the strands is indicated in Fig. 5.28. Further, the wall would con-tain an amount of normal reinforcement of 70 kg/m3. The cost estimations of the in-situ placed wall, including the wall-base connection is summarised in Ta-ble 5.4. The calculated costs for the traditional solution are more than 30% higher than those for the prefab wall. The difference mainly originates from the high costs of the formwork. Namely, the 6 m high wall has to be poured in two stages. Also, for the inner walls of the tank comparable cost differences may be ex-pected between the two solutions, because of the high formwork costs.

tendon

170 - 200

6,00

0 5,

000

Fig. 5.27: Prestressed wall of prefab concrete (dimensions in mm).

specification costs () percentage (%) production and material of elements construction materials tendons adjusting mortar adjusting material salary costs erection freight costs crane costs depreciation molds and materials engineering costs site costs

62,510 14,710 17,160 13,480 4,900 3,680 3,680 2,450

51 12

14 11 4 3 3 2

total 122,570 100

Table 5.3: Construction costs of prefab outer wall structure with standard wall-base connection including all costs, but without VAT.

5-17

For smaller wall heights, the cost difference between both solutions will decline. The costs of the prefab elements are not significantly lower for the smaller wall heights and even increase per m2 wall area. While the costs of the formwork for the in-situ placed wall are considerably less, leading to a decrease in costs per m2. In Fig 5.29 the trend is globally indicated. It can be concluded that with the choice of a prefab structure, next to high quality liquid tightness also an economic solution has been realised. After Goedereede comparable projects followed in the municipalities Stein, St. Maartensdijk and Hengelo. In the last municipality, four tanks were erected with a diameter of 55 m and a wall height of nearly 6 m.

Remark In this case-study, construction with completely prefabricated elements has been discussed. In next case-study (Section 5.2) construction with in-situ placed walls will be highlighted. But it is also possible to choose for a hybrid solution, the so-called composite walls. These walls consist of two prefab con-crete shells that are mutually connected with lattice girders, which will be concreted on site. The walls

tendon

170 - 200

150

6,00

0

5,00

0 Fig. 5.28: Prestressed wall of in-situ concrete (dimensions in mm).

specification costs () adjusting and depreciation of formwork delivery and placement of reinforcement delivery and placement of sealing section delivery and tensioning of tendons delivery and pouring of concrete stripping of formwork

76,200 10,930 3,460 25,710 22,570 6,580

subtotal production costs general costs profit and risk

145,450 12,090 10,180 7,280

contract price engineering and management

175,000 10,500

total 185,500

Table 5.4: Construction costs of traditional wall structure including all costs, but without VAT.

5-18

are placed on an in-situ poured slab or foundation. Since composite walls are a combination of prefab and in-situ placed concrete, it also combines the advantages and disadvantages of both systems [6]: advantages of prefab: less formwork, short erection times, high quality, smooth wall, cost saving for

large numbers and large structures; disadvantages of prefab: limited dimensions of elements (transport), extra transport, limited freedom

in design; advantages of in-situ placed concrete: monolithic wall-wall and wall-base connections can be real-

ised relatively simple; more flexibility during construction; disadvantages of in-situ placed concrete: weather dependence, long erection times. 5.1.6 References [1] Bida M., Grote K.P.: Durchlssigkeit und konstruktive Konzeption von Fugen (Fertiegteilver-

bindungen), Deutscher Ausschluss fr Stahlbeton, Heft 464. [2] Klawa N., Haack A.: Tiefbaufugen. Fugen und Fugenkonstructionen im Beton- und Stahlbeton-

bau, Verlag fr Architektur und Wissenshaften, Berlin [3] Frnay J.W., Straman J.P., Braam C.R.: Circular prefabricated concrete tanks, IMAG-DLO,

Wageningen. [4] Bruggeling A.S.G.: Betonconstructies in de civiele gezondheidstechniek, Stichting Prof. Bak-

kerfonds. [5] Dijkstra F.: Waterzuivering DSM, Cement 32, no. 9, 1980. [6] STUPR-commissie 40: Samengestelde wandconstructies, STUPR-report no. 21, Aug. 1990.

5.2 Cylindrical reservoirs made from in-situ placed concrete 5.2.1 Control of vertical crack formation The goal of this case study is: to discuss the computational procedure for the determination of the crack behaviour of a cylindrical

wall in reinforced concrete, which is loaded by a combination of a normal force and a temperature difference across the wall thickness;

to compare the calculated and observed vertical crack patterns; to illustrate the effect of a light horizontal prestress on the size of the compressive zone. Pure tension - separation cracks In a cylindrical reservoir, the wall is subjected to tension because of the (hydrostatic) liquid loading. If the tensile force in the wall exceeds the tensile strength of the concrete separation cracks will be gener-ated (Fig. 5.30a). In order to guarantee a liquid tight structure, a heavy crack width limiting reinforce-ment should be applied. When the occurrence of separation cracks due to hydrostatic pressure has to be eliminated completely, the structure has to be prestressed.

400

300

200

100

0 0 1 2 3 4 5 6 7 8 9 10

wall height [m]co

sts [

/m

2 ] 247

164

prefab concrete

in-situ concrete

Fig. 5.29: Global cost comparison of the two construction types.

5-19

Combination of tensile forces and imposed curvature Vertical cracks can also be generated by a combination of tensile forces and bending moments resulting from temperature and/or shrinkage gradients. For the combination normal force + bending normally a compressive zone will be present. To be guaranteed of liquid tight behaviour, this compressive zone should possess a minimum depth (see Section 2.6). The presence of a tensile force will rapidly diminish the size of the compressive zone. The application of a small horizontal prestress can be very effective to enlarge the compressive zone.

5.2.2 Internal loads in the cylindrical wall Cylindrical wall loaded by a membrane force and imposed curvature

Liquid loading The tensile force ; ( )lN x in the wall as e result of the liquid pressure can be obtained by the boiler formula (also see Chapter 3:

( ); ( ) ( ) ; ( )l l l l lN x Z x R Z x H x = = [N/m] (5.1) where lH [m] is the liquid height, l [N/m3] is the specific weight of the liquid and R [m] is the radius of the reservoir. The stress ; ( )l x in tangential direction follows from: ;;

( )( ) ll

c

N xx

A

= [N/m2] (5.2)

where cA is the cross-sectional area per running meter wall height. For reservoirs with low walls, the tangential force ; ( )lN x will often be smaller than the cracking tensile force crN , or in other words, the concrete tensile stress will be considerably smaller than the tensile strength ctf of the concrete. How-ever, under the influence of shrinkage and temperature effects stresses are induced that may easily lead to crack formation.

Temperature loading In Fig. 5.30b a part of the cylindrical wall with radius R and wall thickness wh has been depicted, which is loaded by a circumferential force ;lN and a temperature load ( )T z . This temperature load across the wall thickness can be split into an mean part and a linear part, i.e.:

B

BR

bT

A

A z

M

N

M

N

B

BA

AMN

M

N

,c cr (between cracks)c

a) vertical cracks due to hydrostatic pressure; b) Response of cylindrical wall to imposed wall on sliding support curvature ( )bT + normal force N

Fig. 5.30: Crack formation in reservoir wall under the action of hydrostatic pressure and imposed curvature.

5-20

1 12 2( 0)mT T z T = = = (5.3) bT T = (5.4) Because of the mean temperature increase the cylinder will expand. The radius will increase by:

( )m c mR T T R = (5.5) Under influence of the temperature difference bT across the wall, the cylinder has the tendency to curve. The induced curvature becomes:

( ) c bbw

TTh

= (5.6)

Under this imposed curvature the cylinder segment shown in Fig. 5.30b has the tendency to deform. At the positions of the imaginary cuts A-A and B-B gaps will be formed, which have to be annihilated by the moments ( )bM T . For these temperature moments it holds (the lateral contraction is taken into ac-count):

( )( ) ( ) 1b bM T T K = + (5.7) where K is the flexural stiffness of the wall given by:

( )3

212 1c wE bhK = [Nm] (5.8)

where b is the size of the considered segment in height direction, wh is the wall thickness, is Pois-sons ratio and cE is the modulus of elasticity of the concrete. In the uncracked phase, the stresses caused by the hydrostatic pressure and the temperature load can simply be added. But as soon as cracks are formed under this load combination, the determination of the stresses is much more complicated. Te starting point always is that in each cross-section the compatibil-ity of the deformations and the equilibrium of the forces have to be satisfied.

Cracking moment Due to the presence of a circumferential force N and the associated tangential stress ;ct N cN A = , the moment for which cracking occurs will be lower than the cracking moment of an element that is not subjected to a membrane force (Fig. 5.31). The cracking moment follows from:

( ) 2; , ; 16cr N c cr ct N wM b h = (5.9) where ,c cr is the stress for which cracking of the concrete occurs (also see Section 4.3).

Fig. 5.31: Effect of circumferential force on the temperature-induced moment capacity.

1T

1( ) ctT =

2T ;ct N

NN

2 1( ) ( )T T < a) cylindrical wall loaded by b) cylindrical wall loaded by normal force temperature difference 1T N and temperature difference 1T

5-21

Load distribution in the cross-section The -M diagram for the cylindrical wall is shown in Fig. 5.32. For the determination of the cracking behaviour it is assumed that the cracking moment ;cr NM remains constant until the final cracking pat-tern is obtained. Subsequently, the equilibrium of forces and the equilibrium of moments at the position of a crack will be considered. The equilibrium of forces at the position of a vertical crack reads (Fig. 5.33):

1 20 0s s ccN N N N N = + + + = (5.10) where:

1sN = steel force at tensile side 2sN = steel force at compressive side ccN = compressive force in concrete compressive zone N = external normal force (for example due to hydrostatic load or prestressing)

The equilibrium of moments at the position of a vertical crack becomes (Fig. 5.33):

( ) ( ) ( )1 2 ;1 1 1 13 2 3 30 s x w x s w x cr NM N d h N h h N h d h M = = + + (5.11) For 1sN , ccN and 2sN it subsequently follows (Fig. 5.33):

1 1 ,s s s crN A = (5.12)

,c crT wh

;cr NM

N

;cr NM

N

;cr NM

M

cr fdc

( )b mT

constant moment

crT ( )b mT( )b mT

bTFig. 5.32: Moment-curvature diagram for a cylindrical wall subjected to a circumferential force N and a temperature load bT .

Fig. 5.33: Forces, stresses and strains required for the analysis of a vertical crack in a cylindrical wall.

,c crT wh

;cr NM

N

;cr NM

N

xh

dwh

c

N;cr NM

1sN

2sN

ccN

c2s

1s

5-22

( ) ( )( )

2

,1

, ,

,1

2

2

x ccc

c c cx

x cc s crc s x x x

x c s cr s crs x

xs crcs

s

h bN

Ebhh Nh h n d hd h

E n d hd hEE

= = == = = =

(5.13)

2 2 2

2 2

2 2 ,2 12 ,

,1

s s s

s s s

x wx ws s s crs s x w

xx s s crx

s crs

s

N AE

d h hd h h N Ad h h d hd hd h

E

= = + + == + = =

(5.14)

where ,s cr is the steel stress in the crack for a not fully developed crack pattern. Substitution of above relations for 1sN , ccN and 2sN into the force equilibrium (5.10) provides, for a symmetrical reinforcement 1 2s s sA A A= = , the following relation for sA :

( )

( )2

,

,

22 2

x s cr xs

s cr w x

b h n N d hA

n h h

+ = (5.15)

However, substitution of above relations for 1sN and 2sN into the moment equilibrium (5.11) delivers:

( );

,

1 12 3( )

cr N w xs

s cr x

M N h hA

f h

+ = (5.16)

in which ( )xf h is a help function given by:

2 2 22 4

3 3 2 2( ) x w x w wxx

h h h d d h hf h

d h + += (5.17)

The relation (5.15) and (5.16) form a system of two equations with three unknowns, i.e. sA , ,s cr and xh . Once the value of one of these quantities is selected, the two other quantities can be determined.

Determination of the number of vertical cracks in a cylindrical wall The determination of the number of cracks in a cylindrical wall, which is loaded by a circumferential force N N= and a temperature difference bT , is based on the required compatibility of deforma-tions. The imposed curvature at the moment that the first crack occurs (i.e. for b crT T = ) is equal to (Fig. 5.32):

( ) c crcrw

TTh

= (5.18)

With increasing curvature more cracks will be generated. For an increase of the temperature load equal to ( )b mT , m cracks are generated. This increase of the temperature load corresponds with the fol-lowing increase of the imposed curvature:

( )( ) c b mb mw

TTh

= (5.19)

If this additional curvature would be able to occur freely, it would lead to an angular rotation in the cy-lindrical wall of:

5-23

( ) ( ) 2b m b mT T R = (5.20) It is assumed that this fictitious angular rotation is concentrated in the m cracks. Each crack consumes a proportional part of the imposed angular rotation. For the angular rotation per crack cr it approxi-mately holds (Fig. 5.34):

avcrx

wd h

(5.21)

The compatibility condition now becomes:

( ) 2cr b mm T R = (5.22) Substitution of (5.19) and (5.21) into (5.22) provides the relation for the number of vertical cracks:

( )( ) 2b m c xw av

T R d hm

h w = (5.23)

Cylindrical wall in cracked state subjected to pure tension Vertical crack formation often occurs by the joint action of tension + (temperature and/or shrinkage induced) bending. If the imposed (temperature) curvature disappears, the wall that is exposed to the hydrostatic liquid pressure will be subject of pure tension. The tensile force ; ( )lN x might be consid-erably lower than the cracking force crN , especially at the higher positions in the wall where the hydro-static pressure is lower. For the determination of the crack width, the following steel stress s should be used in the crack-width formulae:

;;( )

( ( )) ls s ls

N xN x

A

= = (5.24)

5.2.3 Reinforced and partially prestressed cylindrical wall Description of the structure and loads A cylindrical low-walled reservoir is considered in reinforced concrete (Fig. 5.35). The wall-base con-nection is monolithic.

Data of the reservoir Diameter of the reservoir: D = 18.5 m Wall thickness: wh = 0.25 m Wall height wH = 2.5 m (= liquid height lH ) Diameter horizontal reinforcement = 10 mm Horizontal reinforcement ratio s = 0.16% at each side ( 10-200 ) Strength class of concrete C20/25 = value according to specifications

Fig. 5.34: Curvature distribution near a vertical crack in a cylindrical wall.

( )crT ( )bT

2 stl

dwh

crMxh

xd h

avw

5-24

Actions Temperature liquid: lT = ca 25

0C (waste water) Specific weight liquid l = 10 kN/m3 Outside temperature oT = -10

0C (in winter with moderate wind speeds) oT = -20

0C (in winter with high wind speeds) oT = +30

0C (in summer) Drying shrinkage: This shrinkage is replaced by a temperature load ;b shrT having the same effect:

30

; 50.1 10 10 C

10shr

b shrc

T

= = = (5.25)

For the determination of the effective temperature difference across the wall thickness, one should be aware of the heat transmission resistances at the concrete surfaces. The effect of these resistances is that the situation is more favourable than can be expected on basis of the inside and outside temperatures. For this case, a temperature difference, which comprises both the temperature load and the drying shrinkage, is assumed of:

0;max ; ; 30 10 40 Cb b eff b shrT T T = + = + = (5.26)

Observations of the crack pattern A reservoir, having similar dimensions and subjected to a loading scenario as described above was ob-served with respect to the crack pattern over a period of three years. The results were as follows: Vertical cracks:

o crack width after 7 years: mw = 0.3 mm (mean and max values) maxw = 0.7 mm

o number of (open) cracks: m = 34 at 00 5 CT m = 75 at 00 20 CT (severe frost with wind)

In the upper part of the wall the cracks appeared to be separation cracks The cracks that were open during the winter period, almost closed completely at higher outside tem-

peratures. During the period that the structure was observed, it was recorded that the crack widths of the firstly

initiated cracks increased in the course of years. The cracks that developed later, nearly closed with the rise of the outside temperature.

The firstly initiated cracks, revealed themselves in increasing degree as water discharging cracks. Numerical analysis Force distribution by liquid loading In the present case, a combination load tension + bending occurs. In the wall circumferential forces are generated caused by the liquid load. The calculated circumferential force distribution ; ( )lN x is

variable oT

025 ClT =oT

250 mm 9, 250 mmwh R= =

Hw =

2,5

00 m

m

Fig. 5.35: Cross-section of cylindrical shallow reservoir with loading scheme.

5-25

displayed in Fig. 5.36 (result of shell calculation). The circumferential force reaches a maximum around 76 kN/m, at ca 1.25 m above the base, which is equivalent to a nominal tangential tensile stress of:

; 2;76,000( 1.25) 0.3 N/mm

250 1,000l

lc

Nx

A

= = = =

Cracking moment The cracking moment ( )crM N in the wall is determined by the (effective) tensile strength of the con-crete and by the present normal force in the cross-section. In this case that is the tensile force resulting from the hydrostatic load.

Practical values of the tensile strength of the concrete The analysis of a practical case requires the utilisation of a tensile strength which is actually present. This strength can be derived from the mean compressive strength cmf , which is related to the C value ( ccf ) by: 28.2 N/mmcm ccf f = + For C20/25 this provides: 225 8.2 33.2 N/mmcmf = + = . On basis of the information in a number of BMC yearly reports and practical experience it can be stated that the actual mean cube compressive strength for C20/25 delivered by the manufacturers in the Neth-erlands is about 240 N/mmcmf . However, for other countries this might be different and perhaps the lower value of 33.2 N/mm2 should be used. In the present case, the empirical relations for the mean short-term tensile strength and the mean flex-ural strength are:

( ) ( )2

,

2, ,

1.0 0.05 1.0 0.05 40 3.0 N/mm

1.6 1.6 0.25 3.0 4.1 N/mmcm o cm

cfl o w cm o

f f

f h f

= + = + == = =

For the stress cr at which the concrete cracks it holds (see Section 4.3): pure tension 2,0.75 2.35 N/mmr cm of = = for short-term loading 2,0.60 1.8 N/mmr cm of = = for long-term loading pure flexure (especially for small thicknesses) 2,0.75 3.0 N/mmr cfl of = = for short-term loading 2,0.60 2.4 N/mmr cfl of = = for long-term loading In the discussed case, the combination of tension + bending is present. So, the tensile strength to be used will have a value between those of pure tension and pure flexure, i.e. between 1.8 N/mm2 and 2.5 N/mm2.

+[m]x

2.5

2.0

1.5

1.0

0.5

0.076 100

;lN

wh

2,500 mmlH =

Fig. 5.36: Circumferential forces ; ( )lN x by liquid loading over the height of the cylindrical wall.

5-26

The calculations were carried out for three values of the stress cr for which crack formation occurs. They were cr = 1.8, 2.6 and 3.6 N/mm2. With these values for the concrete tensile stress at the moment of cracking and the nominal concrete tensile stress 2; 0.3 N/mml = , the following values for the cracking moment ;cr NM can be found (formula (5.9)):

2;

2;

2;

1.8 N/mm 15,625 Nm/m

2.6 N/mm 23,960 Nm/m

3.6 N/mm 34,375 Nm/m

cr cr N

cr cr N

cr cr N

M

M

M

= == == =

Calculation of the crack width and the depth of the compressive zone The highest number of cracks observed was 75. For a circumference of the cylinder equal to

18.5 58 mD = = , the mean crack distance was 0.77 m. With this crack distance the crack pattern is not yet fully developed. For the calculation of the crack widths, formula (4.21) can be used. The steel stress can be obtained from the force equilibrium in the (cracked) cross-sections with the equations (5.10) up to (5.17). For the determination of the maximum crack width maxw a scatter factor of 1.3 is in-corporated (not fully developed crack pattern). For the effect of the cyclic character of the temperature loading on the crack width a factor of 1.3 is used as well.

In Fig. 5.37a, the computed crack width is displayed as a function of the considered tensile strengths at the moment of cracking cr . The effect of the cyclic loading is included in the indicated trends. Fig. 5.37b shows the calculated depth of the compressive zone xh for the different values of the consid-ered tensile strength. These values are smaller than the in Section 2.6.3 mentioned minimum values for watertight structures. The fact that a considerable number of cracks were water discharging, or became water discharging in the course of time, is in agreement with the expected criteria for liquid tightness. The number of cracks m as function of the imposed temperature and shrinkage load is visualised in Fig. 5.38. The best approximation for the observed number of cracks can be obtained with the effective tensile strength of 21.8 N/mmcr = . This value lies between the long-term strengths for pure tension and pure flexure.

The effect of prestressing on the crack pattern The depth of the compressive zone is strongly depending on the magnitude of the nominal circumferen-tial stress . The application of a small prestress increases the depth of the compressive zone consid-erably. This is very important because the size of the compressive zone is of paramount importance for

Fig. 5.37: Computed crack width (flexural cracks) and depth of the compressive zone as function of the tensile strength. Crack width: mean value mw , max. value maxw and the effect of cyclic load.

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

xhwh

2 [N/mm ]cr0 1.0 2.0 3.0 4.0 5.0

crac

k w

idth

w [m

m] increase due to

cyclic loading

max1.3 mw w=

com

pres

sive

dep

th h

x [m

m]

30

20

10

00 1.0 2.0 3.0 4.0 5.0

2 [N/mm ]cr

1.8 2.6 3.6

mw

a) crack width w b) depth compressive zone xh

5-27

the liquid tightness. Fig 5.39 shows the relation between the depth xh of the compressive zone and the nominal tangential stress in the wall. The computations are carried out for an effective tensile strength 22 N/mmcr = and for reinforcement ratios at each side of 0.16% and 0.32%, respectively. It is clear that the effect of a small prestress is much larger than the doubling of the ordinary reinforce-ment. For a nominal tangential stress of 20.3 N/mm = + , a doubling of the reinforcement steel at the tensile side would increase the compressive depth with 8 mm . However, the application of a small prestress 20.8 N/mmcp = that brings the tangential stress down to 20.5 N/mm = , delivers an in-crease in the depth of the compressive zone of 25 mm so that 50 mmxh = . In that case the condition for liquid tightness would be satisfied (see Section 2.6). For the combination of normal (tensile) force plus imposed temperature deformation, the wall in above case still experiences tensile stresses, in other words the wall is partially prestressed. The complete re-moval of the temperature induced tensile stresses by the application of more prestressing is in most cases not necessary to get a watertight structure. Moreover, it would require a very high prestress and for that reason it would become too expensive.

experiments

100

90

80

70

60

50

40

30

20

10

0

0[ C]bT0 10 20 30 40 50 60 70

num

ber o

f cra

cks m

2=1.8 N/mmcr

2=2.6 N/mmcr

2=3.6 N/mmcr

Fig. 5.38: Number of vertical cracks m as function of the imposed temperature load; nominal circumferential tensile stress in the concrete is ; 0.3l = N/mm2.

100

90

80

70

60

50

40

30

20

10

2( ) [ N/mm ]N -2.0 -1.5 -1.0 -0.5 0 0.3 0.5 1.0 1.5

h x [m

m]

0.16%at both sides

s = 0.32%at both sides

s =

Fig. 5.39: Depth of compressive zone hx in cylindrical wall as function of the nominal circumferential stress for reinforcement fractions 0.16%s = and 0.32%s = .