Patent Publication Number: US-2023151611-A1

Title: Post-tensioned concrete slab with fibres

Description:
TECHNICAL FIELD 
     The invention relates to a concrete slab comprising conventional concrete and a combined reinforcement of both post-tension steel strands and fibres. 
     BACKGROUND ART 
     Post-tensioned concrete is a variant of pre-stressed concrete where the tendons, i.e. the post tension steel strands, are tensioned after the surrounding concrete structure has been cast and hardened. It is a practice known in the field of civil engineering since the middle of the twentieth century. 
     Steel fibre reinforced concrete is concrete where the reinforcement is provided by short pieces of steel wire that are spread in the concrete. U.S. Pat. No. 1,633,219 disclosed the reinforcement of concrete pipes by means of pieces of steel wire. Other prior art publications U.S. Pat. Nos. 3,429,094, 3,500,728 and 3,808,085 reflect initial work done by the Batelle Development Corporation. The steel fibres were further improved and industrialized by NV Bekaert SA, amongst others by providing anchorage ends at both ends of the pieces of steel wire, see U.S. Pat. No. 3,900,667. Another relevant improvement was disclosed in U.S. Pat. No. 4,284,667 and related to the introduction of glued steel fibres in order to mitigate problems of mixability in concrete. Flattening the bent anchorage ends of steel fibres, as disclosed in EP-B1-0 851 957, increased the anchorage of the steel fibres in concrete. The supply of steel fibres in a chain package was disclosed in EP-B1-1 383 634. 
     Both reinforcement techniques, post-tensioned concrete and fibre reinforced concrete such as steel fibre reinforced concrete not only exist as such but also in combination. The purpose was to combine the advantages of both reinforcement types to obtain an efficient and reliable reinforced concrete slab. 
     Prior art concrete slabs with combined reinforcement of both post-tension strands and fibres suffer from an overdesign or from a complex design. In an attempt to stay on the very safe side and to meet the specifications, the dosage of steel fibres is often that high that problems such as ball forming occur during mixing of the steel fibres in the non-cured concrete, despite the existence of prior art solutions. Alternatively, or in addition to this, the distance between two neighbouring post-tension strands or between two neighbouring bundles of post-tension strands is very small, causing a lot of labour when installing the post-tension strands, attaching anchors and applying tension. In yet other prior art embodiments the composition of the concrete is such that shrinkage during curing is limited, i.e. a low shrinkage concrete or a shrinkage compensating concrete composition is selected. 
     An example of a complex design of a concrete slab with reinforcement by both post-tension steel strands and steel fibres is disclosed in NZ-A-220 693. This prior art concrete slab has an under and upper skin layer with steel fibres with a core layer in-between with post-tension tendons. 
     DISCLOSURE OF INVENTION 
     It is a general aspect of the invention to avoid the disadvantages of the prior art. 
     It is a further general aspect of the invention to avoid overdesign. 
     It is another aspect of the invention to provide a combination reinforcement of both post-tension strands and fibres to reinforce concrete efficiently and effectively. 
     It is still another aspect of the invention to provide a combination reinforcement of both post-tension strands and fibres for conventional concrete. The tendons or post-tension steel strands are thereby post-tensioned which means that tension is applied to them only after the concrete has been cast and/or that the tendons or post-tension steel strands may for example remain in place also once the concrete is completely cured/hardened. The tendons or post-tension steel strands may thus be installed on-site and/or may be installed before or after casting. The tendons or post-tension steel strands may comprise anchor systems, that may especially attach the tendons or post-tension steel strands to the cast concrete of the slab according to the invention, and/or ducts or sheathing. This may especially contributes for example to allow to achieve bigger slabs, to help with continuity, to help with safety, to help with camber, to minimize pre-stress losses, especially due to creep, to increase the freedom regarding possible shapes and to facilitate a draped configuration of the tendons or post-tension steel strands. In contrast, pre-tensioning is used mostly for pre-cast elements casted off-site with tendons fixed to a form and being tensioned before any concrete is cast. The resulting pre-cast elements obtained by pre-tensioning are thus consequently of quite limited size due to the very need to use forms or moulds, so that flooring may usually require multiple pre-cast elements. 
     According to the invention, there is provided a concrete slab comprising conventional concrete and a combined reinforcement of both post-tension steel strands and fibres, e.g. macro-synthetic fibres or steel fibres. The tendons or post-tension steel strands having a diameter ranging from 5 mm to 20 mm, e.g. from 6 mm to 20 mm, e.g. from 6.5 mm to 18.0 mm, e.g. from 13 mm to &lt;18.0 mm. The post-tension steel strands have a tensile strength higher than 1700 MPa, e.g. higher than 1800 MPa, e.g. higher than 1900 MPa, e.g. higher than 2000 MPa, preferably between 1800 MPa and 4000 MPa. The post-tension steel strands may also for example have a maximum breaking load of higher than 190 kN, e.g. higher than 195 kN, e.g. higher than 200 kN, e.g. higher than 220 kN, preferably between 195 kN and 350 kN. 
     The tendons or post-tension steel strands may be bonded or unbonded. 
     Particularly with a view to be used as post-tension steel strand, the steel strand preferably has a low relaxation behaviour, i.e. a high yield point at 0.1% elongation. The yield point at 0.1% can be considered as the maximum elastic limit. Below the yield point, the post-tension strand will remain in elastic mode. Above the yield point, the post-tension strand may start to elongate in plastic mode, i.e. an elongation that is not reversible. Preferably, the ratio of the yield strength R p0.1  to the tensile strength R m  is higher than 0.75. 
     Low relation post-tension steel strands may have relaxation losses of not more than 2.5% when initially loaded to 70% of specified minimum breaking strength or not more than 3.5% when loaded to 80% of specified minimum breaking strength of the post-tension steel strand after 1000 hours. 
     The fibres can be steel fibres and are present in a dosage ranging from 10 kg/m 3  to 40 kg/m 3 , e.g. ranging from 15 kg/m 3  to 35 kg/m 3 , e.g. from 20 kg/m 3  to 30 kg/m 3 , preferably from 10 kg/m 3  to &lt;30 kg/m 3  or further preferred from 10 kg/m 3  to 27 kg/m 3 . In an embodiment, the amount of steel fibers used according to the present invention may be for example preferably below or equal to 1.2 times, preferably 1.0 time, further preferred between &gt;0 and 1.1 times, the amount or level of steel recommended and used for the steel bars or rebars to be replaced and/or the amount or level of steel fibers may be below or equal 1.2 times, preferably 1 time, further preferred between &gt;0 and 1.1 times, the amount or level recommend as rebar or steel bar replacement. The fibres can also be macro-synthetic fibres and may, in such case, be present in a dosage ranging from 1.5 kg/m 3  to 9 kg/m 3 , e.g. from 2.5 kg/m 3  to 7 kg/m 3 , e.g. from 3.5 kg/m 3  to 5.0 kg/m 3 . 
     The fibres are present in all parts of the concrete slab, i.e. the concrete slab is preferably a monolithic slab and the fibres are substantially homogeneously distributed over the concrete slab, except for a very thin upper skin layer that may be applied to provide a flat and wear resistant surface to the slab and to avoid fibres from protruding. A concrete slab in the sense of the present invention may thereby have a uniform average density. This may mean that a slab according to the invention does therefore especially not comprise regions or parts of lower density, especially no aggregated and/or aerated parts, further more preferred no aggregated and/or aerated blocks, which have a lower density, especially compared to cast concrete. A concrete slab in the sense of the present invention may thereby further for example also preferably be cast in one day and/or in one go and/or be fully casted, whereby especially for example no use of or assembly of blocks is involved. A concrete slab in the sense of the present invention may further for example contain only the fibres and the post-tension steel strands as reinforcement elements, which especially for example may mean that the slab may be free of any other reinforcement elements, especially other metal or steel reinforcement elements besides the fibres and the post-tension steel strands, especially free of rebars or steel bars, steel mesh, steel rods or the like. A concrete slab in the sense of the present invention may comprise a slip-sheet, especially for example a perforated slip-sheet. On the other hand, a concrete slab in the sense of the present invention may thereby further for example be free of a vapor barrier, especially at the basis of the concrete slab, so that said slab does preferably not comprise a vapor barrier. 
     The above-mentioned dosages of fibres (10 kg/m 3  to 40 kg/m 3  in case of steel fibres and 1.5 kg/m 3  to 9 kg/m 3  in case of macro-synthetic fibres) are low to moderate in comparison with prior art dosages of more than 40 kg/m 3  or more than 9 kg/m 3 . These low to moderate dosages allow integrating the fibres in a more homogeneous way in the concrete and facilitate the mixing of the fibres in the concrete. 
     The conventional concrete preferably has a characteristic compressive cube strength or comparable cylinder strength of 30 MPa or N/mm 2  or higher. More preferably, the conventional concrete has a strength equal to or higher than the strength of concrete of the C20/25 strength classes as defined in EN206 or equivalent national code requirements and smaller than or equal to the strength of concrete of the C50/60 strength classes as defined in EN206. These types of concrete are widely available and avoid adding ingredients that reduce the shrinkage during hardening. For the avoidance of doubt, self-compacting concrete is considered as conventional concrete. Conventional concrete in the sense of the present invention may thereby especially also for example have normal shrinkage and/or may not encompass low shrinkage concrete. 
     In a preferable embodiment of the invention, the fibres are steel fibres and have a straight middle portion and anchorage ends at both ends. 
     Most preferably the tensile strength of the middle portion is higher than 1400 MPa, e.g. higher than 1500 MPa, e.g. higher than 1600 MPa, preferably higher than 1700 MPa, further preferred higher than 2000 MPa, even further preferred higher than 2200 MPa, preferably between 1400 MPa and 3500 MPa. 
     The anchorage ends preferably each comprise three or four bent sections. Examples of such steel fibres are disclosed in EP-B1-2 652 221 and in EP-B1-2 652 222. These may be particularly useful in view of their good dosage/performance ratio, especially in combination with post tensioning as in the present invention, so that they may contribute to achieve good performance, especially regarding for example crack control, at relatively moderate dosages. 
     In a particular aspect of the invention, the maximum crack width of the concrete slab after hardening is 0.5 mm, e.g. 0.3 mm, e.g. 0.2 mm. In case the concrete slab has a length L greater than 100 m, the concrete slab has joints and a distance between two neighbouring joints is higher than 60 m, e.g. higher than 80 m, e.g. higher than 90 m. 
     In a first particular practical embodiment of the invention, the concrete slab according to the invention is a concrete slab on ground, (e.g. a concrete slab on a subbase prepared on a subgrade) with between the concrete slab and the ground a plastic slip sheet or a multitude of plastic slip sheets or not such a plastic slip sheet. 
     Due to the high tensile strength and the high yield strength, the distance between two neighbouring post-tension steel strands or between two neighbouring bundles of post-tension steel strands 
     may be higher than 0.80 m, e.g. higher than 0.90 m, e.g. higher than 1.0 m. 
     According to a particular and preferable aspect of the invention, the post-tension steel strands exercise in one direction a compression force on the concrete slab that is between 0% and 200% greater, e.g. between 0% and 100%, e.g. between 0.5% and 50% greater than a force according to following formula: 
       μ o ×γ c ×b×h×L/2   (1)
 
     where
         L is the length of the concrete slab;   b is the width of the concrete slab;   h is the thickness of the concrete slab;   μ o  is the coefficient of friction between the concrete slab and a subbase;   γ c  is the specific weight of concrete.       

     This means that the compression force ranges between one time and three times the value of formula (1). 
     A typical value of m o  is 0.5. Generally, m o  can range between 0.3 and 3.5, for example between 0.3 and 1.0 (see ACI 360/06). 
     A typical value of g c  is 23.560.0 N/m 3 , g c  can range between 18.000 N/m 3  and 26.000 N/m 3 . Other typical values are 24.500 N/m 3  and 25.000 N/m 3 . The thickness h of a slab according to the invention may thereby preferably be between 4 cm and 75 cm, preferably 5 cm and 65 cm, further preferred 10 cm and 55 cm. 
     In case the amount of reinforcement by means of post-tension steel strands is determined to be within the above-mentioned range (i.e. one to three times the value of the above-mentioned formula (1)), the tensile stresses caused by the shrinkage of concrete slabs are compensated and overdesign of post-tension steel strands is avoided. 
     In addition, if the amount of reinforcement by means of post-tension steel strand is within the above-mentioned range, the maximum crack with of the concrete slab after hardening can be kept lower than 0.5 mm, e.g. between the range of 0.2 mm to 0.5 mm. 
     In a second particular practical embodiment of the invention, the concrete slab according to the invention is a concrete slab on concrete piles or on gravel columns. 
     In a concrete slab on concrete piles or on gravel columns the post-tension steel strands may be present according to a straight line or be present in so-called draped form, i.e. they are positioned to take away as much as possible the tensile stresses in the concrete: above the concrete piles or gravel columns they are positioned in the upper half of the concrete slab and in-between the piles they are positioned in the lower half of the concrete slab. 
     The concrete piles or gravel columns are usually arranged in a regular rectangular pattern or quadrilaterial shape where a set of four concrete piles or gravel columns or a set of four groups of concrete piles or gravel columns forms a rectangle. The concrete slab comprises straight zones that connect in the two directions, i.e. in length direction and in width direction, the shortest distance between those areas of the concrete slab above the concrete piles or gravel columns. 
     The straight zones have a width that may vary between 50% and 500%, e.g. between 50% and 200% of the greatest cross-sectional dimension of the concrete piles of gravel columns. Post-tension steel strands are present in bundles in those straight zones. The distance between neighbouring post-tension steel strands within bundle in the straight zones may be smaller than 0.80 m. The presence of bundles of post-tension steel strands in the straight zones is often referred to as banded pattern. 
     Post-tension steel strands may or may not be present outside the straight zones. If present, the shortest distance between post-tension steel strands outside the straight zones and the post-tension steel strands in the straight zones is larger than 0.80 m. 
    
    
     
       BRIEF DESCRIPTION OF FIGURES IN THE DRAWINGS 
         FIGS.  1   a   ,  1  b,  1   c ,  1   d ,  1   e ,  1   f ,  1   g ,  1   h ,  1   i  all schematically represent various loading configurations of a concrete slab; 
         FIG.  2    is a schematic presentation of a concrete slab according to the invention; 
         FIG.  3    is a cross-section of a post-tension steel strand to be used in the present invention; 
         FIG.  4    shows a steel fibre that can be used in the present invention. 
     
    
    
     MODE(S) FOR CARRYING OUT THE INVENTION 
     Explanation of the Principle Behind the Invention 
     Concrete is a very brittle material that is hardly resistant to tensile tensions, the purpose is to avoid or at least to reduce the presence of tensile stresses. In  FIGS.  1   a   ,  1  b,  1   c ,  1   d ,  1   e ,  1   f ,  1   g ,  1   h ,  1   i  the ⊕ symbol, a plus sign in a circle, points to compressive stresses, while the ⊖ symbol, a minus sign in a circle, points to tensile stresses. 
       FIG.  1   a    shows a concrete slab  10  reinforced by means of a post-tension steel strand  12  that is located in the middle of the slab  10 . No external loads are present here. The post-tension steel strand  12  creates compressive stresses over the whole thickness of the slab  10 . 
       FIG.  1   b    relates to a situation where the slab  10  has no post-tension steel strand but where a load F represented by arrow  14  is exercised on the slab  10 . The load F creates a bending moment M, represented by arrow  16 . As a result of bending moment M, compressive stresses are present at the top of the slab  10  and tensile stresses at the bottom of the slab  10 . 
       FIG.  1   c    shows the situation where a load F is exercised on a slab  10  that is reinforced by means of a post-tension steel strand  12 . As schematically shown in  FIG.  1   c   , the tensile stresses at the bottom of slab  10  are compensated by the action of the post-tension steel strand  12 . However, in case the load F is a little bit higher, tensile stresses will be present at the bottom of slab  10  and cracks may originate. 
       FIG.  1   d    shows a concrete slab  10  reinforced by means of a post-tension steel strand  12  that is located in the upper part of the slab  10 . No external loads are present here. The post-tension steel strand  12  creates compressive stresses in the upper part of slab  10  and tensile stresses in the lower part of slab  10 . 
       FIG.  1   e    relates to a situation where the slab  10  has no post-tension steel strand but where a load F, represented by arrow  14 , is exercised on the slab  10 . The load F creates a bending moment M, represented by arrow  16 . As a result of bending moment M, compressive stresses are present at the top of the slab  10  and tensile stresses at the bottom of the slab  10 . 
       FIG.  1   f    shows the situation where a load F is exercised on a slab  10  that is reinforced by means of the post-tension steel strand  12  of  FIG.  1   d   . As schematically shown in  FIG.  1   f   , the tensile stresses at the bottom of slab  10  are not compensated by the action of the post-tension steel strand  12 , on the contrary. 
       FIG.  1   g    shows a concrete slab  10  reinforced by means of a post-tension steel strand  12  that is located in the lower part of the slab  10 . No external loads are present here. The post-tension steel strand  12  creates compressive stresses in the lower part of slab  10  and tensile stresses in the upper part of slab  10 . 
       FIG.  1   h    relates to a situation where the slab  10  has no post-tension steel strand but where a load F, represented by arrow  14 , is exercised on the slab  10 . The load F creates a bending moment M, represented by arrow  16 . As a result of bending moment M, compressive stresses are present at the top of the slab  10  and tensile stresses at the bottom of the slab  10 . 
       FIG.  1   i    shows the situation where a load F is exercised on a slab  10  that is reinforced by means of the post-tension steel strand  12  of  FIG.  1   g   . As a result of bending moment M, the tensile stresses present at the top of the slab  10  are compensated and the compressive stresses present at the bottom of slab  10  are compensated as well. 
     Although it is best for a concrete slab on ground to position the post-tension steel strand in the middle of the slab, no position can guarantee absence of tensile stresses. Within the context of the present invention, post-tension steel strands are therefore designed to take up and compensate the tensile stresses that may originate during hardening and shrinkage of a concrete in addition to applied loads. The post-tension steel strands are of a sufficiently high tensile strength, i.e. above 1700 MPa or even above 1800 MPa, so that conventional concrete can be used and ingredients to compensate shrinkage can be avoided. 
     The fibres are mixed in the concrete as homogeneously as possible so that they are present over the whole volume and able to take tensile stresses caused by various loads. 
     In a first embodiment of the invention, the concrete is poured on a slip sheet that is put on a substantially flat or flattened underground. Alternatively, the slip sheet can be avoided and the concrete is poured directly on the subbase. 
     In a second embodiment of the invention, a concrete slab is formed on piles or columns. A slip sheet may be or may not be present between the ground or subbase, the piles and the slab. 
       FIG.  2    schematically illustrates a concrete slab  20  on ground according to the invention. The slab  20  has a width W and a length L. A first series of post-tension steel strands  22  bridge the width W and are anchored at one side with fixed end anchors  23  and at the other side with stressing end anchors  24 . A second series of post-tension steel strands  26  bridge the length L and are anchored at one side with fixed end anchors  27  and at the other side with stressing end anchors  28 . Alternatively, stressing may also occur on both sides, i.e. stressing end anchors are present at both sides. 
     As the length L is greater than the width W, the post-tension steel strands  26  are positioned closer to each other than the post-tension steel strands  22 , but the distance between neighbouring post-tension steel strands  26  can be kept greater than 0.80 m independent of the length L. 
     Steel fibres  29  are spread over the whole volume of the slab  20 . 
     Post-Tension Steel Strand 
       FIG.  3    shows a cross-section of a typical post-tension steel strand  30 . 
     Post-tension steel strand  30  has a 1+6 construction with a core steel wire  32  and six layer steel wires  34  twisted around the core steel wire  32 . In the embodiment of  FIG.  3   , the post-tension steel strand  30  is in a non-compacted form. 
     In an alternative preferable embodiment, the post-tension steel strand may be in a compacted form. In this compacted form, the six layer steel wires no longer have a circular cross-section but a cross-section in the form of a trapezium with rounded edges. A compacted post-tension steel strand has less voids and more steel per cross-sectional area. 
     As mentioned, the post-tension steel strand has a high yield point, i.e. the yield force at 0.1% elongation is high. The ratio yield force F p0.1  to breaking force F m  is higher than 75%, preferably higher than 80%, e.g. higher than 85%. 
     A typical steel composition of a post-tension steel strand is a minimum carbon content of 0.65%, a manganese content ranging from 0.20% to 0.80%, a silicon content ranging from 0.10% to 0.40%, a maximum sulfur content of 0.03%, a maximum phosphorus content of 0.30%, the remainder being iron, all percentages being percentages by weight. Most preferably, the carbon content is higher than 0.75%, e.g. higher than 0.80%. Other elements as copper or chromium may be present in amounts not greater than 0.40%. 
     All steel wires  32 ,  34  may be provided with a metallic coating  36 , such as zinc or a zinc aluminium alloy. A zinc aluminum coating has a better overall corrosion resistance than zinc. In contrast with zinc, the zinc aluminum coating is temperature resistant. Still in contrast with zinc, there is no flaking with the zinc aluminum alloy when exposed to high temperatures. 
     A zinc aluminum coating may have an aluminum content ranging from 2 per cent by weight to 12 per cent by weight, e.g. ranging from 3% to 11%. 
     A preferable composition lies around the eutectoid position: Al about 5 per cent. The zinc alloy coating may further have a wetting agent such as lanthanum or cerium in an amount less than 0.1 per cent of the zinc alloy. The remainder of the coating is zinc and unavoidable impurities. 
     Another preferable composition contains about 10% aluminum. This increased amount of aluminum provides a better corrosion protection then the eutectoid composition with about 5% of aluminum. 
     Other elements such as silicon (Si) and magnesium (Mg) may be added to the zinc aluminum coating. With a view to optimizing the corrosion resistance, a particular good alloy comprises 2% to 10% aluminum and 0.2% to 3,0% magnesium, the remainder being zinc. An example is 5% Al, 0.5% Mg and the rest being Zn. 
     An example of a post-tension steel strand is as follows:
         diameter 15.2 mm;   steel section 166 mm 2 ;   E-modulus: 196000 MPa;   breaking load F m : 338000 N;   yield force F p0.1 : 299021 N;   tensile strength R m  2033 MPa.       

     Steel Fibre 
     Steel fibres adapted to be used in the present invention typically have a middle portion with a diameter D ranging from 0.30 mm to 1.30 mm, e.g. ranging from 0.50 mm to 1.1 mm. The steel fibres have a length   so that the length-to-diameter ratio  /D ranges from 40 to 100. 
     Preferably the steel fibres have ends to improve the anchorage in concrete. These ends may be in the form of bent sections, flattenings, undulations or thickened parts. Most preferably, the ends are in the form of three or more bent sections. 
       FIG.  4    illustrates a preferable embodiment of a steel fibre  40 . The steel fibre  40  has a straight middle portion  42 . At one end of the middle portion  42 , there are three bent sections  44 ,  46 ,  48 . At the other end of the middle portion  42  there are also three bent sections  44 ′,  46 ′ and  48 ′. Bent sections  44 ,  44 ′ make an angle a with respect to a line forming an extension to the middle portion  42 . Bent sections  46 ,  46 ′ make an angle b with respect to a line forming an extension to bent sections  44 ,  44 ′. Bent sections  48 ,  48 ′ make an angle c with respect to bent sections  46 ,  46 ′. 
     The length   of the steel fibre  40  may range between 50 mm and 75 mm and is typically 60 mm. The diameter of the steel fibre may range between 0.80 mm and 1.20 mm. Typical values are 0.90 mm or 1.05 mm. 
     The length of the bent sections  44 ,  44 ′,  46 ,  46 ′,  48  and  48 ′ may range between 2.0 mm and 5.0 mm. Typical values are 3.2 mm, 3.4 mm or 3.7 mm. 
     The angles a, b and c may range between 20° and 50°, e.g. between 24° and 47°. 
     The steel fibres may or may not be provided with a corrosion resistant coating such as zinc or a zinc aluminium alloy. 
     In a particular preferable embodiment of the steel fibre, there are four bent sections at each end of the middle portion. 
     In another particular preferable embodiment of the steel fibre, the middle portio0n has an elongation at maximum load higher than 4%, e.g. higher than 5%, e.g. higher than 5.5%. Steel fibres with such a high elongation at maximum load may be used in structural applications such as floors on piles, elevated systems and structural wall systems. 
     Macro-Synthetic Fibre 
     Examples of macro-synthetic fibres are fibres based upon polyolefins like polypropylene or polyethylene or based upon other thermoplastics. 
     Example of Replacing Steel Bars 
     In an embodiment of the invention, a slab according to the invention preferably may not comprise any further reinforcement or reinforcement elements besides the fibers and the post-tension steel strands, especially no steel bars. 
     For a slab with a thickness of 150 mm and steel bars with a diameter of 6 mm and a spacing 150 mm at the top as well as steelbars with a diameter of 6 mm and a spacing 150 mm at the bottom with a steel cover of 15% this represents 45 kg/m 3  steel and a concrete cover of 30 mm (top and bottom) to achieve a resisting bending moment M Rd =11.44 (positive and negative moment capacity). 
     On the other hand, according to the present invention, an equivalent resisting bending moment M Rd =11.54 can be achieved with only 24 kg/m 3  of steel fibre: DRAMIX® 4D 65/60/BG, i.e. a steel fibre with three bent sections according to  FIG.  4    for the same slab with the same concrete. This means that according to the invention the amount or level of steel can be significantly reduced by using steel fibers compared to the amount of steel required and recommended using steel bars. Furthermore, the amount or level of steel fibers according to the invention may preferably be for example below or equal to 1.2 times, preferably 1 time, the amount or level recommended and determined as rebar replacement, especially for example at equivalent performance, preferably in terms of resisting bending moment (positive and negative moment capacity). Accordingly, the amount of steel fibers used according to the present invention may be for example preferably below or equal to 1.2 times, preferably 1.0 time, further preferred between &gt;0 and 1.1 times, the amount or level of steel recommended and used for the steel bars or rebars to be replaced and/or the amount or level of steel fibers may be below or equal 1.2 times, preferably 1 time, further preferred between &gt;0 and 1.1 times, the amount or level recommend as rebar replacement. 
     Example of a Slab on Ground 
     
         
         
           
             slab thickness h: 150 mm 
             slab length L: 100 m 
             slab width b: 1 m (to calculate forces of post-tension steel strands in one direction) 
             type of steel fibre: DRAMIX® 4D 65/60/BG, i.e. a steel fibre with three bent sections according to  FIG.  4     
             dosage of steel fibres: 25 kg/m 3    
             γ c : 23.560.0 N/m 3    
             μ o : 0.5 
             minimum force exercised by post-tension steel strands: 88.350.0 N/m 
             tensile strength R m  post-tension steel strand: 1860 MPa 
             diameter post-tension steel strand: 15 mm 
             spacing between two neighbouring post-tension steel strand be higher than 2.0 m, even higher than 2.5 m 
             spacing between two neighbouring joints: 90 m, even larger than 120 m 
             maximum crack width: 0.5 mm. 
           
         
       
    
     EXAMPLES OF A SLAB ON CONCRETE PILES 
     First Example 
     
         
         
           
             distance between neighbouring joints: 100 m 
             thickness of concrete slab: 0.229 m 
             upper load: 50 kN/m 2    
             distance between neighbouring concrete piles: 4 m×4 m 
             distance between post-tension steel strands within the straight zones: 0.25 m 
             not necessary that there are post-tension steel strands outside the straight zones, but in case there are post-tension steel strands, the distance between post-tension steel strands outside the straight zones is greater than 0.90 m, preferably greater than 1.60 m 
           
         
       
    
     Second Example 
     
         
         
           
             distance between neighbouring joints: 100 m 
             thickness of concrete slab: 0.495 m 
             upper load: 50 kN/m 2    
             distance between neighbouring concrete piles: 6 m×6 m 
             distance between post-tension steel strands within the straight zones: 0.15 m 
             not necessary that there are post-tension steel strands outside the straight zones, but in case there are post-tension steel strands, the distance between post-tension steel strands outside the straight zones is greater than 0.80 m, preferably greater than 1.50 m