DESIGN OF PRECAST STEEL FIBRE REINFORCED TUNNEL ELEMENTS

Transcription

1 Test and Design Methods for Steel Fibre Reinforced Concrete 145 DESIGN OF PRECAST STEEL FIBRE REINFORCED TUNNEL ELEMENTS Bernd Schnütgen Ruhr-University Bochum, Institute of Structural Engineering, Germany Abstract The following example shows the design of tunnel elements. Conclusion is: The application of steel fibre reinforced concrete also is possible for such techniques. In extreme strengthened parts additional conventional reinforcement is necessary. 1. Introduction The paper gives an example of design of precast tunnel elements with the RILEM recommendations published in /2/. The example includes the design in SLS and ULS, case of excavation (thrust jacks), design of shear keys and splitting behaviour of ring joints. The forces and moments were taken from a study for a metro-tunnel. A similar tunnel was build in Essen but without any conventional reinforcement. 0,40m key stone Ø7,20m 6 standard elements 0,40m 50 mm gap marl Figure 1: Geometrical conditions of the tunnel 2. General remarks hydraulic jacks In general, the efficiency of steel fibre reinforcement increases in ultimate limit state with increasing area of highly stress zones in the structure. In table 1 therefore the benefit is increasing from top to the bottom. The reason for this is, that steel fibre reinforced concrete exhibits large

2 146 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 scatter of its properties. On the other hand steel fibres are more or less randomly distributed. For this reason in similar cross-sections is given analogous moment-deformation-behaviour. With this steel fibre reinforced concrete is highly suitable for structures with possibility of moment distributions. But it is to ensure, that there is no risk for collapse of single cross-sections. Single crosssections have to be developed for a suitable safety-factor additional to the main structure. 3. Problem The problem was to design a metro tunnel for the Ruhr-Region in Germany. For this at first was carried out a solution with conventional reinforcement. We had to change that construction to steel fibre reinforced concrete. The given geometrical conditions are shown in figure 1. key stone standard element driving direction joints hydraulic jacks Figure 2: precast tunnel elements (overview) 4. Design methods 4.1 Direct design by experiments General The direct method of design by experiments will be illustrated by parts of precast tunnel lining elements. Such elements are part of a tunnel lining system as shown in figures 1 and 2. The actions on these elements result from transport (figure 3a), placing process (figure 3b and 3c) and soil pressures in the final state. In the last mentioned state it has to be distinguished between ring strength in a 2D-system (normal forces and bending moments) and strength in the joints between rings in a 3D-system (shear forces) if the soil is inhomogeneous.

3 Test and Design Methods for Steel Fibre Reinforced Concrete 147 a bending test (transportation state) hydraulic jacks plastic deformable supporting pads b test of in-plane actions (placing situation) c splitting test d shear test plastic deformable supporting pads Figure 3: test program of tunnel elements (additional to standard tests) Particularly the two problems: placing of elements by hydraulic jacks and forces in the joints are interesting in the case of experimental based design. The other points are more or less standard cases of design only tested with respect of the geometrical dimensions but designed using a standard method (chapter 5) Splitting behaviour The placing process of the lining elements is executed by hydraulic jacks. Therefore this state of splitting stress was limited in time. The forces of the hydraulic jacks were up to 2000 kn. Including the required safety factor the splitting tensile stresses exceeded the concrete tensile strength. After cracking the tensile stresses should be sustained by the crack-bridging forces providing by the fibres. The experiments have shown a loading capacity after cracking of more than twice of the cracking load. The maximum strain (measured by transducer in cross direction) was 1.2 % at maximum load. This strain is the averaged value of five cracks in minimum with crack widths up to 1.2 mm. This crack width corresponds with the ultimate limit state. In the serviceability limit state kn as the maximum jack force - the average of crack width value was 0.2 mm and the maximum crack width 0.25 mm. These results directly could be used for design.

4 148 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 test arrangement kN 4000kN test results kN kN transducer 1000kN kN strain Figure 4: splitting test and results F max = 4060 kn > 1, F sp = 0, ( )/0.40 = 533 kn Tension area: A ct,sp = 0,8 0,40 0,40 = 0,128 m² sp = 0.533/0.128 = 4.16 MN/m² > 3.6 The model gives results on the safety side. Test results in the Brite/Euram project of RILEM TC 162 confirm this. In case of point loaded constructions the length of the tension zone was 1.14 times greater than the height of the concrete specimen. The above mentioned calculation shows the same effect. Factor = 4.16/3.6 = 1,16 1,14 stress distribution in ULS h Figure 5: computational model and design assumption

5 Test and Design Methods for Steel Fibre Reinforced Concrete Shear of tooth of ring joints Conventional reinforcement of the very small consoles of the ring joints is complicated, expensive and - with respect to the cover of reinforcement - less effective. For this reason experiments were carried out to investigate if steel fibre reinforcement is more efficient. The figures 6 and 7 show results of the tests. According to the results both reinforcement types (conventional and pure steel fibre reinforcement) have more or less the same load carrying capacity. But the ductility of the steel fibre reinforced specimens was about 60% higher. Specimens with a combination of bars and steel fibres had a load capacity of about the sum of the reinforcement types alone and the ductility of that with steel fibre reinforcement. An explanation for this observation can be found in figure 6. The crack direction of specimen with steel fibres is very different from that with conventional reinforcement. 70 a) b) truss model crack direction with reinforcement bars F 52m 25 F F crack direction with steelfibers only assumption of stress distribution Figure 6: crack directions and design model resulting from shear test a) steel fibre reinforced with additional bars in comb form (left side) b) pure steel fibre reinforced (right side) The fibre contend was 50kg/m³ hooked steel fibres l f = 50mm, d f = 0,6mm. With a concrete class C 50/60 the tension strength was f f ct,2 = 3.6 MN/m² f f ct,3 = 2.0 MN/m². From experiment we found in a model shown in figure 6b the forces F c = kn/m F t = kn/m d = 2 52 = 104 mm f ct =0.2095/0.104 = 2.01 MN/m² The model shows a good correspondence to the expected data from bending test. In case of combined reinforcement we have 3 parts of carrying capacity: shear capacity of the concrete in the first part of the crack (equal as in case of conventional reinforcement), increased shear capacity by fibre tension in the first part of the crack and fibre influence in the second part of the crack. F = F + F t1 + F t2 with F ct = f f ct,2 d 1 b = /7 = 298 kn

6 150 RILEM TC 162-TDF Workshop, Bochum, Germany, 2003 The main effect of bars is to influence the crack angles. The effect of fibres is to transfer forces across the crack surfaces. By combining both reinforcing types both effects occur. 4.2 Design by standard methods using - -method load [kn] Geometry of the ring: Thickness: h = 0.40 m Width: b = 1.50 m Length of the element: l = 3,60 m In ring direction the tunnel elements were loaded by: maximum of bending moments: max M d = 360 knm/m normal force: F N,d = kn/m minimum of bending moments: min M = -395 knm/m normal force: F N,k = kn/m Lever arm of the internal forces: z = 0.205m Thickness of the compression zone: x = 0.08m max M ft,d = = 441 knm/m min M ft,d = = -484 knm/m Tension inside: F ct,d = 441/ = = 121 kn/m Tension outside: F ct,d = 485/ = = 126 kn/m Required design value of tensile strength: f f ctd,ii = 0.126/0,32 = MN/m² Required characteristic value of tensile strength: f f ctk,ii = ,25/ = 0.65 MN/m² < 2.0 In final state is no additional reinforcement necessary using a truss model combined reinforcement 171 conventional reinforcement 146 steelfiber reinforcement displacement The most important case is the placing process of the elements. There was to examine if the influence of geometrical tolerances is relevant for the ultimate limit state. For this a system as shown in figure 8 was analysed by FEM. 30 Figure 7: results of shear tests (average of series of 3 specimen)

7 Test and Design Methods for Steel Fibre Reinforced Concrete F = kN realistic system 1.50 C Spr,2 C Spr,1 = 0,1 C Spr,2 C Spr,2 C Spr,1 = 0,1 C Spr,2 0,30 truss model ,90 0, ,60 0,60 Figure 8: system of FEM analysis and deducted truss model max F t,k = 1015 kn on a cross section of A = = 0.12 m safety factors: actions: A = 1.2; fibres: f = 1.25; bars: s = 1.15; f f ctk,3 = 2.0 MN/m² f = 1.2 1,015/0.12 = 10,15 MN/m² >> 2,0/1.25 = 1,60 Additional reinforcement is necessary. req A s = ( ) /500 = 23.6cm² (5 20mm mm) Internal stresses: max = /( )=1.38 MN/m² < No additional bars Shear design Maximum of shear force: V Sd = 290 kn/m; N Sd = 2030kN/m f w,c = / ) = V Rd = V Rd,A,c + V Rd,ct = f w,c f yd b w z + [0.10 (100 f w,c f yk ) 0, c ] b w = /1.15+[0, ( ) 0, /0.40] 0.40 = = MN/m > No shear reinforcement necessary.

8 152 RILEM TC 162-TDF Workshop, Bochum, Germany, Ring joint N d = 2240 kn/m; M d = 105 kn/m; eccentricity: e = 105/2240 = m; b i = 2 (0.20/ ) = m; h i = 2 (0.40/ ) = m Splitting force: F sp = ( )/0.306 = MN/m sp = 0.368/( ) = 1.50 MN/m² < 1.60 No splitting force necessary. pressure N d reference area Figure 9: System of joint with eccentric pressure 5. References [1] L. Vandewalle: Recommendations of RILEM TC 162-TDF: Test and design methods for steel fibre reinforced concrete, bending test, Mat. & Struct., Jan./Febr [2] Recommendations of RILEM TC 162-TDF: Test and design methods for steel fibre reinforced concrete, s e method, Mat. & Struct., March 2000 [3] Deutscher Beton- und Bautechnik-Verein: instructional pamphlet steel fibre reinforced concrete, final draft October 2001, (German language) [4] European Standard Eurocode 2: Design of concrete structures Part 1: General rules and rules for buildings, 1991 [5] German Standard DIN : Part 1, design and construction of concrete, reinforced concrete and prestressed concrete, Beuth-Verlag Berlin, july 2001, (German language) [6] Dams, S. and B. Schnütgen: Stahlfaserbeton im Tunnelbau (Steelfiber Reinforced Concrete in Tunnelling), Beton-Informationen 5/94, Beton-Verlag GmbH, Düsseldorf 1994, (German language)