ON THE COLLAPSE OF A REINFORCED CONCRETE DIGESTER TANK Luis A. Godoy and Sandra Lopez-Bobonis Department of Civil Engineering, University of Puerto Rico, Mayagüez, PR 00681-9041, Puerto Rico ABSTRACT The investigation following the collapse of a large reinforced concrete dome, which was part of a digester tank, is presented. The shell was constructed in 1987, and had construction errors related to the location of the single layer of reinforcement, which were discovered as a consequence of the collapse. The shell collapsed without the occurrence of any natural hazard. It is believed that a high internal pressure developed on the day of the collapse because of a problem with a valve, which allowed the discharge of large quantities of sewage inside the tank and filled the structure completely. A finite element analysis of the structure shows the stress levels in the structure, and support the hypothesis of a failure mechanism which coupled the construction errors with the internal pressure. Finally, the strengthening of the shell with externally bonded fiber composite sheets is described as a possibility to improve the safety of other tanks in similar situations. KEYWORDS Collapse, composite materials, construction errors, digester tanks, reinforced concrete, shells. INTRODUCTION The failure of reinforced concrete shells has been reported in a number of cases, as mentioned in the texts by Billington (1990), Godoy (1996), Gould (1999), and others. For example, Ballesteros (1978) reported the collapse of an elliptical paraboloidal shell during the process of removing the formwork; the structure showed clear imperfections in the geometry and had construction defects. Many cases of reinforced concrete tanks (or similarly shaped structures) that fail due to structural or construction problems are not reported in the open literature; however, this lack of publication does not help other researchers to learn lessons from failures. This paper reports on the collapse of a large reinforced concrete shell dome, which was part of a digester tank, under an internal pressure produced by the accidental filling of the tank. The change in the operational conditions resulted in a limit state for which the tank was not adequately reinforced. Possible ways to repair existing tanks in the same plant with composite sheets are also considered.
THE SHELL STRUCTURE INVESTIGATED The digester studied here is sufficiently far from other digester tanks in the same facility so that it can be considered as an isolated structure. The structure is a closed reinforced concrete containment structure formed by a cylindrical shell, a sector of a spherical shell roof, and a conical shell at the bottom, as shown in Figure 1. Part of the structure was built underground. The horizontal radius of the cylinder is r 0 = 14.5m, the height is 10m, and the wall thickness is 0.5m. According to the plans of the design, the cylinder was reinforced with two layers of steel (#6 bars at 250mm in the vertical direction and #9 bars at 38mm in the horizontal direction). Figure 1. A typical digester tank considered in this study. C L 0.228 m #4@20 0.30 m #4@ 20 cm 0.50 m 3m 11.5 Figure 2. Reinforcement of the dome of the digester tank. The dome is a spherical cap (Figure 2) with radius of curvature R = 30.8m and thickness t = 228mm, so that R / t = 135. This is considered a thin shell for reinforced concrete, and should have been designed according to the ACI provisions already published at the time of design (ACI Committee 334, 1986). As a reference value, large reinforced concrete cooling towers have R/t of the order of 150. The dome is connected to a cylinder by means of a ring. The maximum elevation of the dome with respect to its
supports on the ring is approximately 2.90m. A PVC liner was attached to the bottom surface of the dome. The steel section in both directions was found to be #4 at 200mm, leading to As = 645mm 2 /m. For the area of concrete Ac, the ratio As / Ac = 0.28% is a low amount of reinforcement for this class of shells. The structure was constructed in 1987. The dome should have been designed to resist primary compressive forces due to self-weight and accidental loads, but sufficient bending capacity should have been provided for situations other than gravity load. For this shell, which is exposed to an aggressive environment, it would be expected to have a 38mm concrete cover. Figure 3. Partial view of the dome after the collapse. Figure 4. Location of the reinforcement. Figure 5. Details of damage of the shell. Figure 6. Details of cracks in the shell. CONDITIONS OF THE STRUCTURE PRIOR TO THE COLLAPSE Figure 3 shows the structure following the collapse of a large part of the dome. Because part of the structure did not collapse, it was possible to observe some details of the construction: (a) The single layer of the reinforcement was not placed at the center of the thickness, as indicated in the drawings, but it was displaced to the bottom surface of the shell. This has important consequences for the membrane and bending resistance of the shell.
(b) The concrete cover on the bottom surface of the shell was not sufficient. For this shell, which was constructed to operate in an aggressive environment, the concrete cover was found to be only 12.7mm and perhaps less in some zones. This is illustrated in the photograph of Figure 4. (c) Furthermore, the concrete cover in the zone close to the supports of the dome on the top surface of the dome was not adequate: in some parts of the shell it was possible to see the steel bars in the meridional direction. (d) Corrosion of the steel bars had occurred for some time. This could be seen at many places on the external surface of the dome. Corrosion has the consequence of reducing the effective diameter of a steel bar in a localized way. (e) Meridional cracks are clearly visible on the external surface of the dome (Figures 5 and 6), even in parts of the shell sufficiently far from the area that collapsed. Those are not new cracks formed as a consequence of the collapse, but were formed some time ago. Cracks larger than 3mm in the meridional direction occur at a spacing of about 2m. This reduces the bending capacity of the shell for negative hoop moments. (f) Circumferential cracks on the external surface are visible. Again, this reduces the bending capacity of the shell for negative meridional moments. Both meridional and circumferential cracks reduce the tensile capacity of the shell. (g) There are some flat parts of the shell between meridional cracks, with the consequence that the shell had rotated taking the cracks as hinges. SEQUENCE OF EVENTS LEADING TO THE COLLAPSE OF THE DOME There was no report of high winds, earthquake, or small amplitude ground motion on the day of the collapse. However, a problem was reported on a valve, which caused the filling of the digester up to the top, with large internal pressures acting on the dome. A worker observed that material stored in the digester was being discharged at the top of the roof. A large crack (1.5m) formed on the external surface in the meridional direction, and large quantities of sewage material started flowing through the crack, coming from inside the digester. Next, a bulge formed close to the crack, and extended for at least 2m in the circumferential direction. The amplitude of the bulge (the elevation with respect to the external surface of the shell) was estimated to be at least 0.10m. The 3m part of the shell that had double reinforcement remained in the structure and the central part of the dome collapsed towards the inside of the digester. No explosion was reported. All debris were found inside the digester. STRUCTURAL CONSIDERATIONS The main loading condition of the dome shell is self-weight, leading to compression in two directions. The self-weight of the structure produces in-plane stresses of the order of 363KPa. Such stresses are small compared to the compressive strength of the concrete, f c = 20.7MPa. Even if the weight is increased by accidental loads, the stresses are still small. Failure of concrete under compression is ruled out as a main cause of the collapse. A buckling load of the dome was estimated (Billington 1990, pp. 320) using E = 21.2GPa, leading to a critical pressure p c = 360KPa. This pressure is much higher than any pressure associated to gravity action. Thus, it is not likely that buckling under the main compressive (membrane) action led to a limit state in the shell. It has been shown that for thin-walled shells geometric distortions produced by various causes may induce bending stresses of the same order as the primary stresses. The collapse of several large reinforced concrete shells has been attributed to this effect. A review of several cases and their causes is reported in Godoy (1996). This dome clearly had significant geometric distortions, as reported by engineers previous to the collapse. Since no measurements of the actual shape of the dome were performed, it is difficult to assess the amplitude and extent of such distortions. At the time the shell
showed signs of a critical condition, an engineer reported a bulge with amplitude of about 0.10m and extending with a diameter of at least 2m. This may be a significant source of stress concentrations in the shell. But for the reinforcement present in the shell, an internal pressure may be the triggering cause of the collapse. Notice that a reinforced concrete spherical cap is extremely efficient to resist self-weight because it can develop compression; however, if the load is reversed the dome becomes a most inefficient structure under tension. Had the reinforcement been placed on a single layer at the center of the thickness, a tensile force T could develop due to the contribution of the steel section As. The concrete could have taken a compressive zone at the lower part of the thickness, to produce the required bending and thus equilibrate the internal pressure p i. Cracks were clearly present in the dome, in both directions. Such cracks were not new, and may have been produced by a variety of reasons, including the early life of concrete, thermal action, and others. A factor that must have played a role in the crack formation is the position of the reinforcement, which was displaced towards the bottom of the cross section for some unknown reason. In the real situation, the as-built shell has the steel reinforcement on the inner side. Under bending produced by the reversed load, the tensile force T had to be very large since the distance between the tensile and the compressive forces is small. Furthermore, the compressive force C developed by the concrete small section (the concrete cover) must be extremely high. For a steel with yield stress σ y = 450MPa, a limit state could be reached with an internal pressure higher than the self-weight of the dome. FINITE ELEMENT STRESS ANALYSIS A shell with dimensions similar to the central part of the dome, for which a single layer of reinforcement was present, has been studied using a finite element model. The structure was considered as an axisymmetric solid with quadrilateral elements, as illustrated in Figure 7. The data assumed is shown in Table I. Figure 7. Dimensions of the dome investigated in the analysis. The stresses and displacements of the shell have been computed under an internal pressure to simulate the influence of the sewage at the time a valve permitted the filling of the tank under pressure. It is not known the value of the pressure that was induced by the sewage, so that a reference value of 0.30 times the self-weight is adopted for the computations. Since this is an elastic analysis, the pressure should be scaled to evaluate a limit state.
TABLE I PROPERTIES FOR CONCRETE AND STEEL Properties Concrete Steel E, Elasticity Modulus 20.68 GPa 200 GPa Mass density 2402.7 kg/m 3 7861.4 kg/m 3 ν, Poisson ratio 0.15 0.29 Thermal Coefficient.0000108.0000117 Shear modulus 9.0 GPa 77.2 GPa 0.15 0.1 0.05 Z (m) 0-50000 0 50000 100000 150000 200000 250000 300000 350000-0.05-0.1-0.15 Stresses (N/m 2 ) E=Econcrete/10 E=Econcrete/3 E=Econcrete(2/3) E=E concrete Figure 8. Stresses in the dome with and without deterioration of concrete. 0.0008 0.0007 Econcrete*1/10 2.07E+08 0.0006 Econcrete*1/3 Maximum Displacements (m) 0.0005 0.0004 0.0003 6.90E+09 1.38E+10 Econcrete*2/3 Econcrete 2.07E+10 0.0002 0.0001 0.0000 2.07E+08 5.21E+09 1.02E+10 1.52E+10 2.02E+10 2.52E+10 Elasticity Modulus (N/m^2) Figure 9. Displacements in the shell for various conditions of the concrete.
The stresses in the meridional direction are shown in Figure 8 for E = Ec. This is a linear response including membrane and bending action. For the perfect shell to crack under internal pressure p i, the value of p i should be 3.65 times the self-weight of the shell. However, there are clear signs that the shell had serious deterioration and cracking prior to the occurrence of internal pressure. To investigate the elastic stresses in the shell including damage of the concrete, parametric studies are shown in Figure 8 for several values of the modulus of elasticity. The actual area affected by damage was assumed over the central part of the dome, extending one-third of the total arc in the meridional direction and on the top half of the thickness. The results depart from classical shell theory assumptions, i.e. a linear distribution of stresses through the thickness is lost, with a significant reduction of stresses on the top part. To compensate for that, the stresses in the lower part of the thickness are largely increased, in order to maintain the net tensile force on the overall section (membrane contribution). In the deteriorated section with E = 0.1 Ec the tensile stresses increase by 40%. The bending moment, however, now acts in the opposite direction. The influence of the deterioration of concrete on the maximum displacements is shown in Figure 9, leading to a 100% increase for the case with E = 0.1 Ec. STRENGTHENING THE DOMES In view of the catastrophic consequences of the construction errors for some loading conditions, the safety of other digester tanks in the same plant and with similar characteristics to the tank that collapsed had to be evaluated. Possible ways to strengthen a dome were considered, and the most convenient way evaluated was the use of externally bonded fiber composite sheets. 0.15 0.1 0.05 Z (m) 0-50000 0 50000 100000 150000 200000 250000 300000 350000-0.05-0.1-0.15 One layer of CFRP Stresses (N/m 2 ) Without strengthening Figure 10. Stress redistributions in the shell with an externally bonded carbon fiber sheet. Composite sheets have been employed to strengthen reinforced concrete bridges, columns, and beams, and this is an area of great interest in terms of research and civil engineering practice. A carbon fiber composite (CFRP) could be laid on the external surface of the thickness, to restore the tensile capacity of the dome in case of a reversed bending situation. Due to limitations of space it is not possible to describe in full the behavior of the dome with such reinforcement, and only one plot of the stress redistribution in the meridional direction is shown in Figure 10.
The main problems to be considered in the design of this reinforcement are the shear transfer between the composite and the concrete, and how the behavior of the shell is modified under normal (selfweight) conditions. CONCLUSIONS The preliminary conclusions of this work may be summarized as follows: (a) The shell could resist normal operation under self-weight and accidental loads due to gravity. This was done even taking cracking and the real location of the reinforcement into account. (b) Effects due to buckling of the shell have not been a crucial factor that could explain the collapse. Seismic or wind load were not identified on the day of the collapse so as to study a dynamic action as a possible explanation. (c) Because the digester was accidentally pressure-filled on the day of the collapse, it is expected that high internal pressures developed on the dome. If the shell had been constructed as designed (with a central layer of reinforcement in two directions) then it is expected that it would have resisted an internal pressure. But for the actual shell with the reinforcement at the bottom of the thickness, with cracking on the top part of the concrete, and with geometric distortions, it seems that the structure would not be able to take the internal pressure. (d) Strengthening the dome on the top side with carbon fiber composite sheets may be a convenient way to improve the safety of a structure in such conditions. The results show that the stress levels are reduced in the concrete, and that the bending capacity is restored thanks to the tensile contribution of the composite. REFERENCES ACI Committee 334 (1986), Concrete Shell Structures: Practice and Commentaries, American Concrete Institute, pp. 14. Ballesteros P. (1978). Nonlinear dynamic and creep buckling of elliptical paraboloidal shell. Bulletin of the Int. Association for Shell and Spatial Structures, 66, pp. 39-60. Billington D. P. (1990), Thin Shell Concrete Structures, 2 nd Ed., McGraw-Hill, New York. Godoy L. A. (1996), Thin-Walled Structures with Structural Imperfections: Analysis and Behavior, Pergamon Press, Oxford, UK. Gould P. L. (1999), Analysis of Plates and Shells, Prentice Hall, New Jersey.