Alternative methods to determine the ice load on concrete dams

Dams in countries with cold climate are subjected to ice loads during the winter, and these may have significant influence on the dam stability. The design value of the horizontal ice load varies between 50 – 200 kN/m from the South to the North of Sweden, according to the Swedish guideline for dam safety (RIDAS 2011). However, the size of the ice load cannot be dictated by the geographic location, other factors that influences are variations in temperature and water level, slopes of the banks, wind and currents, etc. Most of the field measurements of static ice loads on dams are performed indirectly by measuring the in-situ pressure in the ice. Several aspects influence the accuracy of these measurements, for instance the pressure is measured at a localized point, stress distributions occur around the cast-in pressure sensor, the influence of the thermal expansion of the sensor, etc. As a consequence, it becomes unclear if these ice loads are representative for the loads acting on the dam. In addition, some of the ice loads that have been measured are extremely high and there are contradicting meanings on whether these extreme loads can occur at all. In this research project, alternative methods to measure ice loads are investigated where different approaches based on measurements performed on the dam are studied. These approaches include methods such as a specific type of pressure panels installed directly on the upstream surface of the dam or utilization of existing measurement equipment for dam safety monitoring (such as pendulums, strain gauges, etc.), in order to perform backward analyses of the ice load. INTRODUCTION The climatic condition in the northern countries results in that ice loads occur during the winter and that these have to be considered in the design, see Figure 1. According to the Swedish guideline RIDAS (2012) a horizontal ice load in an interval between 50 to 200 kN/m (from south to north of Sweden) should be considered in design. Figure 1: Ice growth between intake and spillway at Krångfors hydropower station, from Johansson et al. (2013). Photo: Skellefteå Kraft. The size of the ice loads is, however, not only dependent on the geographic location. Instead other factors such as variation in temperature and water level, slope of the banks, wind and currents etc. also influence the size of the ice load according to Comfort et al (1993) and USACE (2002). Adolfi and Eriksson (2013) compiled available data Hydropower'15 Stavanger, Norway 15-16 June 2015 regarding maximum annual ice loads with the purpose to determine a suitable statistical distribution. The data that they used was obtained from the conventional type of measurements used where the ice load is obtained from indirect measurements of the in-situ pressure in the ice. Based on the compiled data, a log normal distribution curve was determined with the average and standard deviation of the maximum ice load for each year was 81 kN/m and 86 kN/m respectively. This illustrates the large scatter in result regarding the size of the maximum annual ice load. The two measurements performed at Seven Sisters dams with extreme ice loads (324 and 374 kN/m respectively) were, however, excluded from their study. Adolfi and Eriksson (2013) motivated this with that these values are much higher than the capacity of the ice regarding buckling according to Carter et al. (1998). In addition, in their study, they also truncated the lognormal distribution to a maximum value of 253 kN/m, assuming an ice thickness of one meter in the equation presented by Carter et al. (1998) for ice buckling. The size of the ice load acting on the concrete dam is related with large uncertainties. Several aspects influence the accuracy of these in-situ pressure measurements as those analyzed by Adolfi and Eriksson (2013) such as the pressure is measured at a localized point, stress distributions occur around the cast-in pressure sensor, the influence of the thermal expansion of the sensor, etc. In addition, the in-situ pressure sensors are only measuring the compressive stresses. However, due to the temperature gradient over the thickness of the ice where the bottom surface of the ice sheet is equal to 0 °C and the top of the ice sheet can be substantially colder, bending stresses will occur where part the thickness of the ice sheet is subjected to tensile forces. Thereby, only measuring the compressive stresses may result in significant overestimation of the ice load, Johansson et al. (2013). As a consequence of all aforementioned reasons, it becomes unclear whether these measured ice loads are representative for the ice load acting on the dam. Similar conclusions have also been drawn by other researchers, and there are some research projects that also study alternative methods to measure the ice loads, such the measurements performed at Norut, Norway, see for instance Petrich et al. (2014). In order to determine the ice loads that a concrete dam is subjected to, different alternative approaches to the in-situ pressure measurements have been presented by Johansson et al. (2014) and are summarized in this paper. METHODS FOR MEASUREMENTS OF THE ICE LOAD ON CONCRETE DAMS The following approaches suitable for building load panels which measure the ice load acting on the concrete dam has been presented in Johansson et al. (2014): 1. Registration of volume change in a closed box (Meadof panel) 2. Registration of support forces 3. Measuring of tensile forces in an vibrating wire 4. Tactile pressure sensors 5. Fiber optic sensors The Medof panel is based on a principle where the load is proportional to the deformation of a steel plate supported by a large number of rubber gaskets inside a liquid filled box. The load can be calculated indirectly from measurements of the change in volume of the enclosed liquid. Based on assumptions of the load distribution it is possible to calibrate the sensor. The disadvantage of this type of sensor is that the volume of the liquid is dependent on the temperature and that the temperature within the liquid will, due to convection and stratification, vary complexly. (Johansson et al., 2014) Force measurements can also be performed by measuring the support forces of a load panel. This could be performed with load cells or with foil strain gauges glued directly to a polished steel surface. The temperature effect can be compensated for by installing the strain gauges in a Wheatstone bridge and individual calibration of the sensors. For successful measurements over a long term period it is required to use load cells of high quality with stable electric power supply. In this case, the method could be applied so that at least three load cells are installed to measure the reaction forces between two steel plates. This technique has previously been used in the measurements of the lighthouse Norströmsgrund, see Figure 2 and Figure 3. According to Fransson (2001) four load cells where installed as support between two rigid steel plates, which were pre-stressed and sealed with a vulcanized rubber O-ring. The dimensions of these steel panels were 1.2 m x 1.6 m and had a weight of 3500 kg. (Johansson et al., 2014) Hydropower'15 Stavanger, Norway 15-16 June 2015 Figure 2: Example of design of a load plate for measuring ice pressure, from Fransson (2001). Figure 3: Installed load panels at the lighthouse Norströmsgrund, from Johansson et al. (2013). Photo: Lennart Fransson. Measurements can be performed with high accuracy based on the vibrating wire technique. This is done indirectly through measurements of the natural frequency of the wire. The strain of the wire is however, sensitive to temperature variation and it is therefore important that the temperature is measured with high accuracy to perform reliable temperature compensation. However, the long-term reliability of this type of sensor has been questioned due to effects such as relaxation. (Johansson et al., 2014) Tactile pressure sensors could be used where a surface is covered by a large number of sensors placed in a matrix. The sensors are thin (~0.1 mm) and protected by a layer of polyurethane or similar. By measuring the pressure in both rows and columns of the matrix it is possible to determine the position of the signal, its pressure value and thereby obtain a spatial pressure distribution. One downside with the technique is that the pressure recordings are nonlinear and have a poor resolution. One possibility for further development, however unverified, could be to cover the sensors with a steel plate which could sustain tensile and shear forces. (Johansson et al., 2014) One advantage with fiber optic sensors is that it has good long-term stability. Fiber optic measurements of strain with Fiber Bragg Grating Sensors (FBGS) could be used to measure deformations in a metal box as illustrated in Hydropower'15 Stavanger, Norway 15-16 June 2015 Figure 4. One disadvantage is that the fiber optic sensors are sensitive to temperature variations. (Johansson et al., 2014) Figure 4: Sketch of an ice load panel, from Zhou et al. (2005). USE OF INDIRECT MEASUREMENTS AND BACKWARDS CALCULATION OF THE ICE LOAD Most of the concrete dams already have a monitoring system consisting of pendulums, strain gauges and/or crack width sensors. It would be desirable if these types of sensors could be used to determine the ice load through for instance backwards calculation with a numerical model. The ice load will result in a deflection of the concrete dam, which would theoretically be visible in the existing sensors on a dam if the data were sampled with in a sufficient interval. A direct pendulum typically consists of a thin steel wire attached in the crest with a weight at the bottom making the wire stretched and hanging in a vertical direction. When the dam crest is subjected to a displacement this will cause the wire to move which can be seen at the ground level. The displacement of the wire can be measured automatically with an optical measurement with an accuracy of about 0.1 mm. (Johansson et al., 2014) Strain gauges mounted on a concrete dam are often based on a vibrating wire technique where a steel wire is tensioned between two steel plates which are mounted on the concrete. If the concrete dam is subjected to a displacement, the stress/strain of the wire changes which results in an updated natural frequency for the wire. With the proper calibration of the sensor an accuracy of typically 0.1 MPa is obtained (assuming an elastic modulus of concrete of 30 GPa). (Johansson et al., 2014) A typical sensor used to measure the crack width is based on similar technique as the strain gauge. However, in this case the vibrating wire is mounted in a telescope shaft and attached to a spring. Due to deformations, the spring is compressed or elongated which results in a stress/strain in the vibration wire. Typically, the accuracy of this type of sensor is about 0.01 mm. (Johansson et al., 2014) In a previous research project, Malm (2009) it was shown that it was possible to calculate the variation in the crest displacement of a concrete buttress dam due to seasonal temperature variations, with good agreement to those measured in-situ, as seen in Figure 5. However, during a period in April and May, a large discrepancy of about 3 mm was found between the numerical model and the measured crest displacement. Unfortunately, measured displacements were only obtained about once or twice every month. The variation in crack width was, however, sampled with higher frequency and it also showed a large discrepancy. The discrepancy could to some extent depend on an inaccurate temperature field for this period. This could likely explain some smaller discrepancy, but it has been considered unlikely to be the reason for the complete deviation in this period, since the remaining part of the curve was quite accurately captured. In addition, the fluctuation in the water level is marginal for this specific dam and thereby this is also considered as an unlikely source of deviation of the numerical model and the measurements. Therefore, the hypothesis was that this discrepancy in April and May could be explained by the ice load. Hydropower'15 Stavanger, Norway 15-16 June 2015 11/01 12/01 01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 -12 -10 -8 -6 -4 -2 0 C re st d is pl ac em en t ( m m ) Measured (monolith 43) FEA Measured (monolith 43) FEA Measured (monolith 42) Date 2007 2008 -0.10 -0.05 0 0.05 0.10 0.15 C ra ck w id th v ar ia tio n (m m ) 11/01 12/01 01/01 02/01 03/01 04/01 05/01 06/01 07/01 08/01 09/01 10/01 11/01 Crack width Crest displacement Figure 5: Comparison of variations in crest displacement and crack width from measurements and a numerical simulation, from Malm (2009). SIMULATION OF DISPLACEMENTS OF A CONCRETE DAM DUE TO ICE LOAD To analyze the influence from ice loads, numerical analyses have been performed. The simulation has been performed for the same concrete dam studied in Malm (2009), but with further developments of the numerical model. The concrete dam monolith is defined as a 3D model based on solid elements for the concrete and all reinforcement bars are modeled as separate truss elements. For further details regarding the numerical model, see Malm and Tornberg (2014). All types of cracks that have been observed on the concrete dam have been included in the model as discrete cracks. The crack pattern included in the model is based on the crack pattern obtained from the numerical analyses performed in the previous research project, see Malm (2009) or Malm and Ansell (2011).All cracks in the supporting buttress wall and the horizontal cracks in the front-plate are defined to go through the entire thickness of the member. The vertical cracks in the front-plate are defined to go through half the thickness of the front-plate, thereby leaving an intact zone on the downstream side of the crack. The reinforcement crossing the cracks has been considered to be intact. The numerical simulation has been performed in two steps, in the first step the gravity load and hydrostatic pressure were considered. In the second step, an increasing ice load is considered where it is increased continuously from zero to double its design value, i.e. 400 kN/m. Figure 6: Numerical FE model including observed cracks. Hydropower'15 Stavanger, Norway 15-16 June 2015 In Figure 7, the calculated crest displacement is shown as a function of the applied ice load. In the first step, the gravity load and hydrostatic pressure is included which results in a displacement equal to about 4.3 mm. In the second step as the ice load is increased continuously, a displacement of 9.6 mm is obtained for an ice load equal to 400 kN/m. The analysis shows that an ice load equal to 260 kN/m is required to obtain an increase in displacement equal to 3 mm in the downstream direction. The corresponding deformed shape of the concrete monolith is illustrated in Figure 8. 0 2 4 6 8 10 0 50 100 150 200 250 300 350 400 Crest displacement (mm) Ic e lo ad ( kN /m ) Figure 7: Horizontal crest displacement (in the downstream direction) as a function of increasing ice load. Figure 8: Deformation for the case with an ice load of 400 kN/m (deformation scale factor 1000). DISCUSSION AND CONCLUDING REMARKS Based on the screening of suitable methods to measure the ice loads acting on a concrete dam, the most promising technique is the load panels with strain gauges and load cells similar to those previously been used at the lighthouse Norströmsgrund. One downside with these panels was that only compressive forces were able to be measured. Tensile forces will thereby not be recorded, which will result in an overestimation of the resulting force. It is however likely that these load panels may be further developed by using a combination of load cells and foil strain gauges so that tensile forces also can be measured. This is something that is currently being studied. In addition, the dimensions of the load panels may have to be increased further to measure the load over a larger area in order to be suitable capturing the ice loads acting on a complete concrete dam monolith. Hydropower'15 Stavanger, Norway 15-16 June 2015 The accuracy of a pendulum is about 0.1 mm as mentioned previously, and was according to Johansson et al.,(2014) considered to be the most promising method for back analysis of the ice load. Based on the numericalmodel, this corresponds to a change in the ice load of about 5 – 10 kN/m. As shown for the numerical model,despite that the predicted displacements are in close agreement with the measured values there will always be somediscrepancies due to the model uncertainty. For the case presented here the error was typically less than 0.5 mm,but could in some cases be as large as 1 to 2 mm (not considering the period where the ice load assumed to occur).These measurements were however performed manually as discrete readings about once or twice every month. Inaddition, for some period's problems with measuring the temperature had occurred which may have affected themodel accuracy. For a calibrated model and when the crest displacements are measured continuously it is likelythat the maximum error of the numerical model could be less than 0.5 mm. This error in crest displacement would,however, result in that the error in prediction of the ice loads (based on a backward calculation) would be in therange 25 – 50 kN/m in this case. It is thereby considered unlikely that backwards calculation could be a reliableapproach to determine the ice load, at least for the type of dam studied in this paper. However, due to the relativelylow cost (since these types of sensors in general are already installed) it is still considered to be an interestingapproach that should be studied further. REFERENCESAdolfi, E., Eriksson, J. (2013). Islastens inverkan på brottsannolikheten för glidning och stjälpning avbetongdammar. (in Swedish). MSc thesis 13/01. Division of soil and rock mechanics, KTH. Carter, D., Sodhi, D., Stander, E., Caron, O. & Quach, T. (1998) Ice thrust in reservoirs. Journal of Cold RegionsEngineering, 12(4), 169-183. Comfort G., Gong Y., Singh S. & Abdelnour R. (2003), Static ice loads on dams. Canadian Journal of CivilEngineering, Vol. 30, p 42 68 Fransson, L. (2001) Development of ice load panels and installation at lighthouse Norströmsgrund. 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