Formerly Addl. Director
Central Water and Power Research Station, Pune, India
E Mail: firstname.lastname@example.org
Widths of spillways to be located in relatively steep and narrow rocky river gorges often exceed the available waterways. As a result, one or both the ends of a spillway may have to be accommodated by excavating the flanks. Additional excavation in flanks is required for providing water way. When the energy dissipator is in the form of a stilling basin, construction of long and high side walls also poses a problem. If topography and geology permit, the side walls can be formed by providing concrete lining to the excavated and dressed rock face of the flank adjacent to the end of the spillway. The lining is secured to the rock with anchors. Such construction has been adopted for several spillways. However, the concrete lining may get dislodged due to the pull out force caused by the turbulence in the hydraulic jump.
Estimation of hydrodynamic pull out force on the concrete lining is a tricky issue. The origin of such forces lies in the interaction between the fluctuating pressures on the water side face of the lining and pressures propagated behind the lining (at the rock-concrete interface) through joints/cracks in the lining. The magnitude of propagated pressures and hence the pull out force can not be estimated by analytical means. However, instantaneous fluctuating pressures can be experimentally measured by means of electronic pressure transducers. Assuming that at a given instance, the propagated pressure behind the lining reaches the instantaneous maximum value (Pmax), while at the same time, instantaneous minimum pressure (Pmin) exists on the water side face; the pull out pressure (Pl) would be (Pmax-Pmin). It is often argued that the magnitude of the propagated pressure behind the lining should be taken as RMS value of the fluctuating pressure (Prms) or hydrostatic pressure Hs. (whichever is larger). Thus
Pl=Hs-Pmin …………..Prms<Hs or
The above scheme of calculation is depicted in Figure 1.
Figure 1: Scheme of calculation
It is believed that effect of pressure fluctuations on areas as large as side wall monoliths are considerably less than those on the small diaphragm pressure transducers. It is quite likely that instantaneous fluctuating pressures vary with time as well in space. A reliable estimate of pull out force would therefore require averaging of pressure fluctuations over the area of interest with due consideration of space and time.
Averaging of pressure fluctuations over the entire area of a side wall monolith panel is based on the assumption that fluctuating pressures at all points over the area follow the normal distribution. The procedure consists of simultaneously measuring pressure fluctuations on ‘M’ sub areas of the monolith, each associated with a pressure transducer. This is described below:
The above value of F’ is the RMS value. For obtaining the instantaneous maximum or minimum value, it should be multiplied by the coefficient of probability k, which, for the normal distribution, has a value of 3.09 corresponding to a probability of 99.8%. Thus (Fl) min=3.09 F’.
Pull out forces could also be estimated by direct measurement using a force transducer.
It will be apparent that determination of pull out force relies heavily on experiments on hydraulic model for the specific structure. The details of the spillway, stilling basin and side wall, for which, estimation of pull out force was carried out, are shown in Figure 2.
Figure 2: Details of stilling basin, side wall profile and transducers
The maximum head on the spillway, from MWL up to the stilling basin apron level, was 128m and the discharge intensity varied from 100 to 200 cumec/meter width. The maximum height of the side wall was 45m, consisting of both, the concrete lined portion at the base and gravity section above it.
Studies were conducted on a 1:55 scale model reproducing four spans of the spillway. Fluctuating pressures were measured with miniature piezoresistive pressure transducers having diaphragm diameter of 3.8mm. Direct measurement of pull out force was carried out with a force transducer having a capacity of 1kN.
A typical monolith panel of concrete lining, of 16.5m x 16.5m was fitted with 9 pressure transducers to form a symmetric matrix of 3 x 3. Another panel of the same size was fitted with the force transducer, structurally isolating it from the rest of the wall to allow freedom of movement in the direction transverse to the flow. It was found that the natural frequency of this system of about 48 hz was much higher than the dominant frequency of about 2 hz of the exiting forces. Thus, there was no possibility of resonance effects.
Measurements of fluctuating pressures as well as pull out force were carried out at location I to compare the results. At location II, only direct measurement of force was carried out. Measurements were recorded for the discharges of 100%, 75%, 50% and 45% of the design maximum discharge.
When a single location of fluctuating pressures was analyzed form the time-history records, maximum pressure of 52m of water against a minimum of -9m, with RMS values ranging from 1.5m to 43m were revealed. Obviously, any assessment of pull out force based on these results would be too excessive. Thus, a need for averaging the pressures over the time and space was underlined.
Results of averaging of the pressure fluctuations as per the scheme described above are given in Table 1. The pull out forces varied from 12,321 kN to 24,329 kN over the panel. In terms of head of water, these would be equivalent to 4.6m to 9.1m.
Direct measurement of pull out force was carried out at the same locations I and II, for all the four discharges. The results are shown in Table 1.
Table 1: Pull out forces on concrete lining, kN
| Discharge ( as % of the maximum)
|| Location I
A comparison of the results for the location I shows that pull out forces obtained by both the methods agree well. The magnitude of the force increased with the discharge as expected and followed a linear variation as shown in Figure 3. It was also seen that the pull out force reduced from location I to II, which can be explained by the reduction of intensity of turbulence as one moves in the downstream direction.
Figure 3: Variation of pull out force with discharge
The above studies confirmed the fact that any estimation of force exerted on a structure should not be based on measurement of pressure at a single or isolated location but should be based on averaging of pressures at several points in the time and space domain. On the other hand, direct assessment of force using suitable force transducer taking the entire precautions offer an equally reliable means.