August 9, 2010

Hydrostatic Vs Hydrodynamic bending moment on submerged divide walls in a stilling basin

Filed under: Uncategorized — Rajnikant Khatsuria @ 10:50 am


Formerly Addl. Director

Central Water and Power Research Station, Pune, India

E mail: rmkhatsuria@rediffmail.com

Low height submerged divide walls are sometimes provided in large width hydraulic jump stilling basins. Unequal operation of spillway gates causing imbalance of discharge across the width of the stilling basin often results in large horizontal eddies that may also extend downstream of the stilling basin. These eddies have a potential to pick up loose material from downstream and bring inside the basin to cause abrasion damage. Several stilling basins were damaged due to abrasion caused by such eddies. Since simultaneous and equal operation of large number of gates may not be possible all the times, one of the remedies to prevent such damage is to ensure that eddies caused by unequal operation, is at least confined within the stilling basin. Incorporating divide walls in the stilling basin to segregate the basin into a number of bays has been found to be effective towards ensuring the above objective. The hydraulic design, mainly the number and height of such divide walls is finalized from hydraulic model studies. Their structural design requires assessment of bending moment on the divide walls. This is rather a tricky issue.

The conventional design of such divide walls is based on the assumption that the maximum bending moment a divide wall have to resist, would be equal to that caused by the water retained up to its top level on one of the sides, the other side having no water. This is so called hydrostatic bending moment. The calculation of hydrostatic bending moment along the height of a typical divide wall is explained in figure 1.

Figure 1: Comutation of hydrostatic bending moment

This assumption allows a solace that under the submerged condition a moment in the opposite direction from the other side would in fact, have balancing effect. However, divide walls designed on this assumption failed in some projects and the hind casting model studies revealed that the instantaneous forces caused by the turbulence of the hydraulic jump, were much higher than those accounted with the simple assumption and that submergence did not have compensating effect.  Thus, hydrodynamic bending moments must be considered in the design, as opposed to the hydrostatic bending moments.

This issue has been extensively studied on large size hydraulic models using specially designed bending moment transducers. The suitability of strain gauge to respond to the fluctuating forces is well known. Using this property of strain gauge, a transducer consisting of standard strain gauge Wheatstone bridge configuration was designed for these studies. The principle and details of construction of BM Transducer is depicted in figure 2. An apparatus was also designed for calibrating the transducer for the relationship volt output Vs bending moment.



Figure 2: Design of a bending moment transducer

Some results of model studies conducted using the BM transducer is shown in figure 3. In these studies, bending moments over the entire height of the divide wall were measured at two locations along the length. The flow entering the stilling basin had a pre-jump depth of 2.43m with a velocity of 46.1m/s (equivalent prototype), giving a Froude number of 9.44.  Discharges of lower magnitude were also considered.



Figure 3: Hydrostatic Vs Hydrodynamic bending moment

It was indicated that the measured values of hydrodynamic bending moments in the region of intense turbulence were about 1.8 to 2.7 times of those obtained from hydrostatic force distribution. Since these are the instantaneous values, the question a designer might ask is- What is the proportion of time the divide wall would be subjected to this loading? In other words, if this loading would be exerted, only for a small fraction of the time, some calculated risk may be taken and the design may consider a reduced value.

To address this question, the cumulative probability distributions of time history records of bending moment at critical locations were analyzed. It was seen that the divide wall would be subjected to bending moments exceeding the hydrostatic value for about 24 % of time. This is also shown in figure 3.

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