Stability of block mattresses under non-uniform flow

Abstract

Block mattresses are widely used bed protection elements under non-uniform flows. Previous studies show that the turbulence of the flow plays a key role on the instability of the mattress. However, in the available design equations, the turbulence intensity is included as a magnification factor roughly and qualitatively defined. Consequently, the design equations are often used as a rule of thumb, where the engineering criteria of the designer is critical and large safety factor are used. In turbulent non-uniform flows, the available design equations were developed for uniforms flow and the turbulent intensity is included as a magnification factor, usually poorly defined. The stability reduction due to turbulence has been proved by several authors. However, there is not any study in previous literature that investigate the role of velocity fluctuations on block mattress failure. Nevertheless, the literature review showed that an innovative approach, which combines the mean velocity and the turbulence intensity to quantify the flow forces, has been largely study for loose rock by several authors. Following this trend, the option of applying this structure (u ̅+α√k) as a flow quantification on Pilarczyk equation was decided to study. For this purpose, a series of test were done under four different configurations. Two weir heights were used (15 and 18.5cm) and the distances corresponding to 3h and 4h were checked. Four failures were recorded for each configuration for a total of 16 failures. Additionally, a data base was recorded for each configuration where the flow discharge was related to mean velocity and the turbulence intensity. An analysis of the failure mechanism was done by synchronizing the velocity time series with the displacement of the blocks. The results showed that an episode of peak streamwise velocity and downwards (sweep) was present at the failure. However, the analysis of the velocity showed that higher combinations of streamwise velocity and shear stress were present before the failure on almost all the records. Therefore, the streamwise velocity and the induced shear stress cannot solely explain the failure of the block mattress. This conclusion is in line with the work done by Hofland (2005). However, the recorded data did not allow to describe completely the failure mechanism.
The turbulence magnification factor (α) at the stability equation was derived by two different approaches. The first approach was based on the peaks of velocity associated to failure while the second one was described as a fitting parameter. The analysis concluded that the α values were close to 3 for both cases, in line with the expected value from previous studies. Finally, the new developed equation was compared with the original Pilarczyk equation and the modification proposed by the Rock Manual (2007). The comparison shows that the new developed equation described the required thickness of the block more accurately than the available equations. Thus, the results show that the proposed approach described the effect of turbulence accurately on a design equation. Additionally, all the relevant derived conclusions for design propose were summarized in a design guideline.