Force acting on a square cylinder fixed in a free-surface channel flow

Abstract

We describe an experimental study of the forces acting on a square cylinder (of width b) which occupies 10-40 % of a channel (of width w), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, Fr 1 (depth h 1 ), which sets the downstream Froude number, Fr 2 (depth h 2 ). When Fr 1 < Fr 1c , where Fr 1c is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as 2 )/2, where experimentally we find C K 1. The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as F D λρbg

Estimating Tsunami-Induced Building Damage through Fragility Functions: Critical Review and Research Needs

“…Macabuag et al (2016a) is the only study to consider Froude Number as a TIM and found it to be a poor indicator of building damage when used alone, for the dataset considered. However, Froude Number is used to calculate the quasi-steady force discussed below (Qi et al, 2014;Foster et al, 2017), and recommend using different fragility curves for flow conditions characterized by high and low Froude numbers.…”

“…are the only empirical study to consider moment of momentum flux in their fragility curves. Note that nearly all current studies that consider force are using the standard drag equation (all except Macabuag et al (2016a), below, and who additionally consider moment of momentum flux), however, this does not account for alternative estimations, such as equivalent hydrostatic methods (MLIT, 2011), bore impact (Robertson and Riggs, 2011), or changes in flow regime (Qi et al, 2014;Foster et al, 2017). Macabuag et al (2016a) derived fragility functions using an equivalent quasi-steady force proposed by Qi et al (2014) and …”

A proposed methodology for deriving tsunami fragility functions for buildings using optimum intensity measures

“…Froude number will be considered directly as a TIM (TIM6), and a force estimation which depends on the flow regime will also be considered (TIM7). TIM7 is an equivalent quasi-steady force proposed by Qi et al (2014) and suggested by Lloyd (2016) to represent the force of a tsunami inundation on buildings. It is evaluated via two different flow regimes determined by Froude number.…”

“…The equations relate h, v and blockage ratio (building width/channel width) to the force, denoted here as F QS . Increasing the blockage ratio generally has the effect of increasing the force on the structure, and readers are referred to Qi et al (2014) for the calculation procedure. Defining an accurate blockage ratio for each building would require knowledge of the flow direction in order to define the cross section for which ''building width'' and ''channel width'' could be measured.…”

“…Furthermore, all force estimations considered in previous studies have been based on the standard form drag equation. However, this does not account for alternative estimations such as equivalent hydrostatic methods (MLIT 2011), bore impact (Robertson and Riggs 2011) or changes in flow regime (Qi et al 2014). Park et al (2014) compare damage estimates for a case study town in the USA using fragility functions for depth, velocity and momentum flux, concluding that velocity and momentum flux provide the most realistic damage estimates, though this is only based on a qualitative visual assessment of damage locations and the authors acknowledge that this conclusion must be verified with field data.…”