# Presentation: 582628

## EVALUATING SELECTED SCOUR EQUATIONS FOR BRIDGE PIERS IN COARSE STREAMBEDS IN NEW YORK

**EVALUATING SELECTED SCOUR EQUATIONS FOR BRIDGE PIERS IN COARSE STREAMBEDS IN NEW YORK**

**L.J. Welch, Jr.  and  G.K. Butch**

***In cooperation with***
***New York State***
***Department of Transportation***

- by

## Field Conditions

**Turbulent flow**

**Armored streambed**

## Scour is the result of work

***    ******Sf******	*****= stream force (kg***** ********* ****m/s****2****); **
***    ******D******84***** ****	****= grain size >84 % of armor layer (mm).**

## Stream  Force

***Sf*****	****= stream force (kg***** ********* ****m/s****2****); **
********	****= water density (10****3**** kg/m****3****); **
***y******1*****	****= water depth (m); **
***w******	*****= flow width (1 m); **
***V******0*****= flow velocity (m/s).**

## Database Statistics

## Model Calibration

**Calculated 19 scour depths measured in 1996 (10 = 0.0 m)**

**1996 MEAN ERROR**

**MEAN ERROR**

**(m)**

**Notes:**
55 Historical measurements --max flow (1943-89)
42 Discrete measurements ----specific flow (1972-95)
 calculated 19 scour depths measured in 1996 (10 = 0.0 m).
 calculated 9 scour depths (zero scour excluded).

Reason for large number of zero scour unknown ; RI>100-yrs for some peaks.

## New York Equation (1972-96)

-  .

***	******	******Sf   *****=  stream force (kg***** ********* m/s****2****); **
***	******	******D******84***** =****	****grain size >84 % of armor layer (mm).**

## Relation of Scour Depth to Stream Force and Bed Material

## Sensitivity Analysis

## FHWA Equation

- 		***y******s      *****= scour depth; ****	**** *****K******1*****  = pier-nose shape; **
***	******	******a     *****= pier width;****	**** *****K******2   *****= pier shape & flow alignment; **
*** ******	******	******y******1      *****= water depth; ****	**** *****K******3   *****= streambed condition; **
***	******	******Fr******1*****  ****= Froude number; ****	**** *****K******4   *****= armoring by bed-material size.**
***	******	******	******	******	******	***

-  ,

## K4  (modified by Mueller)

**	****If *****D******50***** **_**>**_** 2 mm and *****D******95***** **_**>**_** 20 mm and f(*****V*****) > 0, otherwise *****K******4 *****= 1**
***	******D******50******	****** *****= median grain size;****	*****       D******95 ******= *****grain size >95 percent of  armor layer;**
***	******V******0******	****** ******= *****approach flow velocity;**
***	******V****** ******/******cD******50******= *****approach velocity corresponding to critical velocity at pier for D****50 ****;*****  ***
***	******V ******/******cD******95******= *****approach velocity corresponding to critical velocity at pier for D****95 ****; **
***	******V****** ******cD******50****** = *****critical velocity for incipient motion for D****50 ****.**
***	******	******	******	******	***

-  ,

## Froehlich  Equation

***	******  ******y******s*****	****= scour depth;****	****	****        ***********	*****=  pier shape;**
***	******  ******g******	*****=  gravity;  ****	****    ****	****        *****V******0 ******	*****=  flow velocity; **
***	******  ******y******0******	*****=  water depth; ****	****     ****	****        *****b******	*****=  pier width; **
***	****** ******D******50 ******	*****=  median grain size.**

## EstimatedScourvsMeasuredScour

## Summary ofEstimated and Measured Scour

## New Hampshire Study

**Field measurements**

## New Hampshire Study

**GPR & fixed instruments**

## SUMMARY

**New York equation:****	****- scour a function of *****stream force***** and *****bed material*****	****- derived from field measurements****	****-**** alternative for coarse streambeds****	****- estimates associated with specific peak discharges**
**Mueller modified-*****K******4*****  and Froehlich equations:****	****- less error than FHWA equation in New York study**