PART 2 – SITES EARTH SPILLWAY EVALUATION B. Earth Spillway Integrity Analysis i. Three phase model of spillway performance ii. Phase 1 and phase 2 inputs and equations SPECIALTY WORKSHOP: SITES TRAINING AND INTRODUCTION TO WINDAM ASDSO Dam Safety 2008

Auxiliary Spillway Integrity Analysis  Applied to all reaches, including natural hillslope areas  Based on integral of the FBH  Determines whether spillway breach is expected  Uses a three phase failure model iteratively applied Surface Erosion (vegetal cover failure) Surface Erosion (vegetal cover failure) Headcut Development Headcut Development Headcut Advance Headcut Advance  Generally a vegetal cover with minor discontinuities is assumed for design  Requires geologic information for all materials that could potentially be exposed to hydraulic attack during failure  CONCEPT IS THAT DAMAGE IS ACCEPTABLE SO LONG AS BREACH DOES NOT OCCUR

UNIFORM SPILLWAY

UNIFORM COVER

COVER FAILURE INITIATION

EXPANSION OF ERODING AREA

COVER LOCALLY REMOVED Phase 1 is complete when the cover is locally removed such that the erodible boundary is no longer protected.

CONCENTRATED FLOW EROSION

Phase 2 is complete when an overfall is formed such that the erosion is the result of plunging action of the flow.

HEADCUT Phase 3 includes simultaneous deepening and upstream advance of the headcut.

EXPANDING HEADCUT

ADVANCING HEADCUT

BREACH

SPILLWAY EROSION PHASES 1. SURFACE EROSION 1. SURFACE EROSION (Cover Destruction) 2. CONCENTRATED FLOW EROSION 3. HEADCUT ADVANCE

Effective Stress,  e cc 0 0 Erosion Rate,  r kdkd 1

SURFACE DETACHMENT.  r = the rate of detachment k d = coefficient of detachment  e = erosionally effective stress  c = critical tractive stress. a = exponent (~ 1 )  r = k d (  e -  c ) a

APPLICATION OF DETACHMENT RATE EQUATION WITH VEGETATION  e =  ds(1-C f ) (n s /n) 2.  r = k d (  e -  c )  c would be expected to be small for topsoil material supporting vegetation

Plasticity Index, I w  e dt, (lb/ft 2 )-h

MINOR DISCONTINUITY Minor discontinuities cause erosion to begin where there is no vegetal cover and/or the surface is disturbed.

MAJOR DISCONTINUITY Major discontinuities concentrate the flow where there is no vegetal cover and/or the surface is disturbed.

EFFECTIVE STRESS Maintenance code effect Maintenance code effect  e =  dS(1-C f ) (n s /n) 2 If MC=2, C f  0 If MC=3, Cf  0 and n  n s

SHALLOW-ROOTED COVER

SOD STRIPPING

Peak Stress, lb/ft 2 Potential Rooting Depth, ft

Parameters Impacting Phase 1 Erosion

SPILLWAY EROSION PHASES 1. SURFACE EROSION 1. SURFACE EROSION (Cover Destruction) 2. CONCENTRATED FLOW EROSION (Headcut Formation) (Headcut Formation) 3. HEADCUT ADVANCE

PHASE 2 CONCENTRATED FLOW EROSION

PHASE 2 Concentrated Flow Surface Detachment.  r = k d (  e -  c )  e =  (d+  d)S Stress equation applies when eroded depth (  d) is less than approach critical flow depth (phase 2). k d = coefficient of detachment (material property)  c = critical tractive stress (material property)

CRITICAL STRESS for Detachment Critical stress based on loose particle condition for all materials.

DETACHMENT RATE COEFFICIENT The detachment rate coefficient may be externally determined and entered directly in SITES or estimated by SITES from soil properties.

Parameters Impacting Phase 2 Erosion

SPILLWAY EROSION PHASES 1. SURFACE EROSION 1. SURFACE EROSION (Cover Destruction) 2. CONCENTRATED FLOW EROSION 3. HEADCUT ADVANCE