(ητxy ) - τi cos *s*i

η

(ησx ) -

- *s*iρ*g*η sin(θ + α) = 0

(15)

where

σx =

normal stress in the streamwise direction

τxy =

shear stress at the banks

τi =

shear on the underside of the cover

θ =

slope of the bed

(θ + α)=

slope of the water surface.

Uzuner and Kennedy expressed σx and τxy as functions of the average vertical

stress σ z within the cover

η

σz =

(16)

2

where *p *is jam porosity and γe is the equivalent unit weight of the jam. The Rankine

and Mohr-Coulomb stress theories for granular materials give

σx = *K*p σz

(17)

and

τxy = *C*o σz + *C*i

(18)

where

15, then normalization using *x*o = *x/h*n and ηo = η/*h*n, yields

ηo

= *k*1 + *k*2ηo + *k*3ηo2

ηo

(19)

where

τi

(20)

2*K*pγ ehn

(21)

2*K*pγ e

(22)

1

*f q*

23

(23)

.

8*gS*o

Also

16