1. General-bed scour
(i) The critical shear velocities at threshold condition for the movement of boulders can be obtained from Dey (1999b) curve in rough regime, for which nondimensional shear stress jcr= 0.045.
(ii) The quantity of bed load transport rate (qs) of boulders under stream flow can be calculated using the following equations.
j = (0.461 – 0.022 y) for y £ 16.5
= (0.522 – 0.025 y) for y > 16.5
where y is the flow intensity parameter (= 1/jcr) and j is the bed-load parameter (=qsIps/(rs - r) gd50 ]0.5 /gs), rs is the
mass density of gravels / boulders (in kg/m3), r is the mass density of water (in kg/m3). g is the gravitational
acceleration (9.81 m/s2), d50 is the median particle diameter (in m) and gs is the specific weight of gravels / boulders (= psg).
(iii) The maximum depth of scour in bounder-bed rivers under high stream velocity is equal to the one-diameter of the boulder size (average) below the bed level.
2. Local scour within channel contractions
(i) Formula for Estimation of Maximum Equilibrium Scour Depth
The formula for estimation of maximum equilibrium scour depth dsm (in m) below original bed level in long contractions having gravel or boulder beds is
dsm = h1 [1.28(b1 / b2)0.78 -1) Kσ
Where h is the upstream flow depth (in m), b1 is the approaching channel width (in m), b2 is the width of channel in contracted zone (in ), and K>σ is the coefficient determined from Fig. 5.6 for the known value of ©g
(ii) Design Curves / Charts for Estimation of Maximum Equilibrium Scour Depth
(iii) Maximum Equilibrium Scour Depth within Long Contractions having Layered Beds
The maximum equilibrium scour depth below original bed level in long contractions having layered beds can be estimated by multiplying the scour depth in gravel /boulder-beds by a factor 3.2 and the scour depth in sand beds by a factor 3.6
(iv) Effective Protective Measure To reduce the maintenance cost and to increase the life span of the contractions, it is most appropriate to use pitching in the contracted portion with larger size gravels / boulders that limit the extent of scour depth within the channel contractions effectively. The size of the gravels / boulders that are suitable for pitching can be worked out using the equation given below:
U2 = 4.893"dp
Where U2 is the velocity in the contracted zone (in m/s) and dp is the size of pitching stone (in m)
3. Local scour at bridge piers
(i) Regression Formula for Estimation of Maximum Equilibrium Scour Depth
The formula for estimation of maximum equilibrium scour depth at piers in boulder-beds is
For uniform gravels or boulders ( σg d"1.4), Kσ =1. On the other hand, for non uniform gravels or boulders (σg2 > 1.4), the coefficient Kσ is determined from curve of Kσ for the known value of σg.
(ii) Formula for Estimation of Maximum Equilibrium Scour Depth based on Envelope Curves
The maximum equilibrium scour depth at piers can also be estimated using the following design formula, which is obtained by fitting the envelope curves to the experimental data.
ds = Kh Kl Kd Ks Kσ
where the K-factors can be obtained by the envelope curves / charts. This equation is most appropriate to estimate the maximum equilibrium scour depth at piers as it accounts the effects of all parameters.
(iii) Maximum Equilibrium Scour Depth at Bridge Piers in Layered Beds
The maximum equilibrium scour depth below original bed level at bridge piers having layered beds can be estimated by multiplying the scour depth in boulders and gravel-beds by a factor 1.2 and the scour depth in sand beds obtained from IRC 78 : 2000) or HEC 18 (Richardson and Davis 2001) by a factor 1.6
(iv) Effective Protective Measure
The reduction in scour depth at bridge piers using riprap pitching is about 30% in average, whereas that at pier fitted with a circular collar of diameter three times pier diameter at the river bed is 100%. However, the riprap pitching is most suitable as it is economical and simple to provide for the reduction of maintenance cost and to increase the life span of the bridge piers. The size of riprap can be worked out using the equation given below :
where U1 is the upstream flow velocity (in m/s), and dp is the size of riprap (in m). Ä is (s-1), s is the relative density of
gravels / boulders and g is the gravitational acceleration.